diff --git "a/connectivity/train.jsonl" "b/connectivity/train.jsonl"
new file mode 100644--- /dev/null
+++ "b/connectivity/train.jsonl"
@@ -0,0 +1,1861 @@
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,13) (0,2) (0,14) (0,23) (0,8) (0,1) (0,25) (0,27) (0,10) (1,29) (1,13) (1,19) (1,28) (1,23) (1,30) (1,25) (1,24) (2,12) (2,5) (2,14) (2,17) (2,23) (3,7) (3,12) (3,19) (3,23) (3,8) (3,30) (3,25) (3,24) (4,33) (5,20) (5,23) (5,30) (6,15) (6,11) (7,32) (7,17) (7,23) (7,8) (7,10) (8,29) (8,12) (8,32) (8,20) (8,19) (8,17) (8,30) (9,29) (9,28) (9,30) (9,24) (10,13) (10,20) (10,14) (10,22) (11,31) (12,13) (12,23) (12,27) (12,26) (13,29) (13,32) (13,14) (13,28) (13,30) (13,24) (14,17) (14,30) (14,22) (14,27) (15,16) (15,31) (15,33) (17,32) (17,20) (17,19) (17,27) (17,24) (17,26) (18,21) (20,28) (20,30) (20,25) (21,31) (22,32) (22,28) (22,30) (23,28) (23,25) (23,27) (24,29) (24,28) (24,26) (25,32) (26,29) (26,27) (27,32) (27,30) (28,32) (28,30)\nQ: Is there a path between node 14 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "0"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,7) (0,13) (0,24) (0,19) (0,5) (0,10) (0,4) (0,2) (0,21) (0,17) (0,23) (0,9) (0,20) (0,15) (0,22) (1,3) (1,18) (1,6) (1,14) (1,8) (1,11) (2,12) (2,7) (2,13) (2,24) (2,19) (2,5) (2,10) (2,4) (2,21) (2,17) (2,23) (2,9) (2,20) (2,15) (2,22) (3,18) (3,6) (3,14) (3,8) (3,11) (4,12) (4,7) (4,13) (4,24) (4,19) (4,5) (4,10) (4,21) (4,17) (4,23) (4,9) (4,20) (4,15) (4,22) (5,12) (5,7) (5,13) (5,24) (5,19) (5,10) (5,21) (5,17) (5,23) (5,9) (5,20) (5,15) (5,22) (6,18) (6,14) (6,8) (6,11) (7,12) (7,13) (7,24) (7,19) (7,10) (7,21) (7,17) (7,23) (7,9) (7,20) (7,15) (7,22) (8,18) (8,14) (8,11) (9,12) (9,13) (9,24) (9,19) (9,10) (9,21) (9,17) (9,23) (9,20) (9,15) (9,22) (10,12) (10,13) (10,24) (10,19) (10,21) (10,17) (10,23) (10,20) (10,15) (10,22) (11,18) (11,14) (12,13) (12,24) (12,19) (12,21) (12,17) (12,23) (12,20) (12,15) (12,22) (13,24) (13,19) (13,21) (13,17) (13,23) (13,20) (13,15) (13,22) (14,18) (15,24) (15,19) (15,21) (15,17) (15,23) (15,20) (15,22) (17,24) (17,19) (17,21) (17,23) (17,20) (17,22) (19,24) (19,21) (19,23) (19,20) (19,22) (20,24) (20,21) (20,23) (20,22) (21,24) (21,23) (21,22) (22,24) (22,23) (23,24)\nQ: Is there a path between node 18 and node 22?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (2,8) (2,4) (2,3) (3,8) (5,7) (6,7)\nQ: Is there a path between node 1 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "2"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,6) (0,2) (0,5) (1,7) (1,16) (1,14) (1,17) (1,3) (1,9) (1,13) (1,10) (2,11) (2,6) (2,5) (3,7) (3,16) (3,14) (3,17) (3,9) (3,13) (3,10) (4,8) (4,15) (4,12) (5,11) (5,6) (6,11) (7,16) (7,14) (7,17) (7,9) (7,13) (7,10) (8,15) (8,12) (9,16) (9,14) (9,17) (9,13) (9,10) (10,16) (10,14) (10,17) (10,13) (12,15) (13,16) (13,14) (13,17) (14,16) (14,17) (16,17)\nQ: Is there a path between node 6 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "3"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (1,5) (1,18) (1,7) (1,22) (1,11) (1,20) (1,4) (1,23) (2,14) (2,10) (2,21) (2,15) (2,16) (2,3) (3,14) (3,10) (3,15) (3,16) (3,6) (3,19) (4,18) (4,7) (4,22) (4,11) (4,20) (4,23) (5,13) (5,7) (5,22) (5,11) (5,20) (5,23) (6,10) (6,21) (6,15) (6,16) (6,9) (6,8) (6,19) (7,13) (7,22) (7,20) (7,23) (8,10) (8,9) (8,19) (9,21) (9,15) (9,19) (10,21) (10,16) (10,19) (11,18) (11,13) (11,22) (11,23) (12,17) (13,22) (13,20) (14,15) (14,16) (14,19) (15,16) (15,19) (16,21) (16,19) (18,20) (18,23) (19,21) (20,22) (20,23) (22,23)\nQ: Is there a path between node 12 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "4"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (1,18) (1,8) (1,4) (2,15) (2,18) (2,11) (2,23) (2,4) (3,12) (3,5) (4,23) (4,25) (5,12) (5,17) (6,22) (6,13) (7,18) (7,23) (7,8) (9,17) (10,19) (10,17) (11,15) (12,24) (14,20) (14,22) (15,18) (16,20) (16,22) (20,22) (21,22) (23,25)\nQ: Is there a path between node 18 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "5"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,2) (0,14) (0,7) (0,13) (1,17) (1,3) (1,10) (1,6) (2,11) (2,12) (2,14) (2,13) (3,17) (3,10) (3,6) (4,9) (4,5) (5,9) (5,16) (6,17) (6,8) (6,10) (7,11) (7,12) (7,14) (7,13) (8,17) (8,15) (9,18) (9,16) (10,17) (12,14) (12,13) (13,14) (15,17)\nQ: Is there a path between node 14 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "6"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (0,13) (0,22) (1,12) (1,6) (2,20) (2,14) (2,11) (3,5) (3,23) (3,6) (5,17) (6,19) (7,23) (8,13) (8,15) (9,21) (9,18) (12,24) (12,17) (12,19) (13,21) (13,18) (13,25) (13,15) (13,16) (15,16) (16,21) (16,25) (17,23) (17,19) (19,26) (21,22) (22,25)\nQ: Is there a path between node 1 and node 23?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "7"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,14) (0,12) (1,20) (1,12) (2,13) (2,18) (3,17) (4,20) (7,21) (8,18) (9,20) (9,15) (10,13) (10,19) (13,18) (14,16) (14,15) (15,20)\nQ: Is there a path between node 19 and node 15?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "8"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,5) (0,11) (0,8) (0,6) (0,1) (1,10) (1,3) (1,5) (1,9) (1,6) (1,2) (2,10) (2,3) (2,5) (2,9) (2,8) (2,7) (2,6) (2,13) (3,9) (3,11) (3,8) (3,7) (4,12) (5,10) (5,9) (5,8) (5,7) (5,6) (6,10) (6,9) (6,11) (6,8) (7,10) (7,11) (7,8) (7,13) (8,10) (8,11) (8,13) (9,10) (9,11) (9,13) (10,11) (10,13)\nQ: Is there a path between node 7 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "9"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,13) (0,5) (0,11) (0,15) (0,10) (0,16) (0,14) (0,8) (0,9) (1,18) (1,12) (1,7) (1,6) (2,13) (2,11) (2,15) (2,17) (2,16) (2,14) (2,3) (2,8) (2,9) (3,5) (3,11) (3,4) (3,15) (3,10) (3,14) (3,8) (3,9) (4,13) (4,5) (4,17) (4,16) (4,14) (4,8) (5,17) (5,16) (5,14) (6,12) (6,19) (6,20) (6,7) (7,18) (8,15) (8,17) (8,16) (8,14) (8,9) (9,13) (9,11) (9,17) (9,16) (9,14) (10,11) (10,15) (10,17) (10,16) (10,14) (11,13) (11,15) (11,16) (12,18) (12,19) (12,20) (13,17) (13,14) (14,15) (14,17) (14,16) (15,17) (16,17) (18,19) (18,20) (19,20)\nQ: Is there a path between node 8 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "10"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,29) (0,1) (0,9) (0,20) (0,34) (0,7) (0,19) (0,22) (0,31) (1,11) (1,30) (1,6) (1,21) (1,14) (1,28) (1,19) (1,31) (1,4) (2,3) (2,11) (2,18) (2,21) (2,20) (2,14) (2,7) (2,17) (3,11) (3,33) (3,15) (3,30) (3,18) (3,21) (3,14) (3,5) (4,10) (4,26) (4,27) (4,21) (4,34) (5,9) (5,27) (5,30) (5,6) (5,24) (5,14) (5,34) (5,28) (5,17) (6,11) (6,25) (6,10) (6,26) (6,29) (6,15) (6,16) (6,14) (6,7) (6,12) (6,22) (7,10) (7,26) (7,27) (7,18) (7,24) (7,8) (7,31) (8,11) (8,33) (8,9) (8,30) (8,24) (8,20) (8,16) (8,22) (8,17) (9,10) (9,20) (9,16) (9,14) (10,25) (10,33) (10,30) (10,18) (10,24) (10,20) (10,31) (11,15) (11,12) (11,19) (11,17) (12,25) (12,29) (12,27) (12,30) (12,34) (12,28) (12,17) (14,25) (14,33) (14,26) (14,29) (14,30) (14,21) (14,17) (15,20) (15,17) (16,21) (16,28) (16,19) (16,22) (17,27) (17,30) (17,24) (17,19) (18,26) (18,21) (18,28) (19,33) (19,27) (19,34) (19,22) (20,25) (20,26) (20,27) (20,21) (20,28) (20,31) (21,22) (22,24) (22,31) (24,34) (24,28) (25,26) (25,29) (25,27) (26,33) (26,27) (26,30) (27,30) (27,28) (28,31) (29,30) (29,34) (29,31) (30,33) (30,34) (31,33) (31,34)\nQ: Is there a path between node 4 and node 23?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "11"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,3) (0,2) (0,9) (0,8) (1,6) (1,4) (2,7) (2,10) (2,3) (2,8) (2,5) (3,10) (3,9) (3,8) (4,6) (5,7) (5,10) (5,9) (7,8) (8,9)\nQ: Is there a path between node 2 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "12"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,7) (0,8) (0,9) (0,13) (0,14) (0,15) (0,5) (1,2) (1,12) (1,16) (1,11) (1,3) (1,6) (1,14) (1,4) (2,12) (2,7) (2,9) (2,13) (2,14) (3,16) (3,11) (3,7) (3,8) (3,14) (3,15) (3,5) (3,4) (4,12) (4,11) (4,8) (4,9) (4,13) (4,14) (4,5) (5,12) (5,16) (5,11) (5,7) (5,8) (5,13) (5,14) (5,15) (6,12) (6,16) (6,11) (6,7) (6,14) (6,15) (7,12) (7,16) (7,11) (7,8) (7,9) (7,13) (8,12) (8,16) (8,11) (8,9) (8,13) (8,14) (9,12) (9,16) (9,11) (9,14) (9,15) (11,12) (11,16) (11,14) (12,13) (12,15) (13,16) (13,15) (14,16)\nQ: Is there a path between node 2 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "13"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,34) (0,4) (0,7) (0,28) (0,8) (0,15) (0,23) (0,13) (0,22) (0,32) (0,11) (0,18) (1,7) (1,2) (1,13) (1,27) (1,26) (1,9) (2,14) (2,31) (2,15) (2,23) (2,13) (2,9) (2,22) (2,17) (2,32) (2,18) (3,24) (4,7) (4,27) (4,17) (5,16) (5,12) (5,29) (5,20) (6,34) (6,7) (6,14) (6,31) (6,10) (6,23) (6,26) (6,21) (6,17) (6,18) (7,33) (7,14) (7,28) (7,15) (7,26) (7,19) (8,14) (8,28) (8,31) (8,10) (8,13) (8,25) (8,30) (8,18) (9,14) (9,21) (9,25) (9,22) (9,11) (10,31) (10,15) (10,27) (10,25) (10,17) (10,32) (11,28) (11,31) (11,15) (11,13) (11,27) (11,21) (11,25) (11,22) (12,16) (13,33) (13,14) (13,28) (13,26) (13,21) (13,17) (13,32) (13,18) (14,33) (14,31) (14,23) (14,27) (14,25) (15,34) (15,30) (15,17) (15,19) (16,24) (17,23) (17,26) (17,19) (18,34) (18,21) (18,30) (19,33) (19,21) (19,25) (19,30) (21,33) (21,28) (21,25) (21,30) (22,33) (22,23) (22,26) (22,25) (23,34) (23,25) (25,33) (25,32) (26,33) (26,28) (26,31) (26,32) (27,33) (27,32) (32,33)\nQ: Is there a path between node 17 and node 33?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "14"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,10) (0,12) (0,20) (0,14) (0,8) (0,3) (0,6) (0,5) (0,15) (0,19) (0,7) (0,9) (0,22) (0,2) (0,21) (0,18) (1,4) (1,10) (1,12) (1,20) (1,8) (1,5) (1,15) (1,16) (1,19) (1,7) (1,9) (1,22) (1,2) (1,18) (2,4) (2,10) (2,12) (2,14) (2,3) (2,5) (2,15) (2,19) (2,7) (2,22) (2,21) (2,18) (3,4) (3,12) (3,20) (3,14) (3,6) (3,5) (3,15) (3,16) (3,19) (3,7) (3,9) (3,22) (3,21) (3,18) (4,10) (4,12) (4,8) (4,6) (4,5) (4,15) (4,16) (4,19) (4,7) (4,9) (4,21) (4,18) (5,12) (5,14) (5,8) (5,6) (5,15) (5,16) (5,19) (5,7) (5,9) (5,22) (5,18) (6,10) (6,12) (6,20) (6,14) (6,16) (6,19) (6,7) (6,9) (6,22) (6,21) (6,18) (7,10) (7,12) (7,14) (7,8) (7,16) (7,9) (7,22) (7,21) (7,18) (8,10) (8,12) (8,14) (8,15) (8,16) (8,19) (8,9) (8,21) (9,12) (9,20) (9,15) (9,16) (9,22) (9,21) (9,18) (10,12) (10,20) (10,14) (10,15) (10,16) (10,18) (12,16) (12,19) (13,17) (14,20) (14,16) (15,16) (15,22) (15,21) (16,20) (16,21) (16,18) (18,22) (18,21) (19,20) (19,22) (19,21) (21,22)\nQ: Is there a path between node 14 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "15"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,6) (0,3) (0,18) (0,1) (0,15) (0,12) (0,14) (0,9) (0,16) (0,8) (0,2) (0,11) (0,19) (1,7) (1,6) (1,3) (1,18) (1,15) (1,9) (1,8) (1,2) (1,20) (2,7) (2,3) (2,18) (2,15) (2,12) (2,14) (2,9) (2,16) (2,8) (2,11) (2,19) (2,20) (3,18) (3,15) (3,12) (3,9) (3,16) (3,8) (3,19) (3,20) (4,13) (4,17) (5,17) (6,7) (6,18) (6,15) (6,14) (6,9) (6,16) (6,11) (6,19) (6,20) (7,15) (7,12) (7,14) (7,9) (7,16) (8,18) (8,12) (8,14) (8,9) (8,16) (8,11) (8,19) (8,20) (9,18) (9,15) (9,12) (9,11) (9,19) (9,20) (10,13) (11,18) (11,12) (11,14) (11,16) (11,19) (11,20) (12,18) (12,15) (12,14) (12,19) (12,20) (13,17) (14,19) (16,18) (16,19) (18,20)\nQ: Is there a path between node 0 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "16"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,13) (0,5) (0,11) (0,15) (0,10) (0,16) (0,14) (0,8) (0,9) (1,18) (1,12) (1,7) (1,6) (2,13) (2,11) (2,15) (2,17) (2,16) (2,14) (2,3) (2,8) (2,9) (3,5) (3,11) (3,4) (3,15) (3,10) (3,14) (3,8) (3,9) (4,13) (4,5) (4,17) (4,16) (4,14) (4,8) (5,17) (5,16) (5,14) (6,12) (6,19) (6,20) (6,7) (7,18) (8,15) (8,17) (8,16) (8,14) (8,9) (9,13) (9,11) (9,17) (9,16) (9,14) (10,11) (10,15) (10,17) (10,16) (10,14) (11,13) (11,15) (11,16) (12,18) (12,19) (12,20) (13,17) (13,14) (14,15) (14,17) (14,16) (15,17) (16,17) (18,19) (18,20) (19,20)\nQ: Is there a path between node 17 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "17"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,22) (0,15) (0,8) (0,12) (0,14) (0,2) (0,9) (0,1) (1,15) (1,20) (1,12) (2,20) (2,12) (2,7) (2,16) (3,15) (3,7) (3,16) (3,13) (3,14) (3,17) (3,21) (4,22) (4,8) (4,12) (4,17) (4,11) (6,23) (7,15) (7,17) (7,11) (7,21) (7,18) (8,22) (8,15) (8,20) (8,16) (8,9) (9,22) (9,13) (9,11) (9,21) (9,18) (10,22) (10,13) (10,21) (11,22) (11,15) (11,20) (11,12) (11,21) (11,18) (12,15) (12,13) (13,20) (13,18) (14,20) (17,22) (17,18) (18,20) (19,23) (20,22) (21,22)\nQ: Is there a path between node 5 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "18"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,5) (0,20) (0,7) (0,19) (0,1) (0,14) (0,12) (0,15) (0,18) (0,4) (1,10) (1,5) (1,7) (1,2) (1,14) (1,12) (1,3) (1,15) (1,16) (1,4) (2,10) (2,5) (2,20) (2,7) (2,19) (2,14) (2,12) (2,15) (2,16) (2,17) (2,18) (2,4) (3,5) (3,20) (3,7) (3,19) (3,14) (3,16) (3,17) (3,18) (4,10) (4,5) (4,20) (4,7) (4,19) (4,14) (4,12) (4,15) (4,16) (4,17) (5,20) (5,7) (5,19) (5,14) (5,12) (5,16) (5,17) (5,18) (6,11) (6,8) (7,10) (7,19) (7,14) (7,12) (7,15) (7,16) (7,17) (7,18) (8,11) (9,21) (9,13) (10,19) (10,14) (10,12) (10,16) (10,18) (12,20) (12,19) (12,14) (12,15) (12,16) (12,17) (14,20) (14,19) (14,15) (14,16) (14,17) (15,20) (15,19) (15,16) (15,17) (15,18) (16,20) (16,19) (16,17) (16,18) (17,20) (17,19) (17,18) (18,19) (19,20)\nQ: Is there a path between node 9 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "19"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,29) (0,1) (0,9) (0,20) (0,34) (0,7) (0,19) (0,22) (0,31) (1,11) (1,30) (1,6) (1,21) (1,14) (1,28) (1,19) (1,31) (1,4) (2,3) (2,11) (2,18) (2,21) (2,20) (2,14) (2,7) (2,17) (3,11) (3,33) (3,15) (3,30) (3,18) (3,21) (3,14) (3,5) (4,10) (4,26) (4,27) (4,21) (4,34) (5,9) (5,27) (5,30) (5,6) (5,24) (5,14) (5,34) (5,28) (5,17) (6,11) (6,25) (6,10) (6,26) (6,29) (6,15) (6,16) (6,14) (6,7) (6,12) (6,22) (7,10) (7,26) (7,27) (7,18) (7,24) (7,8) (7,31) (8,11) (8,33) (8,9) (8,30) (8,24) (8,20) (8,16) (8,22) (8,17) (9,10) (9,20) (9,16) (9,14) (10,25) (10,33) (10,30) (10,18) (10,24) (10,20) (10,31) (11,15) (11,12) (11,19) (11,17) (12,25) (12,29) (12,27) (12,30) (12,34) (12,28) (12,17) (14,25) (14,33) (14,26) (14,29) (14,30) (14,21) (14,17) (15,20) (15,17) (16,21) (16,28) (16,19) (16,22) (17,27) (17,30) (17,24) (17,19) (18,26) (18,21) (18,28) (19,33) (19,27) (19,34) (19,22) (20,25) (20,26) (20,27) (20,21) (20,28) (20,31) (21,22) (22,24) (22,31) (24,34) (24,28) (25,26) (25,29) (25,27) (26,33) (26,27) (26,30) (27,30) (27,28) (28,31) (29,30) (29,34) (29,31) (30,33) (30,34) (31,33) (31,34)\nQ: Is there a path between node 3 and node 32?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "20"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (0,1) (0,19) (0,15) (0,20) (0,9) (0,21) (0,3) (0,22) (0,32) (0,24) (0,14) (0,11) (0,17) (0,5) (0,34) (0,4) (0,26) (0,10) (0,8) (1,27) (1,23) (1,30) (1,6) (1,19) (1,20) (1,2) (1,9) (1,21) (1,3) (1,22) (1,24) (1,14) (1,11) (1,17) (1,5) (1,4) (1,26) (1,8) (2,27) (2,30) (2,6) (2,19) (2,20) (2,9) (2,21) (2,3) (2,22) (2,32) (2,7) (2,11) (2,17) (2,5) (2,34) (2,4) (2,26) (2,12) (2,10) (3,27) (3,23) (3,30) (3,6) (3,19) (3,15) (3,20) (3,9) (3,22) (3,24) (3,14) (3,34) (3,4) (3,12) (3,10) (3,8) (3,28) (4,27) (4,23) (4,30) (4,19) (4,15) (4,20) (4,9) (4,21) (4,32) (4,24) (4,14) (4,7) (4,11) (4,17) (4,5) (4,26) (4,12) (4,8) (4,28) (5,30) (5,19) (5,9) (5,21) (5,24) (5,7) (5,11) (5,17) (5,34) (5,12) (6,27) (6,23) (6,30) (6,19) (6,20) (6,9) (6,21) (6,22) (6,32) (6,24) (6,14) (6,7) (6,11) (6,17) (6,34) (6,26) (6,8) (6,28) (7,23) (7,30) (7,19) (7,15) (7,20) (7,21) (7,32) (7,24) (7,11) (7,17) (7,34) (7,12) (7,10) (7,8) (7,28) (8,23) (8,15) (8,20) (8,24) (8,14) (8,11) (8,17) (8,34) (8,26) (8,12) (8,10) (8,28) (9,30) (9,19) (9,15) (9,20) (9,22) (9,32) (9,24) (9,11) (9,34) (9,12) (9,10) (9,28) (10,27) (10,23) (10,30) (10,19) (10,21) (10,32) (10,24) (10,26) (10,12) (11,27) (11,30) (11,19) (11,20) (11,21) (11,22) (11,32) (11,24) (11,14) (11,17) (11,34) (11,12) (12,27) (12,30) (12,19) (12,20) (12,22) (12,32) (12,24) (12,14) (12,17) (12,34) (12,28) (14,27) (14,23) (14,30) (14,19) (14,15) (14,21) (14,22) (14,32) (14,17) (14,34) (14,28) (15,19) (15,20) (15,21) (15,22) (15,32) (15,24) (15,34) (15,26) (15,28) (16,33) (16,29) (16,18) (16,31) (17,27) (17,23) (17,30) (17,19) (17,20) (17,21) (17,22) (17,32) (17,24) (17,34) (17,28) (18,33) (18,31) (18,25) (19,27) (19,23) (19,30) (19,20) (19,22) (19,32) (19,34) (19,26) (19,28) (20,23) (20,30) (20,21) (20,22) (20,32) (20,24) (20,34) (20,26) (21,27) (21,23) (21,30) (21,22) (21,32) (21,24) (21,34) (21,26) (21,28) (22,27) (22,23) (22,24) (22,34) (22,26) (22,28) (23,32) (23,26) (23,28) (24,27) (24,32) (24,34) (24,26) (25,33) (26,30) (26,32) (26,34) (27,30) (27,32) (27,28) (28,30) (28,32) (28,34) (29,33) (29,31) (31,33) (32,34)\nQ: Is there a path between node 19 and node 28?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "21"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (0,10) (0,23) (0,3) (0,9) (0,26) (1,8) (1,20) (1,6) (1,4) (1,19) (1,16) (1,13) (1,24) (2,8) (2,20) (2,4) (2,19) (2,16) (2,13) (2,24) (2,12) (3,10) (3,9) (3,21) (3,22) (4,6) (4,19) (4,13) (4,24) (4,12) (5,15) (5,25) (5,11) (5,7) (6,8) (6,20) (6,19) (6,16) (6,13) (6,24) (7,15) (7,25) (7,14) (8,19) (8,13) (8,24) (8,12) (9,18) (9,23) (10,18) (10,23) (10,21) (10,26) (11,15) (11,17) (11,25) (12,20) (12,19) (12,16) (12,24) (13,20) (13,19) (13,16) (13,24) (14,17) (14,25) (15,17) (15,25) (16,20) (16,24) (17,25) (18,21) (18,22) (19,20) (19,24) (20,24) (21,23) (22,23) (22,26) (23,26)\nQ: Is there a path between node 5 and node 17?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "22"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,18) (0,12) (0,2) (0,11) (0,8) (0,13) (1,4) (1,10) (1,17) (1,5) (1,14) (1,7) (1,6) (1,15) (2,3) (2,18) (2,12) (2,11) (2,8) (2,13) (3,18) (3,12) (3,11) (3,8) (3,13) (4,10) (4,17) (4,5) (4,14) (4,7) (4,6) (4,15) (5,10) (5,17) (5,14) (5,7) (5,6) (5,15) (6,10) (6,17) (6,14) (6,7) (6,15) (7,10) (7,17) (7,14) (7,15) (8,18) (8,12) (8,11) (8,13) (9,16) (10,17) (10,14) (10,15) (11,18) (11,12) (11,13) (12,18) (12,13) (13,18) (14,17) (14,15) (15,17)\nQ: Is there a path between node 6 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "23"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,1) (0,6) (0,2) (0,3) (0,7) (0,5) (1,8) (1,6) (1,2) (1,3) (1,7) (1,5) (2,8) (2,6) (2,3) (2,7) (2,5) (3,8) (3,6) (3,7) (3,5) (5,8) (5,6) (5,7) (6,8) (6,7) (7,8)\nQ: Is there a path between node 4 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "24"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,3) (0,4) (1,3) (1,4) (3,4)\nQ: Is there a path between node 2 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "25"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,2) (0,3) (1,5) (2,4) (2,3) (3,4)\nQ: Is there a path between node 5 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "26"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (3,8) (3,9) (4,5) (8,9)\nQ: Is there a path between node 5 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "27"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,1) (1,11) (1,5) (1,8) (2,14) (2,10) (2,6) (2,3) (2,13) (2,4) (3,7) (3,14) (3,6) (3,12) (3,13) (3,4) (4,9) (4,7) (4,10) (4,12) (4,13) (5,11) (5,8) (6,7) (6,10) (6,12) (6,13) (7,9) (7,14) (7,10) (7,13) (8,11) (10,14) (10,12) (10,13) (12,14) (12,13) (13,14)\nQ: Is there a path between node 4 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "28"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,11) (0,1) (0,3) (0,10) (0,4) (1,11) (1,3) (1,10) (1,4) (2,7) (3,11) (3,4) (4,5) (4,11) (5,11) (6,9) (6,8) (7,9) (7,8) (8,9) (10,11)\nQ: Is there a path between node 10 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "29"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,25) (0,3) (1,25) (1,29) (2,14) (2,13) (2,20) (2,18) (2,31) (2,9) (2,27) (2,21) (2,12) (2,7) (2,33) (2,11) (2,24) (2,26) (2,30) (3,25) (4,23) (4,22) (4,34) (4,5) (5,23) (5,22) (5,34) (6,14) (6,13) (6,20) (6,18) (6,27) (6,21) (6,12) (6,7) (6,28) (6,24) (6,26) (6,30) (7,14) (7,13) (7,20) (7,31) (7,17) (7,9) (7,27) (7,21) (7,12) (7,10) (7,33) (7,28) (7,30) (8,14) (8,13) (8,31) (8,17) (8,9) (8,27) (8,12) (8,33) (8,11) (8,28) (8,26) (8,30) (9,14) (9,13) (9,20) (9,18) (9,27) (9,21) (9,12) (9,10) (9,33) (9,24) (9,26) (9,19) (9,30) (10,13) (10,20) (10,18) (10,31) (10,17) (10,27) (10,12) (10,33) (10,11) (10,28) (10,24) (11,14) (11,13) (11,20) (11,18) (11,31) (11,12) (11,33) (11,28) (11,24) (11,26) (11,30) (12,14) (12,13) (12,20) (12,18) (12,17) (12,27) (12,21) (12,33) (12,19) (13,14) (13,20) (13,18) (13,31) (13,17) (13,21) (13,28) (13,24) (13,26) (14,18) (14,31) (14,17) (14,27) (14,21) (14,33) (14,26) (15,32) (17,18) (17,31) (17,27) (17,33) (17,28) (17,24) (17,26) (17,19) (17,30) (18,20) (18,31) (18,33) (18,24) (18,26) (18,19) (18,30) (19,31) (19,27) (19,21) (19,33) (19,28) (19,26) (20,31) (20,27) (20,21) (20,33) (20,24) (20,26) (20,30) (21,27) (21,33) (21,28) (21,24) (21,30) (22,23) (22,34) (23,34) (24,33) (24,26) (25,29) (26,31) (26,33) (26,30) (27,31) (27,33) (27,28) (27,30) (28,31) (28,33) (28,30) (30,31) (30,33) (31,33)\nQ: Is there a path between node 3 and node 25?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "30"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,9) (1,10) (1,3) (2,6) (2,4) (2,7) (3,6) (3,10) (3,9) (3,12) (4,8) (5,9) (5,12) (6,9) (6,12) (6,7) (7,10) (7,9) (7,14) (8,10) (8,9) (8,14) (12,14)\nQ: Is there a path between node 8 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "31"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,12) (0,1) (0,7) (0,16) (0,13) (0,9) (0,2) (0,10) (0,21) (0,19) (0,3) (0,20) (0,8) (0,23) (0,5) (0,4) (0,6) (0,22) (1,15) (1,12) (1,7) (1,16) (1,13) (1,9) (1,2) (1,10) (1,21) (1,19) (1,3) (1,20) (1,8) (1,23) (1,5) (1,4) (1,6) (1,22) (2,15) (2,12) (2,7) (2,16) (2,13) (2,9) (2,10) (2,21) (2,19) (2,3) (2,20) (2,8) (2,23) (2,5) (2,4) (2,6) (2,22) (3,15) (3,12) (3,7) (3,16) (3,13) (3,9) (3,10) (3,21) (3,19) (3,20) (3,8) (3,23) (3,5) (3,4) (3,6) (3,22) (4,15) (4,12) (4,7) (4,16) (4,13) (4,9) (4,10) (4,21) (4,19) (4,20) (4,8) (4,23) (4,5) (4,6) (4,22) (5,15) (5,12) (5,7) (5,16) (5,13) (5,9) (5,10) (5,21) (5,19) (5,20) (5,8) (5,23) (5,6) (5,22) (6,15) (6,12) (6,7) (6,16) (6,13) (6,9) (6,10) (6,21) (6,19) (6,20) (6,8) (6,23) (6,22) (7,15) (7,12) (7,16) (7,13) (7,9) (7,10) (7,21) (7,19) (7,20) (7,8) (7,23) (7,22) (8,15) (8,12) (8,16) (8,13) (8,9) (8,10) (8,21) (8,19) (8,20) (8,23) (8,22) (9,15) (9,12) (9,16) (9,13) (9,10) (9,21) (9,19) (9,20) (9,23) (9,22) (10,15) (10,12) (10,16) (10,13) (10,21) (10,19) (10,20) (10,23) (10,22) (11,17) (11,14) (11,18) (12,15) (12,16) (12,13) (12,21) (12,19) (12,20) (12,23) (12,22) (13,15) (13,16) (13,21) (13,19) (13,20) (13,23) (13,22) (14,17) (14,18) (15,16) (15,21) (15,19) (15,20) (15,23) (15,22) (16,21) (16,19) (16,20) (16,23) (16,22) (17,18) (19,21) (19,20) (19,23) (19,22) (20,21) (20,23) (20,22) (21,23) (21,22) (22,23)\nQ: Is there a path between node 10 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "32"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,5) (0,20) (0,7) (0,19) (0,1) (0,14) (0,12) (0,15) (0,18) (0,4) (1,10) (1,5) (1,7) (1,2) (1,14) (1,12) (1,3) (1,15) (1,16) (1,4) (2,10) (2,5) (2,20) (2,7) (2,19) (2,14) (2,12) (2,15) (2,16) (2,17) (2,18) (2,4) (3,5) (3,20) (3,7) (3,19) (3,14) (3,16) (3,17) (3,18) (4,10) (4,5) (4,20) (4,7) (4,19) (4,14) (4,12) (4,15) (4,16) (4,17) (5,20) (5,7) (5,19) (5,14) (5,12) (5,16) (5,17) (5,18) (6,11) (6,8) (7,10) (7,19) (7,14) (7,12) (7,15) (7,16) (7,17) (7,18) (8,11) (9,21) (9,13) (10,19) (10,14) (10,12) (10,16) (10,18) (12,20) (12,19) (12,14) (12,15) (12,16) (12,17) (14,20) (14,19) (14,15) (14,16) (14,17) (15,20) (15,19) (15,16) (15,17) (15,18) (16,20) (16,19) (16,17) (16,18) (17,20) (17,19) (17,18) (18,19) (19,20)\nQ: Is there a path between node 7 and node 18?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "33"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,2) (0,4) (0,5) (0,15) (0,7) (1,9) (1,13) (1,12) (1,3) (2,14) (2,10) (2,4) (2,8) (2,15) (2,7) (3,9) (3,13) (3,12) (3,11) (4,14) (4,6) (4,10) (4,8) (4,15) (5,6) (5,8) (5,7) (6,14) (6,8) (6,15) (7,14) (7,10) (7,8) (7,15) (8,14) (8,10) (8,15) (9,13) (9,12) (9,11) (10,14) (10,15) (11,13) (11,12) (12,13) (14,15)\nQ: Is there a path between node 2 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "34"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,13) (0,6) (0,5) (0,15) (0,14) (0,1) (0,10) (0,8) (0,7) (0,2) (0,11) (0,3) (1,12) (1,13) (1,6) (1,5) (1,15) (1,14) (1,10) (1,8) (1,7) (1,2) (1,11) (1,3) (2,12) (2,13) (2,6) (2,5) (2,15) (2,14) (2,10) (2,8) (2,7) (2,11) (2,3) (3,12) (3,13) (3,6) (3,5) (3,15) (3,14) (3,10) (3,8) (3,7) (3,11) (4,9) (5,12) (5,13) (5,6) (5,15) (5,14) (5,10) (5,8) (5,7) (5,11) (6,12) (6,13) (6,15) (6,14) (6,10) (6,8) (6,7) (6,11) (7,12) (7,13) (7,15) (7,14) (7,10) (7,8) (7,11) (8,12) (8,13) (8,15) (8,14) (8,10) (8,11) (10,12) (10,13) (10,15) (10,14) (10,11) (11,12) (11,13) (11,15) (11,14) (12,13) (12,15) (12,14) (13,15) (13,14) (14,15)\nQ: Is there a path between node 13 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "35"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,3) (0,5) (1,2) (1,8) (1,7) (2,8) (2,7) (3,11) (3,9) (3,13) (5,11) (5,12) (10,11) (11,12) (12,13)\nQ: Is there a path between node 2 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "36"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,7) (0,10) (0,6) (0,2) (0,8) (0,4) (0,1) (1,3) (1,7) (1,10) (1,6) (1,2) (1,8) (1,4) (2,3) (2,7) (2,10) (2,6) (2,8) (2,4) (3,7) (3,10) (3,6) (3,8) (3,4) (4,7) (4,10) (4,6) (4,8) (5,9) (6,7) (6,10) (6,8) (7,10) (7,8) (8,10)\nQ: Is there a path between node 5 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "37"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,9) (0,2) (0,5) (0,10) (0,1) (1,4) (1,9) (1,2) (1,5) (1,10) (2,4) (2,9) (2,5) (2,10) (3,11) (3,8) (3,12) (3,7) (3,6) (4,9) (4,5) (4,10) (5,9) (5,10) (6,11) (6,8) (6,12) (6,7) (7,11) (7,8) (7,12) (8,11) (8,12) (9,10) (11,12)\nQ: Is there a path between node 12 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "38"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,4) (0,12) (0,11) (0,10) (0,3) (0,17) (0,21) (0,27) (0,15) (0,23) (0,31) (0,29) (0,2) (0,8) (0,9) (0,14) (0,18) (1,5) (1,26) (1,13) (1,20) (1,32) (1,7) (2,19) (2,4) (2,28) (2,22) (2,16) (2,12) (2,10) (2,3) (2,17) (2,21) (2,27) (2,15) (2,23) (2,31) (2,29) (2,8) (2,9) (2,14) (2,18) (3,4) (3,22) (3,16) (3,12) (3,10) (3,17) (3,21) (3,27) (3,23) (3,31) (3,29) (3,6) (3,9) (3,14) (3,18) (4,16) (4,12) (4,11) (4,17) (4,21) (4,15) (4,30) (4,23) (4,29) (4,6) (4,8) (4,9) (4,18) (5,26) (5,13) (5,25) (5,24) (5,32) (5,7) (6,19) (6,22) (6,12) (6,11) (6,10) (6,17) (6,21) (6,27) (6,15) (6,30) (6,23) (6,31) (6,29) (6,9) (6,14) (7,26) (7,25) (7,32) (8,19) (8,28) (8,10) (8,17) (8,27) (8,15) (8,30) (8,23) (9,19) (9,28) (9,22) (9,16) (9,12) (9,10) (9,17) (9,21) (9,15) (9,30) (9,23) (9,29) (9,18) (10,19) (10,28) (10,22) (10,12) (10,11) (10,17) (10,21) (10,27) (10,15) (10,30) (10,23) (10,31) (10,29) (10,14) (10,18) (11,16) (11,12) (11,17) (11,21) (11,27) (11,15) (11,30) (11,31) (11,29) (11,14) (11,18) (12,19) (12,28) (12,22) (12,17) (12,27) (12,15) (12,30) (12,23) (12,31) (12,29) (12,14) (12,18) (13,26) (13,25) (13,20) (13,32) (14,28) (14,16) (14,17) (14,21) (14,27) (14,15) (14,31) (14,29) (14,18) (15,19) (15,22) (15,16) (15,17) (15,21) (15,27) (15,30) (15,23) (15,31) (15,29) (15,18) (16,19) (16,28) (16,22) (16,17) (16,21) (16,27) (16,30) (16,31) (16,18) (17,22) (17,21) (17,30) (17,31) (17,29) (17,18) (18,19) (18,28) (18,22) (18,21) (18,27) (18,29) (19,28) (19,22) (19,21) (19,30) (19,31) (19,29) (20,32) (21,28) (21,22) (21,27) (21,29) (22,28) (22,30) (22,23) (22,31) (22,29) (23,28) (23,27) (23,30) (23,31) (23,29) (24,26) (24,25) (25,26) (25,32) (26,32) (27,28) (27,30) (27,29) (28,30) (28,31) (28,29) (29,30) (29,31)\nQ: Is there a path between node 18 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "39"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,13) (1,6) (1,8) (1,3) (1,4) (2,5) (2,9) (3,12) (3,9) (3,13) (4,6) (4,10) (5,6) (5,9) (6,12) (6,8) (8,9) (9,10) (12,13)\nQ: Is there a path between node 7 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "40"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,1) (0,2) (0,7) (0,6) (1,2) (1,8) (1,7) (1,4) (1,6) (2,7) (2,4) (2,6) (3,5) (4,9) (4,8) (4,7) (6,9) (6,7) (7,8)\nQ: Is there a path between node 5 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "41"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,7) (0,6) (0,8) (0,4) (0,1) (1,2) (1,7) (1,6) (1,8) (1,4) (2,7) (2,6) (2,8) (2,4) (3,5) (4,7) (4,6) (4,8) (6,7) (6,8) (7,8)\nQ: Is there a path between node 4 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "42"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,5) (0,7) (0,6) (0,2) (0,4) (0,8) (0,9) (1,10) (2,3) (2,5) (2,7) (2,6) (2,4) (2,8) (2,9) (2,11) (3,5) (3,4) (3,8) (3,11) (4,5) (4,6) (4,9) (4,11) (5,6) (5,8) (5,9) (6,7) (6,8) (6,9) (6,11) (7,8) (7,11) (8,9) (9,11)\nQ: Is there a path between node 10 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "43"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,13) (0,1) (0,9) (0,5) (0,7) (0,3) (0,10) (0,23) (0,26) (0,27) (0,8) (0,14) (0,22) (0,20) (0,15) (0,4) (0,2) (1,25) (1,11) (1,21) (1,13) (1,9) (1,3) (1,10) (1,23) (1,26) (1,27) (1,14) (1,20) (1,15) (1,2) (1,28) (2,25) (2,11) (2,16) (2,21) (2,6) (2,13) (2,9) (2,7) (2,23) (2,26) (2,8) (2,20) (2,15) (3,25) (3,6) (3,13) (3,9) (3,10) (3,27) (3,20) (3,15) (3,4) (3,28) (4,11) (4,16) (4,6) (4,13) (4,10) (4,23) (4,26) (4,27) (4,8) (4,14) (4,22) (4,15) (4,28) (5,25) (5,16) (5,21) (5,6) (5,13) (5,9) (5,7) (5,26) (5,8) (5,22) (5,15) (5,28) (6,11) (6,16) (6,21) (6,13) (6,9) (6,7) (6,10) (6,27) (6,22) (6,20) (6,15) (7,25) (7,16) (7,21) (7,9) (7,10) (7,27) (7,8) (7,14) (7,22) (7,20) (7,15) (7,28) (8,25) (8,13) (8,23) (8,26) (8,27) (8,14) (8,20) (8,28) (9,25) (9,11) (9,16) (9,21) (9,10) (9,23) (9,26) (9,27) (9,22) (9,20) (9,28) (10,11) (10,16) (10,21) (10,13) (10,23) (10,26) (10,27) (10,14) (10,22) (10,20) (10,15) (10,28) (11,25) (11,16) (11,21) (11,13) (11,23) (11,26) (11,27) (11,14) (11,22) (11,20) (12,24) (12,19) (13,25) (13,16) (13,14) (13,22) (13,15) (13,28) (14,25) (14,21) (14,23) (14,26) (14,20) (14,15) (15,16) (15,21) (15,26) (15,27) (15,22) (15,28) (16,21) (16,23) (16,26) (16,27) (16,28) (17,18) (20,25) (20,23) (20,26) (20,27) (20,22) (20,28) (21,25) (21,23) (21,26) (21,22) (22,25) (22,23) (22,27) (23,25) (23,26) (23,27) (23,28) (25,26) (25,27) (26,27) (27,28)\nQ: Is there a path between node 0 and node 17?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "44"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,15) (0,22) (0,18) (1,5) (1,14) (1,21) (1,16) (1,19) (1,3) (1,17) (1,13) (1,11) (1,2) (1,20) (1,8) (1,6) (1,12) (1,9) (1,7) (2,5) (2,14) (2,21) (2,16) (2,19) (2,3) (2,17) (2,13) (2,11) (2,20) (2,8) (2,6) (2,12) (2,9) (2,7) (3,5) (3,14) (3,21) (3,16) (3,19) (3,17) (3,13) (3,11) (3,20) (3,8) (3,6) (3,12) (3,9) (3,7) (5,14) (5,21) (5,16) (5,19) (5,17) (5,13) (5,11) (5,20) (5,8) (5,6) (5,12) (5,9) (5,7) (6,14) (6,21) (6,16) (6,19) (6,17) (6,13) (6,11) (6,20) (6,8) (6,12) (6,9) (6,7) (7,14) (7,21) (7,16) (7,19) (7,17) (7,13) (7,11) (7,20) (7,8) (7,12) (7,9) (8,14) (8,21) (8,16) (8,19) (8,17) (8,13) (8,11) (8,20) (8,12) (8,9) (9,14) (9,21) (9,16) (9,19) (9,17) (9,13) (9,11) (9,20) (9,12) (10,15) (10,22) (10,18) (11,14) (11,21) (11,16) (11,19) (11,17) (11,13) (11,20) (11,12) (12,14) (12,21) (12,16) (12,19) (12,17) (12,13) (12,20) (13,14) (13,21) (13,16) (13,19) (13,17) (13,20) (14,21) (14,16) (14,19) (14,17) (14,20) (15,22) (15,18) (16,21) (16,19) (16,17) (16,20) (17,21) (17,19) (17,20) (18,22) (19,21) (19,20) (20,21)\nQ: Is there a path between node 17 and node 20?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "45"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,3) (0,11) (0,8) (0,2) (0,12) (0,9) (0,1) (1,4) (1,3) (1,6) (1,11) (1,8) (1,7) (1,10) (1,2) (1,12) (2,3) (2,6) (2,11) (2,8) (2,9) (3,6) (3,11) (3,8) (3,7) (3,10) (3,9) (4,6) (4,11) (4,8) (4,7) (4,10) (4,12) (4,9) (6,8) (6,10) (7,10) (7,12) (7,9) (8,11) (8,10) (8,12) (9,10) (10,12)\nQ: Is there a path between node 6 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "46"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,16) (0,9) (0,3) (0,4) (0,8) (0,17) (1,6) (1,12) (1,13) (1,18) (1,2) (1,4) (1,8) (1,17) (2,6) (2,12) (2,15) (2,9) (2,13) (2,18) (2,4) (2,8) (2,17) (3,6) (3,16) (3,12) (3,9) (3,13) (3,18) (3,8) (3,17) (3,5) (4,6) (4,16) (4,12) (4,9) (4,18) (4,17) (4,5) (5,6) (5,12) (5,15) (5,9) (5,17) (6,12) (6,15) (6,9) (6,13) (6,18) (6,8) (7,10) (7,11) (7,19) (8,16) (8,15) (8,9) (8,18) (9,16) (9,12) (9,15) (9,13) (9,18) (9,17) (10,19) (11,14) (11,19) (12,16) (12,15) (12,13) (12,17) (13,18) (14,19) (15,17) (16,17) (17,18)\nQ: Is there a path between node 6 and node 12?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "47"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,4) (0,1) (0,5) (0,24) (0,3) (0,21) (0,19) (0,9) (0,15) (0,20) (0,27) (0,13) (1,24) (1,21) (1,31) (1,10) (1,7) (1,20) (1,27) (1,13) (2,6) (2,5) (2,24) (2,3) (2,21) (2,19) (2,9) (2,31) (2,15) (2,7) (2,27) (2,13) (3,6) (3,4) (3,5) (3,22) (3,24) (3,21) (3,19) (3,9) (3,31) (3,18) (3,7) (3,20) (4,5) (4,21) (4,19) (4,9) (4,31) (4,7) (4,20) (4,27) (4,13) (5,6) (5,22) (5,24) (5,21) (5,9) (5,31) (5,10) (5,15) (5,18) (5,20) (5,27) (5,13) (6,22) (6,21) (6,19) (6,9) (6,31) (6,10) (6,15) (6,18) (6,7) (6,27) (6,13) (7,22) (7,9) (7,10) (7,15) (7,18) (7,20) (7,27) (7,13) (8,16) (8,11) (8,28) (8,12) (8,25) (8,30) (8,14) (8,32) (8,29) (9,22) (9,24) (9,21) (9,19) (9,31) (9,10) (9,15) (9,18) (9,20) (10,22) (10,19) (10,31) (10,15) (10,20) (10,27) (10,13) (11,16) (11,28) (11,26) (11,23) (11,30) (11,14) (11,32) (11,17) (12,16) (12,28) (12,23) (12,30) (12,14) (12,33) (12,32) (12,17) (12,29) (13,22) (13,24) (13,21) (13,19) (13,15) (13,18) (13,20) (14,28) (14,26) (14,23) (14,25) (14,33) (14,32) (14,29) (15,22) (15,24) (15,21) (15,19) (15,20) (15,27) (16,26) (16,25) (16,30) (16,33) (16,32) (16,17) (16,29) (17,28) (17,26) (17,25) (17,30) (17,33) (17,32) (17,29) (18,24) (18,19) (18,31) (19,22) (19,24) (19,31) (19,20) (19,27) (20,21) (20,31) (20,27) (21,31) (23,28) (23,26) (23,25) (23,30) (24,31) (24,27) (25,26) (25,30) (25,33) (25,32) (25,29) (26,28) (26,33) (26,32) (28,30) (28,29) (29,30) (29,33) (29,32) (30,32)\nQ: Is there a path between node 8 and node 30?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "48"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,19) (0,17) (0,3) (0,10) (0,14) (1,7) (1,8) (1,15) (1,13) (2,9) (2,12) (2,18) (2,4) (3,6) (3,19) (3,17) (3,16) (3,10) (3,14) (4,12) (4,18) (5,9) (5,18) (6,19) (6,17) (6,16) (6,14) (6,20) (7,8) (7,15) (7,13) (9,12) (9,18) (10,16) (10,14) (10,20) (11,15) (12,18) (13,15) (14,19) (14,17) (14,20) (16,19) (16,17) (17,20) (19,20)\nQ: Is there a path between node 1 and node 18?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "49"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (0,13) (0,22) (1,12) (1,6) (2,20) (2,14) (2,11) (3,5) (3,23) (3,6) (5,17) (6,19) (7,23) (8,13) (8,15) (9,21) (9,18) (12,24) (12,17) (12,19) (13,21) (13,18) (13,25) (13,15) (13,16) (15,16) (16,21) (16,25) (17,23) (17,19) (19,26) (21,22) (22,25)\nQ: Is there a path between node 0 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "50"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,32) (0,29) (0,7) (0,15) (1,30) (1,10) (1,8) (2,27) (2,18) (2,20) (2,7) (2,26) (3,14) (3,9) (4,18) (4,11) (4,13) (4,15) (5,30) (5,21) (6,14) (6,21) (6,17) (7,18) (7,22) (7,31) (7,29) (7,26) (8,14) (8,10) (9,21) (10,12) (10,21) (10,17) (11,19) (11,22) (11,28) (11,32) (11,29) (11,15) (11,26) (12,30) (12,21) (13,27) (13,20) (13,28) (13,31) (14,17) (15,20) (15,31) (15,26) (16,27) (16,32) (17,30) (18,27) (18,28) (18,32) (18,26) (18,24) (18,23) (19,27) (19,20) (19,31) (19,29) (19,26) (19,24) (20,25) (20,28) (20,32) (20,26) (22,31) (22,23) (23,27) (23,28) (23,26) (25,26) (26,27) (26,28) (26,29) (28,32) (28,31) (29,31)\nQ: Is there a path between node 30 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "51"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,15) (0,18) (0,27) (0,9) (0,13) (0,25) (0,3) (1,8) (1,5) (1,26) (1,12) (1,2) (1,16) (1,14) (2,8) (2,26) (2,12) (2,16) (2,14) (3,7) (3,4) (3,15) (3,18) (3,27) (3,13) (4,7) (4,15) (4,18) (4,27) (4,13) (5,8) (5,12) (5,11) (5,16) (5,14) (5,20) (6,17) (6,21) (6,29) (6,28) (7,15) (7,18) (7,27) (7,9) (7,13) (8,26) (8,23) (8,16) (8,14) (9,15) (10,29) (10,24) (11,12) (11,16) (11,14) (11,20) (12,22) (12,23) (12,14) (12,20) (13,18) (13,27) (14,26) (14,22) (14,23) (14,20) (15,18) (15,27) (15,25) (16,26) (16,22) (16,23) (16,20) (17,21) (17,19) (17,24) (17,28) (19,21) (19,29) (19,24) (19,28) (20,26) (20,22) (20,23) (21,29) (21,24) (22,26) (22,23) (24,29) (24,28) (25,27)\nQ: Is there a path between node 25 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "52"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,17) (1,4) (2,10) (3,19) (3,30) (3,13) (3,25) (3,8) (4,31) (5,16) (6,29) (6,11) (6,32) (7,14) (7,17) (8,21) (8,30) (8,13) (8,28) (9,20) (9,25) (11,29) (11,26) (11,22) (13,21) (13,15) (13,28) (13,23) (15,31) (15,16) (15,28) (15,23) (16,21) (16,25) (16,23) (18,29) (18,24) (20,31) (20,30) (20,25) (21,25) (22,24) (23,25) (23,28) (24,29) (24,32) (25,30) (26,32) (28,30)\nQ: Is there a path between node 23 and node 31?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "53"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (0,11) (0,8) (0,17) (0,13) (0,6) (0,3) (0,15) (0,7) (1,14) (1,19) (1,9) (1,21) (1,12) (1,22) (1,4) (1,18) (1,5) (1,10) (1,20) (2,16) (3,23) (3,11) (3,8) (3,17) (3,13) (3,6) (3,15) (3,7) (4,14) (4,19) (4,9) (4,21) (4,12) (4,22) (4,18) (4,5) (4,10) (4,20) (5,14) (5,19) (5,9) (5,21) (5,12) (5,22) (5,18) (5,10) (5,20) (6,23) (6,11) (6,8) (6,17) (6,13) (6,15) (6,7) (7,23) (7,11) (7,8) (7,17) (7,13) (7,15) (8,23) (8,11) (8,17) (8,13) (8,15) (9,14) (9,19) (9,21) (9,12) (9,22) (9,18) (9,10) (9,20) (10,14) (10,19) (10,21) (10,12) (10,22) (10,18) (10,20) (11,23) (11,17) (11,13) (11,15) (12,14) (12,19) (12,21) (12,22) (12,18) (12,20) (13,23) (13,17) (13,15) (14,19) (14,21) (14,22) (14,18) (14,20) (15,23) (15,17) (17,23) (18,19) (18,21) (18,22) (18,20) (19,21) (19,22) (19,20) (20,21) (20,22) (21,22)\nQ: Is there a path between node 0 and node 13?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "54"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,9) (0,13) (0,3) (0,1) (0,2) (0,7) (0,8) (0,11) (1,14) (1,13) (1,8) (1,10) (1,11) (1,5) (2,9) (2,13) (2,3) (2,7) (2,8) (2,10) (3,14) (3,9) (3,13) (3,8) (3,11) (3,5) (4,6) (4,12) (5,14) (5,9) (5,7) (5,8) (5,10) (5,11) (6,12) (7,14) (7,13) (7,8) (7,10) (8,14) (8,9) (8,10) (9,14) (9,13) (10,14) (10,13) (11,14) (13,14)\nQ: Is there a path between node 8 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "55"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,23) (0,8) (1,6) (1,26) (1,11) (2,6) (2,11) (3,12) (3,19) (3,20) (4,13) (4,21) (4,17) (4,10) (4,6) (4,23) (4,8) (5,13) (5,7) (5,21) (5,17) (5,28) (5,6) (5,23) (5,8) (5,26) (5,24) (5,11) (6,13) (6,17) (6,10) (6,23) (6,24) (7,17) (7,28) (7,23) (8,21) (8,10) (9,15) (10,13) (10,21) (10,23) (10,11) (11,13) (11,17) (12,19) (12,14) (12,27) (12,15) (12,22) (13,17) (13,16) (14,22) (15,19) (16,17) (16,28) (16,24) (17,24) (18,19) (18,27) (19,27) (21,26) (21,24) (22,25) (23,28) (24,28) (25,27)\nQ: Is there a path between node 4 and node 19?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "56"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,31) (0,11) (0,27) (0,18) (1,4) (1,12) (1,31) (1,7) (1,25) (1,8) (1,18) (2,17) (2,14) (2,6) (2,10) (2,19) (3,17) (3,22) (3,9) (4,12) (4,30) (4,31) (4,13) (4,27) (4,18) (5,29) (5,16) (5,22) (5,21) (5,20) (5,28) (5,19) (6,29) (6,9) (6,10) (6,28) (7,11) (7,27) (7,15) (7,18) (8,30) (8,23) (8,11) (9,14) (9,21) (9,10) (11,23) (11,18) (12,30) (12,31) (12,27) (12,25) (12,15) (12,18) (13,23) (13,25) (13,15) (14,29) (14,17) (16,24) (16,17) (16,20) (17,29) (18,30) (18,26) (20,29) (21,24) (22,24) (23,27) (23,25) (25,26) (25,27) (26,31) (27,31) (28,29)\nQ: Is there a path between node 8 and node 13?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "57"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,17) (0,10) (0,28) (0,30) (0,29) (0,3) (1,14) (1,2) (2,25) (2,20) (2,7) (2,32) (2,22) (3,24) (3,19) (3,23) (3,4) (3,12) (3,29) (4,26) (4,24) (4,23) (4,8) (4,13) (5,26) (5,19) (5,23) (5,8) (5,15) (5,21) (6,14) (7,32) (8,16) (8,12) (8,29) (9,26) (9,13) (9,18) (9,29) (9,31) (10,17) (10,11) (10,30) (10,23) (10,13) (11,16) (11,17) (11,19) (11,28) (11,23) (12,26) (12,24) (12,21) (13,26) (13,17) (13,19) (13,30) (13,31) (14,25) (14,22) (15,16) (15,17) (15,23) (15,18) (15,29) (16,26) (16,24) (16,18) (16,21) (17,24) (17,19) (17,28) (17,30) (17,23) (18,24) (18,21) (19,26) (19,24) (19,28) (19,23) (20,32) (22,32) (22,27) (24,26) (24,30) (26,29) (28,29)\nQ: Is there a path between node 10 and node 21?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "58"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,13) (0,2) (0,15) (0,6) (0,17) (0,8) (0,16) (0,18) (0,9) (0,12) (0,11) (1,10) (1,14) (1,7) (1,5) (1,4) (2,3) (2,13) (2,15) (2,6) (2,17) (2,8) (2,16) (2,18) (2,9) (2,12) (2,11) (3,13) (3,15) (3,6) (3,17) (3,8) (3,16) (3,18) (3,9) (3,12) (3,11) (4,10) (4,14) (4,7) (4,5) (5,10) (5,14) (5,7) (6,13) (6,15) (6,17) (6,8) (6,16) (6,18) (6,9) (6,12) (6,11) (7,10) (7,14) (8,13) (8,15) (8,17) (8,16) (8,18) (8,9) (8,12) (8,11) (9,13) (9,15) (9,17) (9,16) (9,18) (9,12) (9,11) (10,14) (11,13) (11,15) (11,17) (11,16) (11,18) (11,12) (12,13) (12,15) (12,17) (12,16) (12,18) (13,15) (13,17) (13,16) (13,18) (15,17) (15,16) (15,18) (16,17) (16,18) (17,18)\nQ: Is there a path between node 6 and node 16?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "59"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (1,20) (2,11) (2,23) (2,14) (2,8) (3,17) (3,14) (3,16) (4,7) (4,16) (4,8) (4,24) (5,6) (5,10) (5,20) (6,20) (7,12) (7,16) (7,8) (7,24) (8,12) (8,23) (8,21) (9,18) (10,18) (10,20) (11,17) (11,19) (11,24) (12,22) (12,17) (12,14) (13,24) (14,23) (14,24) (15,17) (15,19) (15,24) (16,22) (16,19) (17,19) (17,24) (19,24) (23,24)\nQ: Is there a path between node 21 and node 17?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "60"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,8) (1,5) (1,10) (1,8) (2,6) (2,7) (3,9) (3,10) (4,11) (4,8) (6,7) (8,9) (8,10) (11,12)\nQ: Is there a path between node 9 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "61"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (1,27) (1,24) (1,21) (1,3) (2,10) (2,22) (2,6) (2,18) (2,25) (2,12) (3,19) (3,27) (3,24) (4,10) (4,6) (4,18) (4,25) (5,28) (5,16) (6,10) (6,13) (6,25) (6,12) (6,9) (7,28) (8,10) (8,14) (8,18) (8,29) (8,25) (8,23) (9,13) (9,14) (10,29) (10,25) (12,22) (12,18) (12,17) (13,29) (13,26) (14,20) (14,17) (15,19) (17,25) (18,20) (18,25) (20,29) (20,26) (20,23) (21,27) (21,24) (23,26) (23,25) (24,27) (26,29)\nQ: Is there a path between node 17 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "62"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,8) (0,4) (0,5) (0,13) (0,2) (0,17) (1,15) (1,8) (1,3) (1,4) (1,5) (1,13) (1,17) (2,15) (2,8) (2,3) (2,4) (2,5) (2,13) (3,8) (3,5) (3,17) (4,15) (4,13) (4,17) (5,15) (5,8) (5,17) (6,14) (6,7) (6,10) (6,16) (6,9) (6,12) (7,14) (7,16) (7,9) (8,13) (9,14) (9,10) (9,11) (9,16) (9,12) (10,14) (10,12) (11,14) (11,12) (12,14) (12,16) (13,17) (15,17)\nQ: Is there a path between node 11 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "63"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,6) (1,2) (3,7) (3,5)\nQ: Is there a path between node 6 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "64"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (1,4) (1,11) (2,21) (2,20) (2,24) (3,24) (4,13) (4,15) (4,8) (5,19) (5,24) (6,20) (6,24) (7,25) (7,21) (8,17) (8,15) (8,12) (9,13) (9,12) (10,16) (11,13) (11,18) (11,23) (11,14) (11,12) (13,17) (14,23) (15,18) (15,23) (18,23) (19,25) (19,24) (20,21) (21,25) (24,25)\nQ: Is there a path between node 1 and node 23?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "65"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,10) (0,13) (0,12) (0,9) (0,18) (0,24) (0,5) (0,20) (0,21) (0,7) (0,3) (0,23) (1,2) (1,13) (1,16) (1,12) (1,18) (1,24) (1,20) (1,4) (1,7) (1,3) (1,19) (1,23) (2,13) (2,16) (2,12) (2,9) (2,11) (2,18) (2,24) (2,5) (2,20) (2,4) (2,21) (2,7) (2,3) (2,23) (3,13) (3,16) (3,12) (3,9) (3,11) (3,24) (3,5) (3,20) (3,21) (3,7) (3,19) (3,23) (4,10) (4,16) (4,12) (4,11) (4,18) (4,24) (4,5) (4,20) (4,21) (4,7) (4,19) (4,23) (5,13) (5,12) (5,11) (5,18) (5,24) (5,20) (5,21) (5,7) (5,23) (6,15) (6,25) (6,22) (6,8) (7,13) (7,12) (7,9) (7,11) (7,18) (7,20) (7,21) (7,19) (8,17) (8,15) (8,22) (8,14) (9,10) (9,13) (9,16) (9,11) (9,18) (9,21) (9,19) (9,23) (10,13) (10,12) (10,11) (10,24) (10,20) (10,21) (10,19) (10,23) (11,13) (11,16) (11,24) (11,20) (11,21) (11,19) (11,23) (12,13) (12,16) (12,18) (12,24) (12,20) (12,21) (12,19) (12,23) (13,16) (13,24) (13,21) (13,23) (14,17) (14,15) (14,22) (15,17) (15,25) (15,22) (16,18) (16,24) (16,21) (16,23) (17,25) (17,22) (18,20) (18,21) (18,19) (18,23) (19,20) (19,23) (20,24) (20,21) (21,23) (22,25) (23,24)\nQ: Is there a path between node 21 and node 13?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "66"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,8) (0,10) (0,4) (0,16) (0,5) (0,2) (0,7) (0,9) (0,15) (0,13) (0,1) (0,12) (0,14) (0,3) (1,11) (1,8) (1,10) (1,4) (1,16) (1,5) (1,2) (1,7) (1,9) (1,15) (1,13) (1,12) (1,14) (1,3) (2,11) (2,8) (2,10) (2,4) (2,16) (2,5) (2,7) (2,9) (2,15) (2,13) (2,12) (2,14) (2,3) (3,11) (3,8) (3,10) (3,4) (3,16) (3,5) (3,7) (3,9) (3,15) (3,13) (3,12) (3,14) (4,11) (4,8) (4,10) (4,16) (4,5) (4,7) (4,9) (4,15) (4,13) (4,12) (4,14) (5,11) (5,8) (5,10) (5,16) (5,7) (5,9) (5,15) (5,13) (5,12) (5,14) (7,11) (7,8) (7,10) (7,16) (7,9) (7,15) (7,13) (7,12) (7,14) (8,11) (8,10) (8,16) (8,9) (8,15) (8,13) (8,12) (8,14) (9,11) (9,10) (9,16) (9,15) (9,13) (9,12) (9,14) (10,11) (10,16) (10,15) (10,13) (10,12) (10,14) (11,16) (11,15) (11,13) (11,12) (11,14) (12,16) (12,15) (12,13) (12,14) (13,16) (13,15) (13,14) (14,16) (14,15) (15,16)\nQ: Is there a path between node 10 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "67"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (1,4) (1,11) (2,21) (2,20) (2,24) (3,24) (4,13) (4,15) (4,8) (5,19) (5,24) (6,20) (6,24) (7,25) (7,21) (8,17) (8,15) (8,12) (9,13) (9,12) (10,16) (11,13) (11,18) (11,23) (11,14) (11,12) (13,17) (14,23) (15,18) (15,23) (18,23) (19,25) (19,24) (20,21) (21,25) (24,25)\nQ: Is there a path between node 15 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "68"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,4) (0,11) (0,13) (1,8) (1,21) (1,10) (1,7) (1,2) (2,24) (2,8) (2,9) (2,10) (2,22) (3,5) (3,11) (3,13) (4,15) (4,6) (4,16) (4,11) (5,12) (5,15) (5,19) (5,18) (5,27) (6,19) (6,11) (7,26) (7,23) (7,9) (8,23) (8,9) (8,10) (8,22) (9,25) (9,14) (10,25) (10,17) (10,23) (11,20) (11,27) (12,15) (12,16) (12,18) (14,22) (15,19) (15,27) (16,19) (17,26) (17,24) (17,28) (17,23) (17,22) (19,20) (19,27) (21,26) (21,25) (21,29) (21,22) (22,29) (23,24) (23,29) (26,28)\nQ: Is there a path between node 5 and node 21?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "69"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,8) (0,2) (0,20) (0,16) (0,14) (0,15) (0,7) (1,18) (1,24) (1,22) (1,5) (1,19) (1,11) (1,17) (2,6) (2,4) (2,23) (2,8) (2,20) (2,16) (2,21) (2,14) (2,15) (2,10) (3,6) (3,4) (3,23) (3,8) (3,16) (3,14) (3,25) (3,15) (3,7) (4,6) (4,23) (4,8) (4,20) (4,16) (4,21) (4,14) (4,15) (4,10) (4,7) (5,18) (5,24) (5,22) (5,13) (5,9) (5,11) (5,12) (6,23) (6,8) (6,20) (6,16) (6,14) (6,25) (6,15) (7,23) (7,20) (7,16) (7,21) (7,14) (7,25) (7,15) (7,10) (8,20) (8,16) (8,14) (8,25) (8,15) (9,18) (9,24) (9,22) (9,19) (9,11) (9,17) (9,12) (10,23) (10,20) (10,16) (10,21) (10,14) (10,25) (11,22) (11,19) (11,17) (11,12) (12,18) (12,13) (12,19) (13,18) (13,24) (13,22) (13,17) (14,23) (14,20) (14,16) (14,25) (15,20) (15,16) (15,21) (15,25) (16,23) (16,20) (16,25) (17,18) (17,22) (17,19) (18,24) (18,22) (18,19) (19,24) (19,22) (20,21) (20,25) (21,23) (21,25) (22,24) (23,25)\nQ: Is there a path between node 5 and node 14?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "70"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,12) (0,11) (0,8) (0,1) (0,13) (0,10) (0,3) (1,2) (1,5) (1,12) (1,11) (1,8) (1,13) (1,10) (1,3) (2,5) (2,12) (2,11) (2,8) (2,13) (2,10) (2,3) (3,5) (3,12) (3,11) (3,8) (3,13) (3,10) (4,9) (4,6) (4,7) (4,14) (5,12) (5,11) (5,8) (5,13) (5,10) (6,9) (6,7) (6,14) (7,9) (7,14) (8,12) (8,11) (8,13) (8,10) (9,14) (10,12) (10,11) (10,13) (11,12) (11,13) (12,13)\nQ: Is there a path between node 6 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "71"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (1,24) (1,13) (1,7) (2,24) (2,15) (2,18) (2,8) (2,13) (2,7) (3,23) (3,6) (5,20) (5,14) (6,11) (6,23) (7,12) (7,10) (7,21) (7,8) (7,13) (8,10) (8,15) (8,18) (8,22) (8,13) (9,21) (9,13) (10,12) (10,15) (10,13) (12,24) (13,24) (13,22) (14,20) (15,24) (17,24) (19,20) (21,24)\nQ: Is there a path between node 17 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "72"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,12) (0,1) (0,7) (0,16) (0,13) (0,9) (0,2) (0,10) (0,21) (0,19) (0,3) (0,20) (0,8) (0,23) (0,5) (0,4) (0,6) (0,22) (1,15) (1,12) (1,7) (1,16) (1,13) (1,9) (1,2) (1,10) (1,21) (1,19) (1,3) (1,20) (1,8) (1,23) (1,5) (1,4) (1,6) (1,22) (2,15) (2,12) (2,7) (2,16) (2,13) (2,9) (2,10) (2,21) (2,19) (2,3) (2,20) (2,8) (2,23) (2,5) (2,4) (2,6) (2,22) (3,15) (3,12) (3,7) (3,16) (3,13) (3,9) (3,10) (3,21) (3,19) (3,20) (3,8) (3,23) (3,5) (3,4) (3,6) (3,22) (4,15) (4,12) (4,7) (4,16) (4,13) (4,9) (4,10) (4,21) (4,19) (4,20) (4,8) (4,23) (4,5) (4,6) (4,22) (5,15) (5,12) (5,7) (5,16) (5,13) (5,9) (5,10) (5,21) (5,19) (5,20) (5,8) (5,23) (5,6) (5,22) (6,15) (6,12) (6,7) (6,16) (6,13) (6,9) (6,10) (6,21) (6,19) (6,20) (6,8) (6,23) (6,22) (7,15) (7,12) (7,16) (7,13) (7,9) (7,10) (7,21) (7,19) (7,20) (7,8) (7,23) (7,22) (8,15) (8,12) (8,16) (8,13) (8,9) (8,10) (8,21) (8,19) (8,20) (8,23) (8,22) (9,15) (9,12) (9,16) (9,13) (9,10) (9,21) (9,19) (9,20) (9,23) (9,22) (10,15) (10,12) (10,16) (10,13) (10,21) (10,19) (10,20) (10,23) (10,22) (11,17) (11,14) (11,18) (12,15) (12,16) (12,13) (12,21) (12,19) (12,20) (12,23) (12,22) (13,15) (13,16) (13,21) (13,19) (13,20) (13,23) (13,22) (14,17) (14,18) (15,16) (15,21) (15,19) (15,20) (15,23) (15,22) (16,21) (16,19) (16,20) (16,23) (16,22) (17,18) (19,21) (19,20) (19,23) (19,22) (20,21) (20,23) (20,22) (21,23) (21,22) (22,23)\nQ: Is there a path between node 18 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "73"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,4) (0,16) (0,21) (0,1) (0,25) (0,14) (0,9) (0,5) (0,6) (0,12) (0,17) (0,24) (0,23) (1,29) (1,4) (1,27) (1,16) (1,21) (1,14) (1,9) (1,6) (1,24) (1,23) (2,26) (2,10) (2,22) (2,15) (2,28) (2,8) (2,30) (2,19) (3,26) (3,10) (3,11) (3,22) (3,15) (3,28) (3,8) (3,30) (3,19) (3,20) (4,29) (4,27) (4,16) (4,21) (4,14) (4,9) (4,5) (4,6) (4,12) (4,24) (5,29) (5,27) (5,21) (5,7) (5,14) (5,12) (5,17) (5,24) (5,23) (6,29) (6,27) (6,7) (6,25) (6,14) (6,9) (6,12) (6,24) (6,23) (7,25) (7,14) (7,9) (7,12) (7,17) (7,23) (8,26) (8,10) (8,11) (8,13) (8,30) (8,19) (9,29) (9,27) (9,16) (9,14) (9,12) (9,24) (9,23) (10,26) (10,13) (10,15) (10,28) (10,19) (10,20) (11,26) (11,13) (11,15) (11,28) (11,30) (11,19) (11,20) (12,29) (12,27) (12,16) (12,21) (12,25) (12,17) (12,24) (12,23) (13,26) (13,28) (13,30) (14,29) (14,16) (14,21) (14,25) (14,17) (14,24) (14,23) (15,26) (15,28) (15,30) (15,20) (16,27) (16,21) (16,17) (16,24) (16,23) (17,29) (17,27) (17,21) (17,25) (17,24) (19,26) (19,22) (19,30) (19,20) (20,26) (20,22) (20,28) (21,29) (21,27) (21,25) (21,24) (21,23) (22,26) (22,28) (22,30) (23,29) (23,27) (23,25) (24,29) (24,27) (24,25) (25,29) (26,28) (28,30)\nQ: Is there a path between node 20 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "74"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,11) (3,15) (3,8) (5,18) (5,7) (6,17) (6,7) (7,13) (7,8) (7,14) (8,18) (8,12) (9,11) (9,15) (9,13) (9,17) (10,18) (11,13) (11,17) (12,18) (12,17) (12,14) (13,17) (14,17) (17,18)\nQ: Is there a path between node 4 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "75"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,3) (0,5) (1,2) (1,8) (1,7) (2,8) (2,7) (3,11) (3,9) (3,13) (5,11) (5,12) (10,11) (11,12) (12,13)\nQ: Is there a path between node 3 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "76"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,8) (0,4) (0,5) (0,13) (0,2) (0,17) (1,15) (1,8) (1,3) (1,4) (1,5) (1,13) (1,17) (2,15) (2,8) (2,3) (2,4) (2,5) (2,13) (3,8) (3,5) (3,17) (4,15) (4,13) (4,17) (5,15) (5,8) (5,17) (6,14) (6,7) (6,10) (6,16) (6,9) (6,12) (7,14) (7,16) (7,9) (8,13) (9,14) (9,10) (9,11) (9,16) (9,12) (10,14) (10,12) (11,14) (11,12) (12,14) (12,16) (13,17) (15,17)\nQ: Is there a path between node 9 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "77"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,17) (1,4) (2,10) (3,19) (3,30) (3,13) (3,25) (3,8) (4,31) (5,16) (6,29) (6,11) (6,32) (7,14) (7,17) (8,21) (8,30) (8,13) (8,28) (9,20) (9,25) (11,29) (11,26) (11,22) (13,21) (13,15) (13,28) (13,23) (15,31) (15,16) (15,28) (15,23) (16,21) (16,25) (16,23) (18,29) (18,24) (20,31) (20,30) (20,25) (21,25) (22,24) (23,25) (23,28) (24,29) (24,32) (25,30) (26,32) (28,30)\nQ: Is there a path between node 23 and node 17?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "78"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,30) (0,6) (0,12) (1,15) (2,17) (2,4) (3,25) (3,30) (3,12) (4,18) (4,16) (4,20) (4,22) (4,28) (4,8) (4,17) (5,12) (5,11) (6,19) (7,9) (7,10) (8,22) (8,28) (8,21) (9,23) (10,12) (10,11) (11,30) (11,19) (11,12) (12,25) (12,19) (13,27) (13,26) (15,26) (16,18) (16,29) (16,20) (16,24) (16,22) (16,28) (16,17) (17,22) (17,28) (17,21) (18,29) (18,20) (18,24) (18,22) (19,30) (20,22) (20,28) (21,24) (24,28) (25,30)\nQ: Is there a path between node 4 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "79"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,7) (0,6) (0,8) (0,4) (0,1) (1,2) (1,7) (1,6) (1,8) (1,4) (2,7) (2,6) (2,8) (2,4) (3,5) (4,7) (4,6) (4,8) (6,7) (6,8) (7,8)\nQ: Is there a path between node 0 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "80"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,4) (0,16) (0,21) (0,1) (0,25) (0,14) (0,9) (0,5) (0,6) (0,12) (0,17) (0,24) (0,23) (1,29) (1,4) (1,27) (1,16) (1,21) (1,14) (1,9) (1,6) (1,24) (1,23) (2,26) (2,10) (2,22) (2,15) (2,28) (2,8) (2,30) (2,19) (3,26) (3,10) (3,11) (3,22) (3,15) (3,28) (3,8) (3,30) (3,19) (3,20) (4,29) (4,27) (4,16) (4,21) (4,14) (4,9) (4,5) (4,6) (4,12) (4,24) (5,29) (5,27) (5,21) (5,7) (5,14) (5,12) (5,17) (5,24) (5,23) (6,29) (6,27) (6,7) (6,25) (6,14) (6,9) (6,12) (6,24) (6,23) (7,25) (7,14) (7,9) (7,12) (7,17) (7,23) (8,26) (8,10) (8,11) (8,13) (8,30) (8,19) (9,29) (9,27) (9,16) (9,14) (9,12) (9,24) (9,23) (10,26) (10,13) (10,15) (10,28) (10,19) (10,20) (11,26) (11,13) (11,15) (11,28) (11,30) (11,19) (11,20) (12,29) (12,27) (12,16) (12,21) (12,25) (12,17) (12,24) (12,23) (13,26) (13,28) (13,30) (14,29) (14,16) (14,21) (14,25) (14,17) (14,24) (14,23) (15,26) (15,28) (15,30) (15,20) (16,27) (16,21) (16,17) (16,24) (16,23) (17,29) (17,27) (17,21) (17,25) (17,24) (19,26) (19,22) (19,30) (19,20) (20,26) (20,22) (20,28) (21,29) (21,27) (21,25) (21,24) (21,23) (22,26) (22,28) (22,30) (23,29) (23,27) (23,25) (24,29) (24,27) (24,25) (25,29) (26,28) (28,30)\nQ: Is there a path between node 24 and node 23?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "81"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,11) (3,15) (3,8) (5,18) (5,7) (6,17) (6,7) (7,13) (7,8) (7,14) (8,18) (8,12) (9,11) (9,15) (9,13) (9,17) (10,18) (11,13) (11,17) (12,18) (12,17) (12,14) (13,17) (14,17) (17,18)\nQ: Is there a path between node 5 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "82"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,8) (0,10) (0,4) (0,16) (0,5) (0,2) (0,7) (0,9) (0,15) (0,13) (0,1) (0,12) (0,14) (0,3) (1,11) (1,8) (1,10) (1,4) (1,16) (1,5) (1,2) (1,7) (1,9) (1,15) (1,13) (1,12) (1,14) (1,3) (2,11) (2,8) (2,10) (2,4) (2,16) (2,5) (2,7) (2,9) (2,15) (2,13) (2,12) (2,14) (2,3) (3,11) (3,8) (3,10) (3,4) (3,16) (3,5) (3,7) (3,9) (3,15) (3,13) (3,12) (3,14) (4,11) (4,8) (4,10) (4,16) (4,5) (4,7) (4,9) (4,15) (4,13) (4,12) (4,14) (5,11) (5,8) (5,10) (5,16) (5,7) (5,9) (5,15) (5,13) (5,12) (5,14) (7,11) (7,8) (7,10) (7,16) (7,9) (7,15) (7,13) (7,12) (7,14) (8,11) (8,10) (8,16) (8,9) (8,15) (8,13) (8,12) (8,14) (9,11) (9,10) (9,16) (9,15) (9,13) (9,12) (9,14) (10,11) (10,16) (10,15) (10,13) (10,12) (10,14) (11,16) (11,15) (11,13) (11,12) (11,14) (12,16) (12,15) (12,13) (12,14) (13,16) (13,15) (13,14) (14,16) (14,15) (15,16)\nQ: Is there a path between node 10 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "83"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,4) (0,11) (0,13) (1,8) (1,21) (1,10) (1,7) (1,2) (2,24) (2,8) (2,9) (2,10) (2,22) (3,5) (3,11) (3,13) (4,15) (4,6) (4,16) (4,11) (5,12) (5,15) (5,19) (5,18) (5,27) (6,19) (6,11) (7,26) (7,23) (7,9) (8,23) (8,9) (8,10) (8,22) (9,25) (9,14) (10,25) (10,17) (10,23) (11,20) (11,27) (12,15) (12,16) (12,18) (14,22) (15,19) (15,27) (16,19) (17,26) (17,24) (17,28) (17,23) (17,22) (19,20) (19,27) (21,26) (21,25) (21,29) (21,22) (22,29) (23,24) (23,29) (26,28)\nQ: Is there a path between node 8 and node 18?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "84"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,16) (0,22) (0,4) (0,15) (0,9) (1,8) (1,17) (1,12) (1,3) (1,5) (1,21) (1,6) (1,13) (1,19) (2,20) (2,16) (2,22) (2,4) (2,9) (3,8) (3,17) (3,14) (3,6) (3,10) (3,19) (4,20) (4,16) (4,22) (4,15) (4,9) (5,8) (5,17) (5,12) (5,14) (5,13) (5,10) (5,19) (6,17) (6,12) (6,14) (6,21) (6,13) (6,10) (6,19) (8,17) (8,12) (8,13) (8,19) (9,20) (9,22) (9,15) (10,17) (10,14) (10,21) (11,18) (11,23) (12,17) (12,21) (12,13) (12,19) (13,17) (13,14) (13,21) (15,20) (16,22) (17,21) (18,23)\nQ: Is there a path between node 21 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "85"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,10) (0,26) (0,13) (0,23) (0,14) (0,27) (0,30) (0,31) (0,28) (0,2) (0,8) (0,12) (0,9) (0,24) (0,5) (1,19) (1,15) (1,6) (1,11) (1,29) (1,17) (1,21) (1,4) (1,25) (1,7) (2,3) (2,14) (2,31) (2,28) (2,18) (2,8) (2,12) (2,9) (2,24) (2,5) (3,10) (3,13) (3,23) (3,27) (3,30) (3,31) (3,28) (3,18) (3,8) (3,12) (3,9) (3,24) (3,5) (4,20) (4,19) (4,15) (4,11) (4,29) (4,16) (4,22) (4,7) (5,10) (5,13) (5,23) (5,14) (5,27) (5,31) (5,18) (5,8) (5,12) (5,9) (6,20) (6,15) (6,11) (6,29) (6,17) (6,21) (6,16) (6,25) (6,7) (7,20) (7,15) (7,11) (7,29) (7,17) (7,21) (7,25) (8,10) (8,26) (8,13) (8,23) (8,14) (8,27) (8,30) (8,12) (8,24) (9,10) (9,26) (9,13) (9,14) (9,27) (9,30) (9,31) (9,18) (9,24) (10,26) (10,13) (10,23) (10,14) (10,27) (10,30) (10,31) (10,18) (11,20) (11,19) (11,15) (11,29) (11,17) (11,21) (11,16) (11,25) (11,22) (12,13) (12,23) (12,14) (12,27) (12,28) (13,26) (13,23) (13,14) (13,27) (13,31) (13,28) (14,23) (14,30) (14,28) (14,18) (14,24) (15,19) (15,29) (15,21) (15,16) (15,22) (16,20) (16,19) (16,29) (16,17) (16,21) (16,25) (17,20) (17,19) (17,29) (17,21) (17,25) (17,22) (18,26) (18,27) (18,30) (18,31) (18,28) (19,29) (19,21) (19,25) (19,22) (20,29) (20,22) (21,29) (21,25) (21,22) (22,25) (23,26) (23,27) (23,30) (23,31) (23,24) (24,27) (24,30) (24,31) (25,29) (26,27) (26,30) (26,28) (27,30) (27,31) (28,30) (28,31) (30,31)\nQ: Is there a path between node 2 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "86"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,8) (0,5) (0,4) (0,25) (0,22) (0,16) (0,24) (0,21) (2,15) (2,23) (2,26) (2,10) (2,3) (2,11) (2,6) (2,27) (3,15) (3,23) (3,14) (3,26) (3,10) (3,11) (3,27) (4,8) (4,13) (4,5) (4,20) (4,18) (4,7) (4,22) (4,16) (4,24) (5,8) (5,13) (5,20) (5,7) (5,22) (5,24) (5,21) (6,15) (6,23) (6,14) (6,26) (6,10) (6,11) (6,27) (7,12) (7,20) (7,25) (7,16) (7,21) (8,12) (8,20) (8,25) (8,16) (8,24) (10,15) (10,23) (10,14) (10,26) (10,19) (10,11) (10,27) (11,15) (11,23) (11,26) (11,27) (12,16) (12,24) (12,21) (13,20) (13,18) (13,25) (13,22) (13,16) (13,24) (13,21) (14,15) (14,26) (15,26) (15,27) (16,22) (16,24) (16,21) (18,25) (18,22) (18,21) (19,23) (19,26) (19,27) (20,25) (20,24) (21,25) (21,24) (22,25) (22,24) (23,26) (23,27) (24,25) (26,27)\nQ: Is there a path between node 9 and node 20?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "87"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,3) (0,13) (0,15) (0,7) (1,4) (1,6) (2,9) (2,18) (2,13) (3,12) (4,11) (6,8) (6,17) (7,16) (7,12) (7,13) (7,14) (8,11) (8,17) (8,20) (9,18) (9,21) (9,14) (9,15) (10,12) (12,16) (12,15) (13,18) (13,15) (14,16) (14,21) (15,16) (15,18) (16,18)\nQ: Is there a path between node 19 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "88"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,8) (0,11) (0,17) (0,1) (0,2) (0,12) (0,6) (0,18) (0,7) (0,15) (1,19) (1,8) (1,9) (1,11) (1,2) (1,12) (1,6) (1,7) (1,15) (2,19) (2,4) (2,9) (2,11) (2,17) (2,12) (2,6) (2,18) (2,15) (3,5) (3,13) (3,10) (4,19) (4,8) (4,9) (4,11) (4,17) (4,12) (4,6) (4,7) (4,15) (5,13) (5,10) (6,9) (6,11) (6,12) (6,18) (7,19) (7,8) (7,9) (7,11) (7,17) (7,15) (8,19) (8,11) (8,17) (8,12) (9,17) (9,12) (9,18) (10,13) (11,17) (11,15) (12,19) (12,17) (12,18) (12,15) (14,20) (14,21) (15,17) (15,18) (17,19) (17,18) (18,19) (20,21)\nQ: Is there a path between node 6 and node 19?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "89"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,10) (0,25) (0,16) (0,24) (0,4) (0,8) (0,27) (0,19) (1,5) (1,28) (2,15) (3,12) (3,13) (3,21) (3,24) (3,4) (3,8) (4,26) (4,20) (4,21) (4,11) (4,9) (6,13) (6,14) (6,22) (6,21) (6,7) (6,23) (6,11) (7,12) (7,26) (7,20) (7,17) (7,14) (7,10) (7,25) (7,24) (7,8) (7,11) (7,19) (7,9) (8,25) (8,27) (8,11) (9,17) (9,14) (9,21) (9,23) (9,27) (9,11) (10,26) (10,20) (10,14) (10,25) (10,23) (10,24) (11,13) (11,17) (11,21) (11,25) (11,23) (11,19) (12,20) (12,17) (12,24) (13,26) (13,20) (13,17) (13,22) (13,25) (13,24) (13,19) (14,20) (14,16) (15,28) (15,18) (16,26) (16,21) (16,23) (17,26) (17,22) (17,23) (17,27) (18,28) (19,22) (20,23) (20,24) (20,27) (21,26) (21,27) (23,25) (24,25) (24,27) (25,27)\nQ: Is there a path between node 28 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "90"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,10) (0,26) (0,13) (0,23) (0,14) (0,27) (0,30) (0,31) (0,28) (0,2) (0,8) (0,12) (0,9) (0,24) (0,5) (1,19) (1,15) (1,6) (1,11) (1,29) (1,17) (1,21) (1,4) (1,25) (1,7) (2,3) (2,14) (2,31) (2,28) (2,18) (2,8) (2,12) (2,9) (2,24) (2,5) (3,10) (3,13) (3,23) (3,27) (3,30) (3,31) (3,28) (3,18) (3,8) (3,12) (3,9) (3,24) (3,5) (4,20) (4,19) (4,15) (4,11) (4,29) (4,16) (4,22) (4,7) (5,10) (5,13) (5,23) (5,14) (5,27) (5,31) (5,18) (5,8) (5,12) (5,9) (6,20) (6,15) (6,11) (6,29) (6,17) (6,21) (6,16) (6,25) (6,7) (7,20) (7,15) (7,11) (7,29) (7,17) (7,21) (7,25) (8,10) (8,26) (8,13) (8,23) (8,14) (8,27) (8,30) (8,12) (8,24) (9,10) (9,26) (9,13) (9,14) (9,27) (9,30) (9,31) (9,18) (9,24) (10,26) (10,13) (10,23) (10,14) (10,27) (10,30) (10,31) (10,18) (11,20) (11,19) (11,15) (11,29) (11,17) (11,21) (11,16) (11,25) (11,22) (12,13) (12,23) (12,14) (12,27) (12,28) (13,26) (13,23) (13,14) (13,27) (13,31) (13,28) (14,23) (14,30) (14,28) (14,18) (14,24) (15,19) (15,29) (15,21) (15,16) (15,22) (16,20) (16,19) (16,29) (16,17) (16,21) (16,25) (17,20) (17,19) (17,29) (17,21) (17,25) (17,22) (18,26) (18,27) (18,30) (18,31) (18,28) (19,29) (19,21) (19,25) (19,22) (20,29) (20,22) (21,29) (21,25) (21,22) (22,25) (23,26) (23,27) (23,30) (23,31) (23,24) (24,27) (24,30) (24,31) (25,29) (26,27) (26,30) (26,28) (27,30) (27,31) (28,30) (28,31) (30,31)\nQ: Is there a path between node 30 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "91"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (1,8) (1,4) (1,5) (1,7) (1,2) (1,9) (1,6) (2,8) (2,4) (2,5) (2,7) (2,9) (2,6) (4,8) (4,5) (4,7) (4,9) (4,6) (5,8) (5,7) (5,9) (5,6) (6,8) (6,7) (6,9) (7,8) (7,9) (8,9)\nQ: Is there a path between node 5 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "92"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,10) (0,19) (0,16) (0,7) (0,8) (0,4) (0,3) (0,11) (0,1) (0,18) (0,9) (0,5) (0,2) (0,13) (1,17) (1,10) (1,19) (1,16) (1,7) (1,8) (1,4) (1,3) (1,11) (1,18) (1,9) (1,5) (1,2) (1,13) (2,17) (2,10) (2,19) (2,16) (2,7) (2,8) (2,4) (2,3) (2,11) (2,18) (2,9) (2,5) (2,13) (3,17) (3,10) (3,19) (3,16) (3,7) (3,8) (3,4) (3,11) (3,18) (3,9) (3,5) (3,13) (4,17) (4,10) (4,19) (4,16) (4,7) (4,8) (4,11) (4,18) (4,9) (4,5) (4,13) (5,17) (5,10) (5,19) (5,16) (5,7) (5,8) (5,11) (5,18) (5,9) (5,13) (6,15) (7,17) (7,10) (7,19) (7,16) (7,8) (7,11) (7,18) (7,9) (7,13) (8,17) (8,10) (8,19) (8,16) (8,11) (8,18) (8,9) (8,13) (9,17) (9,10) (9,19) (9,16) (9,11) (9,18) (9,13) (10,17) (10,19) (10,16) (10,11) (10,18) (10,13) (11,17) (11,19) (11,16) (11,18) (11,13) (12,14) (13,17) (13,19) (13,16) (13,18) (16,17) (16,19) (16,18) (17,19) (17,18) (18,19)\nQ: Is there a path between node 18 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "93"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,12) (0,11) (0,8) (0,1) (0,13) (0,10) (0,3) (1,2) (1,5) (1,12) (1,11) (1,8) (1,13) (1,10) (1,3) (2,5) (2,12) (2,11) (2,8) (2,13) (2,10) (2,3) (3,5) (3,12) (3,11) (3,8) (3,13) (3,10) (4,9) (4,6) (4,7) (4,14) (5,12) (5,11) (5,8) (5,13) (5,10) (6,9) (6,7) (6,14) (7,9) (7,14) (8,12) (8,11) (8,13) (8,10) (9,14) (10,12) (10,11) (10,13) (11,12) (11,13) (12,13)\nQ: Is there a path between node 2 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "94"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,1) (0,12) (0,4) (1,13) (1,3) (1,6) (1,9) (2,15) (2,14) (2,11) (4,7) (5,16) (5,6) (5,9) (6,13) (6,8) (10,13) (10,12) (11,15) (11,14)\nQ: Is there a path between node 6 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "95"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,17) (0,10) (0,28) (0,30) (0,29) (0,3) (1,14) (1,2) (2,25) (2,20) (2,7) (2,32) (2,22) (3,24) (3,19) (3,23) (3,4) (3,12) (3,29) (4,26) (4,24) (4,23) (4,8) (4,13) (5,26) (5,19) (5,23) (5,8) (5,15) (5,21) (6,14) (7,32) (8,16) (8,12) (8,29) (9,26) (9,13) (9,18) (9,29) (9,31) (10,17) (10,11) (10,30) (10,23) (10,13) (11,16) (11,17) (11,19) (11,28) (11,23) (12,26) (12,24) (12,21) (13,26) (13,17) (13,19) (13,30) (13,31) (14,25) (14,22) (15,16) (15,17) (15,23) (15,18) (15,29) (16,26) (16,24) (16,18) (16,21) (17,24) (17,19) (17,28) (17,30) (17,23) (18,24) (18,21) (19,26) (19,24) (19,28) (19,23) (20,32) (22,32) (22,27) (24,26) (24,30) (26,29) (28,29)\nQ: Is there a path between node 1 and node 26?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "96"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,3) (0,2) (1,5) (1,3) (2,5) (2,3) (3,5)\nQ: Is there a path between node 3 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "97"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,13) (0,17) (0,10) (0,5) (0,4) (0,16) (0,19) (0,20) (0,7) (0,8) (0,15) (0,1) (0,18) (0,9) (0,12) (1,13) (1,17) (1,10) (1,5) (1,4) (1,16) (1,19) (1,20) (1,7) (1,8) (1,15) (1,18) (1,9) (1,12) (2,11) (2,21) (2,3) (2,14) (3,11) (3,21) (3,14) (4,13) (4,17) (4,10) (4,5) (4,16) (4,19) (4,20) (4,7) (4,8) (4,15) (4,18) (4,9) (4,12) (5,13) (5,17) (5,10) (5,16) (5,19) (5,20) (5,7) (5,8) (5,15) (5,18) (5,9) (5,12) (7,13) (7,17) (7,10) (7,16) (7,19) (7,20) (7,8) (7,15) (7,18) (7,9) (7,12) (8,13) (8,17) (8,10) (8,16) (8,19) (8,20) (8,15) (8,18) (8,9) (8,12) (9,13) (9,17) (9,10) (9,16) (9,19) (9,20) (9,15) (9,18) (9,12) (10,13) (10,17) (10,16) (10,19) (10,20) (10,15) (10,18) (10,12) (11,21) (11,14) (12,13) (12,17) (12,16) (12,19) (12,20) (12,15) (12,18) (13,17) (13,16) (13,19) (13,20) (13,15) (13,18) (14,21) (15,17) (15,16) (15,19) (15,20) (15,18) (16,17) (16,19) (16,20) (16,18) (17,19) (17,20) (17,18) (18,19) (18,20) (19,20)\nQ: Is there a path between node 9 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "98"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,5) (0,7) (0,2) (0,8) (0,4) (0,9) (0,1) (0,12) (0,3) (0,11) (0,13) (1,10) (1,5) (1,7) (1,2) (1,8) (1,4) (1,9) (1,12) (1,3) (1,11) (1,13) (2,10) (2,5) (2,7) (2,8) (2,4) (2,9) (2,12) (2,3) (2,11) (2,13) (3,10) (3,5) (3,7) (3,8) (3,4) (3,9) (3,12) (3,11) (3,13) (4,10) (4,5) (4,7) (4,8) (4,9) (4,12) (4,11) (4,13) (5,10) (5,7) (5,8) (5,9) (5,12) (5,11) (5,13) (7,10) (7,8) (7,9) (7,12) (7,11) (7,13) (8,10) (8,9) (8,12) (8,11) (8,13) (9,10) (9,12) (9,11) (9,13) (10,12) (10,11) (10,13) (11,12) (11,13) (12,13)\nQ: Is there a path between node 6 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "99"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,12) (0,1) (0,13) (0,14) (0,11) (0,20) (0,7) (0,21) (1,4) (1,13) (1,14) (1,16) (1,7) (1,21) (2,5) (2,22) (2,8) (2,15) (2,25) (2,9) (2,17) (2,26) (3,11) (3,20) (3,7) (4,13) (4,14) (4,11) (4,20) (4,21) (5,22) (5,18) (5,15) (5,23) (5,25) (5,17) (5,26) (5,24) (6,19) (7,12) (7,13) (7,14) (7,11) (7,20) (7,21) (8,22) (8,15) (8,23) (8,9) (8,17) (8,24) (9,18) (9,15) (9,23) (9,25) (9,17) (11,13) (11,14) (11,16) (11,20) (12,13) (12,14) (12,16) (12,20) (12,21) (13,16) (13,20) (14,16) (14,20) (14,21) (15,22) (15,18) (15,23) (15,25) (15,26) (15,24) (16,21) (17,22) (17,18) (17,23) (17,25) (18,25) (18,24) (20,21) (22,23) (22,25) (22,26) (22,24) (23,26) (23,24) (24,25) (25,26)\nQ: Is there a path between node 16 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "100"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,4) (0,1) (1,2) (1,5) (1,4) (2,5) (2,4) (4,5)\nQ: Is there a path between node 1 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "101"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,7) (0,12) (0,32) (0,22) (0,9) (0,20) (0,2) (0,5) (0,14) (0,4) (0,26) (0,21) (1,11) (1,8) (1,24) (1,3) (1,31) (1,28) (1,6) (2,16) (2,7) (2,32) (2,22) (2,9) (2,20) (2,14) (2,4) (2,21) (3,11) (3,8) (3,24) (3,31) (3,28) (4,16) (4,32) (4,22) (4,9) (4,20) (4,5) (4,14) (4,26) (5,16) (5,7) (5,12) (5,32) (5,22) (5,9) (5,20) (5,14) (5,26) (5,21) (6,8) (6,24) (6,31) (6,28) (7,12) (7,32) (7,22) (7,9) (7,14) (7,26) (7,21) (8,24) (8,31) (8,28) (9,16) (9,12) (9,32) (9,20) (9,26) (9,21) (10,23) (10,13) (10,29) (10,19) (10,25) (10,18) (12,32) (12,22) (12,20) (12,26) (12,21) (13,30) (13,27) (13,29) (13,19) (13,25) (13,18) (14,16) (14,32) (14,22) (14,20) (14,26) (15,30) (15,29) (15,25) (15,18) (16,32) (16,22) (16,20) (16,26) (16,21) (17,30) (17,27) (18,30) (18,29) (19,30) (19,23) (19,27) (19,25) (20,32) (20,22) (20,26) (21,32) (21,26) (22,32) (22,26) (23,30) (23,29) (23,25) (24,28) (26,32) (27,30) (27,29) (28,31) (29,30)\nQ: Is there a path between node 7 and node 18?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "102"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,3) (0,2) (1,5) (1,3) (2,5) (2,3) (3,5)\nQ: Is there a path between node 2 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "103"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,11) (0,1) (0,3) (0,10) (0,4) (1,11) (1,3) (1,10) (1,4) (2,7) (3,11) (3,4) (4,5) (4,11) (5,11) (6,9) (6,8) (7,9) (7,8) (8,9) (10,11)\nQ: Is there a path between node 10 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "104"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "105"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,1) (0,2) (0,7) (0,6) (1,2) (1,8) (1,7) (1,4) (1,6) (2,7) (2,4) (2,6) (3,5) (4,9) (4,8) (4,7) (6,9) (6,7) (7,8)\nQ: Is there a path between node 5 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "106"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,8) (0,18) (0,6) (0,1) (0,12) (0,3) (0,7) (0,14) (0,10) (0,19) (0,16) (0,13) (1,17) (1,8) (1,18) (1,2) (1,19) (2,8) (2,6) (2,20) (2,14) (3,17) (3,18) (3,6) (3,14) (3,10) (3,19) (4,17) (4,18) (4,6) (4,19) (4,13) (5,15) (6,17) (6,8) (6,18) (6,13) (7,17) (7,14) (7,10) (8,20) (9,15) (9,11) (10,17) (10,18) (11,15) (12,17) (12,18) (12,14) (12,19) (13,17) (13,18) (13,20) (14,17) (14,18) (14,20) (18,20) (19,20)\nQ: Is there a path between node 1 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "107"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,21) (0,7) (0,6) (0,3) (0,17) (0,20) (0,22) (0,16) (0,23) (0,25) (0,27) (1,5) (1,21) (1,4) (1,7) (1,15) (1,18) (1,2) (1,24) (1,20) (1,11) (1,16) (1,25) (1,27) (2,14) (2,5) (2,21) (2,4) (2,15) (2,24) (2,22) (2,11) (2,23) (2,25) (2,27) (3,14) (3,13) (3,21) (3,7) (3,15) (3,6) (3,17) (3,24) (3,22) (3,11) (3,16) (3,23) (4,14) (4,13) (4,5) (4,19) (4,7) (4,18) (4,17) (4,22) (4,11) (4,23) (4,25) (4,27) (5,13) (5,19) (5,15) (5,18) (5,24) (5,20) (5,22) (5,11) (5,23) (5,27) (6,14) (6,21) (6,19) (6,7) (6,15) (6,18) (6,17) (6,24) (6,20) (6,11) (6,16) (6,25) (6,27) (7,14) (7,13) (7,21) (7,19) (7,15) (7,18) (7,17) (7,20) (7,22) (7,11) (7,23) (7,27) (8,30) (8,28) (9,31) (9,10) (9,26) (9,29) (10,31) (10,26) (10,29) (11,13) (11,21) (11,19) (11,15) (11,24) (11,22) (11,25) (11,27) (12,28) (13,14) (13,21) (13,15) (13,18) (13,17) (13,24) (13,20) (13,16) (13,23) (13,25) (13,27) (14,21) (14,19) (14,24) (14,20) (14,22) (14,16) (14,23) (14,25) (15,21) (15,18) (15,17) (15,24) (15,20) (15,22) (15,16) (15,25) (15,27) (16,21) (16,18) (16,17) (16,24) (16,20) (16,22) (16,25) (17,21) (17,19) (17,18) (17,24) (17,20) (17,22) (17,23) (17,25) (17,27) (18,21) (18,24) (18,20) (18,25) (18,27) (19,21) (19,20) (19,22) (19,27) (20,21) (20,24) (20,22) (20,23) (20,27) (21,24) (21,22) (21,25) (21,27) (22,25) (23,25) (23,27) (25,27) (26,31) (26,29) (29,31)\nQ: Is there a path between node 11 and node 22?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "108"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (1,3) (1,2) (1,6) (2,5) (2,6) (3,5) (5,6)\nQ: Is there a path between node 0 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "109"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,11) (0,2) (0,7) (0,8) (0,16) (0,15) (1,11) (1,2) (1,7) (1,8) (1,16) (1,15) (1,14) (2,4) (2,11) (2,5) (2,7) (2,12) (2,16) (2,15) (3,13) (3,10) (4,6) (4,5) (4,7) (4,8) (4,12) (4,16) (4,15) (4,14) (5,6) (5,7) (5,8) (5,12) (5,16) (5,14) (6,11) (6,7) (6,8) (6,12) (6,16) (6,15) (6,14) (7,11) (7,8) (7,16) (7,14) (8,11) (8,12) (8,16) (11,12) (11,16) (11,15) (11,14) (12,14) (14,16) (14,15)\nQ: Is there a path between node 0 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "110"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (0,13) (0,22) (1,12) (1,6) (2,20) (2,14) (2,11) (3,5) (3,23) (3,6) (5,17) (6,19) (7,23) (8,13) (8,15) (9,21) (9,18) (12,24) (12,17) (12,19) (13,21) (13,18) (13,25) (13,15) (13,16) (15,16) (16,21) (16,25) (17,23) (17,19) (19,26) (21,22) (22,25)\nQ: Is there a path between node 15 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "111"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,21) (1,17) (1,15) (1,2) (1,4) (1,18) (2,8) (2,13) (2,17) (2,15) (2,23) (2,22) (2,4) (2,18) (2,12) (4,21) (4,8) (4,13) (4,15) (4,23) (4,22) (4,18) (4,12) (5,21) (5,8) (5,13) (5,17) (5,15) (5,22) (5,18) (7,14) (7,16) (7,10) (7,11) (7,19) (8,21) (8,17) (8,23) (8,18) (9,14) (9,24) (10,14) (10,24) (10,19) (11,14) (11,16) (11,24) (12,21) (12,13) (12,17) (12,15) (12,23) (12,22) (12,18) (13,21) (13,17) (13,15) (13,23) (13,22) (14,24) (15,21) (15,17) (15,23) (15,22) (15,18) (16,19) (17,21) (17,18) (18,21) (18,23) (21,22) (22,23)\nQ: Is there a path between node 15 and node 17?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "112"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,7) (0,10) (0,6) (0,2) (0,8) (0,4) (0,1) (1,3) (1,7) (1,10) (1,6) (1,2) (1,8) (1,4) (2,3) (2,7) (2,10) (2,6) (2,8) (2,4) (3,7) (3,10) (3,6) (3,8) (3,4) (4,7) (4,10) (4,6) (4,8) (5,9) (6,7) (6,10) (6,8) (7,10) (7,8) (8,10)\nQ: Is there a path between node 4 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "113"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (2,8) (2,4) (2,3) (3,8) (5,7) (6,7)\nQ: Is there a path between node 7 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "114"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,2) (2,3)\nQ: Is there a path between node 4 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "115"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,18) (0,1) (0,8) (0,10) (0,11) (0,7) (0,4) (0,2) (0,6) (0,17) (0,14) (1,19) (1,18) (1,8) (1,10) (1,11) (1,7) (1,4) (1,2) (1,6) (1,17) (1,14) (2,19) (2,18) (2,8) (2,10) (2,11) (2,7) (2,4) (2,6) (2,17) (2,14) (3,13) (3,9) (3,15) (4,19) (4,18) (4,8) (4,10) (4,11) (4,7) (4,6) (4,17) (4,14) (5,12) (5,16) (6,19) (6,18) (6,8) (6,10) (6,11) (6,7) (6,17) (6,14) (7,19) (7,18) (7,8) (7,10) (7,11) (7,17) (7,14) (8,19) (8,18) (8,10) (8,11) (8,17) (8,14) (9,13) (9,15) (10,19) (10,18) (10,11) (10,17) (10,14) (11,19) (11,18) (11,17) (11,14) (12,16) (13,15) (14,19) (14,18) (14,17) (17,19) (17,18) (18,19)\nQ: Is there a path between node 14 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "116"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (1,27) (1,24) (1,21) (1,3) (2,10) (2,22) (2,6) (2,18) (2,25) (2,12) (3,19) (3,27) (3,24) (4,10) (4,6) (4,18) (4,25) (5,28) (5,16) (6,10) (6,13) (6,25) (6,12) (6,9) (7,28) (8,10) (8,14) (8,18) (8,29) (8,25) (8,23) (9,13) (9,14) (10,29) (10,25) (12,22) (12,18) (12,17) (13,29) (13,26) (14,20) (14,17) (15,19) (17,25) (18,20) (18,25) (20,29) (20,26) (20,23) (21,27) (21,24) (23,26) (23,25) (24,27) (26,29)\nQ: Is there a path between node 23 and node 18?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "117"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,20) (0,27) (0,29) (0,26) (0,17) (0,3) (0,1) (0,16) (1,6) (1,7) (1,20) (1,19) (1,3) (1,33) (1,4) (2,27) (2,34) (2,26) (2,19) (2,17) (2,3) (2,21) (2,4) (3,6) (3,7) (3,11) (3,28) (3,29) (4,6) (4,28) (4,27) (4,29) (4,26) (4,19) (4,33) (4,23) (5,7) (5,11) (5,28) (5,19) (5,33) (5,16) (6,7) (6,28) (6,27) (6,26) (6,21) (7,34) (8,13) (8,12) (8,22) (8,15) (9,24) (9,12) (9,10) (10,25) (11,16) (11,23) (12,32) (12,18) (12,22) (12,15) (13,14) (14,18) (14,15) (15,30) (15,18) (16,27) (16,17) (16,23) (17,29) (17,19) (17,33) (17,23) (18,31) (18,24) (19,28) (19,27) (19,34) (19,29) (19,33) (19,21) (20,21) (21,26) (21,33) (22,30) (22,25) (25,30) (25,31) (26,28) (26,34) (26,29) (27,28) (30,32) (31,32)\nQ: Is there a path between node 17 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "118"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (0,3) (0,4) (0,1) (1,2) (1,5) (1,6) (1,3) (1,4) (2,5) (2,6) (2,3) (2,4) (3,5) (3,6) (3,4) (4,5) (4,6) (5,6)\nQ: Is there a path between node 2 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "119"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,1) (3,4)\nQ: Is there a path between node 1 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "120"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,3) (0,5) (1,2) (1,10) (1,3) (1,5) (2,6) (2,10) (3,17) (3,14) (3,6) (3,9) (4,14) (4,7) (4,9) (5,17) (5,14) (5,6) (5,10) (5,7) (6,14) (6,16) (6,7) (9,17) (9,16) (9,10) (10,14) (11,15) (12,13) (14,17) (14,16) (14,15) (15,17)\nQ: Is there a path between node 4 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "121"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,18) (1,12) (1,15) (1,7) (2,17) (2,3) (3,17) (4,12) (5,17) (5,19) (6,18) (6,10) (6,9) (6,12) (6,16) (7,18) (7,9) (7,13) (7,8) (8,14) (9,18) (9,14) (9,12) (9,13) (10,12) (10,15) (11,17) (12,16) (14,18)\nQ: Is there a path between node 11 and node 14?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "122"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,21) (0,11) (0,15) (0,4) (0,22) (0,5) (0,3) (0,6) (0,20) (0,13) (0,18) (0,9) (0,1) (0,12) (0,24) (0,16) (0,8) (0,23) (0,2) (1,21) (1,11) (1,15) (1,4) (1,22) (1,5) (1,3) (1,6) (1,20) (1,13) (1,18) (1,9) (1,12) (1,24) (1,16) (1,8) (1,23) (1,2) (2,21) (2,11) (2,15) (2,4) (2,22) (2,5) (2,3) (2,6) (2,20) (2,13) (2,18) (2,9) (2,12) (2,24) (2,16) (2,8) (2,23) (3,21) (3,11) (3,15) (3,4) (3,22) (3,5) (3,6) (3,20) (3,13) (3,18) (3,9) (3,12) (3,24) (3,16) (3,8) (3,23) (4,21) (4,11) (4,15) (4,22) (4,5) (4,6) (4,20) (4,13) (4,18) (4,9) (4,12) (4,24) (4,16) (4,8) (4,23) (5,21) (5,11) (5,15) (5,22) (5,6) (5,20) (5,13) (5,18) (5,9) (5,12) (5,24) (5,16) (5,8) (5,23) (6,21) (6,11) (6,15) (6,22) (6,20) (6,13) (6,18) (6,9) (6,12) (6,24) (6,16) (6,8) (6,23) (7,10) (7,14) (7,17) (7,19) (8,21) (8,11) (8,15) (8,22) (8,20) (8,13) (8,18) (8,9) (8,12) (8,24) (8,16) (8,23) (9,21) (9,11) (9,15) (9,22) (9,20) (9,13) (9,18) (9,12) (9,24) (9,16) (9,23) (10,14) (10,17) (10,19) (11,21) (11,15) (11,22) (11,20) (11,13) (11,18) (11,12) (11,24) (11,16) (11,23) (12,21) (12,15) (12,22) (12,20) (12,13) (12,18) (12,24) (12,16) (12,23) (13,21) (13,15) (13,22) (13,20) (13,18) (13,24) (13,16) (13,23) (14,17) (14,19) (15,21) (15,22) (15,20) (15,18) (15,24) (15,16) (15,23) (16,21) (16,22) (16,20) (16,18) (16,24) (16,23) (17,19) (18,21) (18,22) (18,20) (18,24) (18,23) (20,21) (20,22) (20,24) (20,23) (21,22) (21,24) (21,23) (22,24) (22,23) (23,24)\nQ: Is there a path between node 1 and node 19?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "123"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,10) (0,18) (0,21) (0,30) (0,28) (0,15) (1,27) (1,24) (1,22) (1,32) (1,14) (1,5) (2,29) (2,10) (2,18) (2,21) (2,19) (2,30) (2,16) (2,28) (2,15) (3,24) (3,13) (3,22) (3,20) (3,5) (4,17) (4,11) (4,6) (4,26) (4,23) (4,31) (4,25) (5,27) (5,13) (5,22) (5,20) (5,32) (5,14) (6,17) (6,9) (6,23) (6,31) (6,25) (7,29) (7,10) (7,18) (7,19) (7,30) (7,16) (7,15) (8,17) (8,11) (8,26) (8,23) (8,31) (9,17) (9,26) (9,23) (9,31) (9,25) (10,29) (10,18) (10,21) (10,30) (10,28) (10,15) (11,17) (11,26) (11,23) (12,27) (12,24) (12,13) (12,22) (12,32) (13,27) (13,24) (13,22) (13,20) (13,32) (13,14) (14,27) (14,22) (14,32) (15,29) (15,18) (15,21) (15,19) (15,28) (16,29) (16,21) (16,19) (16,28) (17,23) (18,29) (18,21) (18,30) (18,28) (19,29) (19,21) (19,30) (19,28) (20,24) (20,22) (20,32) (21,29) (21,30) (21,28) (22,27) (22,24) (22,32) (23,31) (24,27) (25,26) (26,31) (28,30)\nQ: Is there a path between node 14 and node 27?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "124"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (1,17) (2,9) (3,16) (5,18) (5,11) (5,21) (6,21) (6,15) (7,19) (7,21) (8,10) (8,12) (8,16) (10,16) (14,23) (15,21) (16,19) (17,20) (18,19) (20,23)\nQ: Is there a path between node 14 and node 21?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "125"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,26) (2,26) (2,30) (2,6) (3,19) (4,29) (4,8) (4,11) (4,9) (5,25) (6,30) (6,19) (6,13) (6,25) (7,23) (7,29) (7,10) (7,28) (7,14) (8,23) (8,15) (8,27) (8,18) (8,11) (8,28) (8,9) (9,23) (9,29) (9,15) (9,18) (9,12) (10,15) (11,29) (11,27) (11,28) (11,14) (12,27) (13,16) (13,26) (14,17) (15,29) (15,21) (15,28) (16,25) (17,23) (17,29) (17,18) (19,20) (19,22) (20,22) (21,27) (21,28) (22,26) (23,29) (23,28) (24,26) (24,30) (25,26) (25,30) (27,28)\nQ: Is there a path between node 14 and node 20?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "126"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,2) (0,14) (0,7) (0,13) (1,17) (1,3) (1,10) (1,6) (2,11) (2,12) (2,14) (2,13) (3,17) (3,10) (3,6) (4,9) (4,5) (5,9) (5,16) (6,17) (6,8) (6,10) (7,11) (7,12) (7,14) (7,13) (8,17) (8,15) (9,18) (9,16) (10,17) (12,14) (12,13) (13,14) (15,17)\nQ: Is there a path between node 12 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "127"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (0,1) (0,19) (0,15) (0,20) (0,9) (0,21) (0,3) (0,22) (0,32) (0,24) (0,14) (0,11) (0,17) (0,5) (0,34) (0,4) (0,26) (0,10) (0,8) (1,27) (1,23) (1,30) (1,6) (1,19) (1,20) (1,2) (1,9) (1,21) (1,3) (1,22) (1,24) (1,14) (1,11) (1,17) (1,5) (1,4) (1,26) (1,8) (2,27) (2,30) (2,6) (2,19) (2,20) (2,9) (2,21) (2,3) (2,22) (2,32) (2,7) (2,11) (2,17) (2,5) (2,34) (2,4) (2,26) (2,12) (2,10) (3,27) (3,23) (3,30) (3,6) (3,19) (3,15) (3,20) (3,9) (3,22) (3,24) (3,14) (3,34) (3,4) (3,12) (3,10) (3,8) (3,28) (4,27) (4,23) (4,30) (4,19) (4,15) (4,20) (4,9) (4,21) (4,32) (4,24) (4,14) (4,7) (4,11) (4,17) (4,5) (4,26) (4,12) (4,8) (4,28) (5,30) (5,19) (5,9) (5,21) (5,24) (5,7) (5,11) (5,17) (5,34) (5,12) (6,27) (6,23) (6,30) (6,19) (6,20) (6,9) (6,21) (6,22) (6,32) (6,24) (6,14) (6,7) (6,11) (6,17) (6,34) (6,26) (6,8) (6,28) (7,23) (7,30) (7,19) (7,15) (7,20) (7,21) (7,32) (7,24) (7,11) (7,17) (7,34) (7,12) (7,10) (7,8) (7,28) (8,23) (8,15) (8,20) (8,24) (8,14) (8,11) (8,17) (8,34) (8,26) (8,12) (8,10) (8,28) (9,30) (9,19) (9,15) (9,20) (9,22) (9,32) (9,24) (9,11) (9,34) (9,12) (9,10) (9,28) (10,27) (10,23) (10,30) (10,19) (10,21) (10,32) (10,24) (10,26) (10,12) (11,27) (11,30) (11,19) (11,20) (11,21) (11,22) (11,32) (11,24) (11,14) (11,17) (11,34) (11,12) (12,27) (12,30) (12,19) (12,20) (12,22) (12,32) (12,24) (12,14) (12,17) (12,34) (12,28) (14,27) (14,23) (14,30) (14,19) (14,15) (14,21) (14,22) (14,32) (14,17) (14,34) (14,28) (15,19) (15,20) (15,21) (15,22) (15,32) (15,24) (15,34) (15,26) (15,28) (16,33) (16,29) (16,18) (16,31) (17,27) (17,23) (17,30) (17,19) (17,20) (17,21) (17,22) (17,32) (17,24) (17,34) (17,28) (18,33) (18,31) (18,25) (19,27) (19,23) (19,30) (19,20) (19,22) (19,32) (19,34) (19,26) (19,28) (20,23) (20,30) (20,21) (20,22) (20,32) (20,24) (20,34) (20,26) (21,27) (21,23) (21,30) (21,22) (21,32) (21,24) (21,34) (21,26) (21,28) (22,27) (22,23) (22,24) (22,34) (22,26) (22,28) (23,32) (23,26) (23,28) (24,27) (24,32) (24,34) (24,26) (25,33) (26,30) (26,32) (26,34) (27,30) (27,32) (27,28) (28,30) (28,32) (28,34) (29,33) (29,31) (31,33) (32,34)\nQ: Is there a path between node 7 and node 21?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "128"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,11) (0,22) (0,30) (0,25) (0,19) (0,12) (0,13) (0,10) (0,29) (1,17) (1,4) (1,18) (1,7) (1,27) (1,2) (1,3) (1,9) (1,23) (1,28) (2,4) (2,21) (2,26) (2,7) (2,27) (2,9) (2,23) (2,28) (3,17) (3,4) (3,21) (3,26) (3,18) (3,7) (3,27) (3,14) (3,9) (3,23) (3,28) (3,24) (4,17) (4,21) (4,26) (4,18) (4,14) (4,9) (4,28) (4,24) (5,11) (5,22) (5,20) (5,25) (5,29) (6,8) (7,21) (7,26) (7,18) (7,27) (7,23) (7,28) (7,24) (9,21) (9,26) (9,18) (9,27) (9,14) (9,23) (9,28) (9,24) (10,11) (10,22) (10,20) (10,30) (10,25) (10,16) (10,19) (10,15) (10,13) (10,29) (11,22) (11,20) (11,30) (11,25) (11,16) (11,19) (11,12) (11,15) (11,13) (11,29) (12,22) (12,20) (12,30) (12,16) (12,15) (12,13) (13,22) (13,20) (13,30) (13,25) (13,16) (13,19) (13,15) (13,29) (14,26) (14,18) (14,23) (14,28) (14,24) (15,22) (15,30) (15,16) (15,19) (15,29) (16,22) (16,30) (16,25) (16,19) (16,29) (17,26) (17,18) (17,27) (17,23) (17,28) (18,21) (18,26) (18,27) (18,24) (19,20) (19,30) (19,25) (19,29) (20,22) (20,25) (20,29) (21,26) (21,27) (21,28) (21,24) (22,30) (22,29) (23,26) (23,27) (23,28) (23,24) (24,27) (24,28) (25,29) (26,27) (27,28) (29,30)\nQ: Is there a path between node 9 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "129"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,3) (0,11) (0,18) (0,7) (0,8) (0,9) (0,1) (0,10) (0,15) (0,17) (0,13) (0,16) (0,19) (0,2) (0,6) (0,5) (0,14) (1,12) (1,3) (1,11) (1,18) (1,7) (1,8) (1,9) (1,10) (1,15) (1,17) (1,13) (1,16) (1,19) (1,2) (1,6) (1,5) (1,14) (2,12) (2,3) (2,11) (2,18) (2,7) (2,8) (2,9) (2,10) (2,15) (2,17) (2,13) (2,16) (2,19) (2,6) (2,5) (2,14) (3,12) (3,11) (3,18) (3,7) (3,8) (3,9) (3,10) (3,15) (3,17) (3,13) (3,16) (3,19) (3,6) (3,5) (3,14) (4,20) (4,21) (5,12) (5,11) (5,18) (5,7) (5,8) (5,9) (5,10) (5,15) (5,17) (5,13) (5,16) (5,19) (5,6) (5,14) (6,12) (6,11) (6,18) (6,7) (6,8) (6,9) (6,10) (6,15) (6,17) (6,13) (6,16) (6,19) (6,14) (7,12) (7,11) (7,18) (7,8) (7,9) (7,10) (7,15) (7,17) (7,13) (7,16) (7,19) (7,14) (8,12) (8,11) (8,18) (8,9) (8,10) (8,15) (8,17) (8,13) (8,16) (8,19) (8,14) (9,12) (9,11) (9,18) (9,10) (9,15) (9,17) (9,13) (9,16) (9,19) (9,14) (10,12) (10,11) (10,18) (10,15) (10,17) (10,13) (10,16) (10,19) (10,14) (11,12) (11,18) (11,15) (11,17) (11,13) (11,16) (11,19) (11,14) (12,18) (12,15) (12,17) (12,13) (12,16) (12,19) (12,14) (13,18) (13,15) (13,17) (13,16) (13,19) (13,14) (14,18) (14,15) (14,17) (14,16) (14,19) (15,18) (15,17) (15,16) (15,19) (16,18) (16,17) (16,19) (17,18) (17,19) (18,19) (20,21)\nQ: Is there a path between node 5 and node 18?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "130"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,7) (0,2) (0,8) (1,6) (2,3) (3,6) (3,7) (4,6) (4,5) (5,8) (7,8)\nQ: Is there a path between node 9 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "131"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,6) (3,4) (4,5) (5,10) (6,8) (8,9)\nQ: Is there a path between node 6 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "132"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,9) (1,8) (1,4) (2,8) (2,4) (2,3) (3,7) (3,6) (3,10) (3,12) (3,11) (4,10) (4,12) (6,14) (6,8) (6,10) (7,14) (7,11) (8,14) (8,12) (10,14) (11,14) (12,14)\nQ: Is there a path between node 1 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "133"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,9) (1,10) (1,3) (2,6) (2,4) (2,7) (3,6) (3,10) (3,9) (3,12) (4,8) (5,9) (5,12) (6,9) (6,12) (6,7) (7,10) (7,9) (7,14) (8,10) (8,9) (8,14) (12,14)\nQ: Is there a path between node 0 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "134"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,1) (3,4)\nQ: Is there a path between node 3 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "135"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,8) (0,2) (0,20) (0,16) (0,14) (0,15) (0,7) (1,18) (1,24) (1,22) (1,5) (1,19) (1,11) (1,17) (2,6) (2,4) (2,23) (2,8) (2,20) (2,16) (2,21) (2,14) (2,15) (2,10) (3,6) (3,4) (3,23) (3,8) (3,16) (3,14) (3,25) (3,15) (3,7) (4,6) (4,23) (4,8) (4,20) (4,16) (4,21) (4,14) (4,15) (4,10) (4,7) (5,18) (5,24) (5,22) (5,13) (5,9) (5,11) (5,12) (6,23) (6,8) (6,20) (6,16) (6,14) (6,25) (6,15) (7,23) (7,20) (7,16) (7,21) (7,14) (7,25) (7,15) (7,10) (8,20) (8,16) (8,14) (8,25) (8,15) (9,18) (9,24) (9,22) (9,19) (9,11) (9,17) (9,12) (10,23) (10,20) (10,16) (10,21) (10,14) (10,25) (11,22) (11,19) (11,17) (11,12) (12,18) (12,13) (12,19) (13,18) (13,24) (13,22) (13,17) (14,23) (14,20) (14,16) (14,25) (15,20) (15,16) (15,21) (15,25) (16,23) (16,20) (16,25) (17,18) (17,22) (17,19) (18,24) (18,22) (18,19) (19,24) (19,22) (20,21) (20,25) (21,23) (21,25) (22,24) (23,25)\nQ: Is there a path between node 13 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "136"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,20) (0,8) (0,31) (0,22) (1,4) (1,24) (1,19) (1,16) (1,5) (1,2) (1,8) (1,18) (1,27) (2,4) (2,19) (2,12) (2,17) (2,21) (2,31) (2,22) (3,25) (3,20) (3,14) (3,31) (3,22) (3,27) (4,7) (4,21) (4,26) (4,27) (5,11) (5,24) (5,20) (5,19) (5,12) (5,16) (5,17) (5,21) (5,9) (5,22) (6,15) (7,24) (7,20) (7,19) (7,16) (7,29) (7,17) (7,21) (7,14) (7,9) (7,8) (7,18) (7,22) (7,30) (8,20) (8,12) (8,14) (9,20) (9,16) (9,14) (9,18) (9,26) (9,23) (10,15) (11,25) (11,28) (11,20) (11,21) (11,26) (12,28) (12,24) (12,20) (12,29) (12,14) (12,18) (12,26) (12,22) (12,27) (12,23) (14,24) (14,16) (14,18) (14,31) (16,25) (16,26) (16,31) (16,23) (17,31) (17,27) (18,25) (18,28) (18,24) (18,21) (18,26) (18,27) (19,29) (19,21) (19,22) (20,25) (20,21) (20,26) (21,24) (21,29) (21,31) (21,23) (22,29) (22,26) (22,23) (23,25) (23,26) (24,25) (24,26) (24,30) (25,29) (25,31) (26,29) (26,31) (27,28) (27,31) (28,29) (29,31) (29,30) (30,31)\nQ: Is there a path between node 1 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "137"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (0,10) (0,23) (0,3) (0,9) (0,26) (1,8) (1,20) (1,6) (1,4) (1,19) (1,16) (1,13) (1,24) (2,8) (2,20) (2,4) (2,19) (2,16) (2,13) (2,24) (2,12) (3,10) (3,9) (3,21) (3,22) (4,6) (4,19) (4,13) (4,24) (4,12) (5,15) (5,25) (5,11) (5,7) (6,8) (6,20) (6,19) (6,16) (6,13) (6,24) (7,15) (7,25) (7,14) (8,19) (8,13) (8,24) (8,12) (9,18) (9,23) (10,18) (10,23) (10,21) (10,26) (11,15) (11,17) (11,25) (12,20) (12,19) (12,16) (12,24) (13,20) (13,19) (13,16) (13,24) (14,17) (14,25) (15,17) (15,25) (16,20) (16,24) (17,25) (18,21) (18,22) (19,20) (19,24) (20,24) (21,23) (22,23) (22,26) (23,26)\nQ: Is there a path between node 20 and node 12?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "138"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,1) (0,12) (0,4) (1,13) (1,3) (1,6) (1,9) (2,15) (2,14) (2,11) (4,7) (5,16) (5,6) (5,9) (6,13) (6,8) (10,13) (10,12) (11,15) (11,14)\nQ: Is there a path between node 7 and node 15?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "139"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,8) (0,18) (0,6) (0,1) (0,12) (0,3) (0,7) (0,14) (0,10) (0,19) (0,16) (0,13) (1,17) (1,8) (1,18) (1,2) (1,19) (2,8) (2,6) (2,20) (2,14) (3,17) (3,18) (3,6) (3,14) (3,10) (3,19) (4,17) (4,18) (4,6) (4,19) (4,13) (5,15) (6,17) (6,8) (6,18) (6,13) (7,17) (7,14) (7,10) (8,20) (9,15) (9,11) (10,17) (10,18) (11,15) (12,17) (12,18) (12,14) (12,19) (13,17) (13,18) (13,20) (14,17) (14,18) (14,20) (18,20) (19,20)\nQ: Is there a path between node 13 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "140"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,2) (0,3) (1,5) (2,4) (2,3) (3,4)\nQ: Is there a path between node 3 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "141"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,7) (0,8) (0,9) (0,13) (0,14) (0,15) (0,5) (1,2) (1,12) (1,16) (1,11) (1,3) (1,6) (1,14) (1,4) (2,12) (2,7) (2,9) (2,13) (2,14) (3,16) (3,11) (3,7) (3,8) (3,14) (3,15) (3,5) (3,4) (4,12) (4,11) (4,8) (4,9) (4,13) (4,14) (4,5) (5,12) (5,16) (5,11) (5,7) (5,8) (5,13) (5,14) (5,15) (6,12) (6,16) (6,11) (6,7) (6,14) (6,15) (7,12) (7,16) (7,11) (7,8) (7,9) (7,13) (8,12) (8,16) (8,11) (8,9) (8,13) (8,14) (9,12) (9,16) (9,11) (9,14) (9,15) (11,12) (11,16) (11,14) (12,13) (12,15) (13,16) (13,15) (14,16)\nQ: Is there a path between node 8 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "142"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,28) (0,26) (0,7) (0,22) (0,6) (0,1) (0,30) (0,3) (1,16) (1,28) (1,26) (1,22) (1,10) (1,30) (2,4) (2,29) (2,24) (2,14) (2,21) (2,25) (2,13) (2,12) (2,31) (2,19) (2,33) (2,27) (2,23) (2,8) (2,18) (3,16) (3,28) (3,26) (3,9) (3,7) (3,10) (4,29) (4,32) (4,24) (4,21) (4,25) (4,15) (4,12) (4,31) (4,19) (4,33) (4,27) (4,17) (4,23) (4,18) (5,32) (5,14) (5,21) (5,15) (5,12) (5,19) (5,33) (5,27) (5,23) (5,8) (6,28) (6,26) (6,7) (6,22) (6,10) (7,16) (7,9) (7,22) (7,10) (8,29) (8,32) (8,24) (8,21) (8,15) (8,13) (8,33) (8,27) (8,23) (8,18) (9,16) (9,28) (9,26) (9,22) (9,10) (10,28) (10,22) (10,30) (12,29) (12,14) (12,21) (12,25) (12,15) (12,13) (12,31) (12,19) (12,33) (12,17) (12,23) (12,18) (13,20) (13,29) (13,24) (13,21) (13,25) (13,15) (13,31) (13,19) (13,33) (13,27) (13,17) (13,23) (13,18) (14,20) (14,29) (14,32) (14,24) (14,21) (14,15) (14,31) (14,19) (14,33) (14,17) (14,18) (15,20) (15,29) (15,32) (15,24) (15,21) (15,25) (15,31) (15,19) (15,33) (15,27) (15,17) (15,23) (15,18) (16,28) (16,26) (16,22) (16,30) (17,20) (17,29) (17,32) (17,24) (17,21) (17,25) (17,31) (17,19) (17,18) (18,20) (18,29) (18,32) (18,24) (18,21) (18,25) (18,31) (18,19) (18,27) (18,23) (19,32) (19,24) (19,33) (19,27) (19,23) (20,29) (20,32) (20,24) (20,21) (20,25) (20,31) (20,33) (20,27) (20,23) (21,32) (21,24) (21,25) (21,31) (21,33) (21,27) (21,23) (22,26) (22,30) (23,29) (23,32) (23,24) (23,25) (23,31) (23,33) (23,27) (24,32) (24,25) (24,31) (24,27) (25,29) (25,33) (25,27) (26,28) (26,30) (27,29) (27,31) (27,33) (28,30) (29,32) (29,31) (29,33) (31,32) (31,33) (32,33)\nQ: Is there a path between node 5 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "143"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,13) (0,5) (0,11) (0,15) (0,10) (0,16) (0,14) (0,8) (0,9) (1,18) (1,12) (1,7) (1,6) (2,13) (2,11) (2,15) (2,17) (2,16) (2,14) (2,3) (2,8) (2,9) (3,5) (3,11) (3,4) (3,15) (3,10) (3,14) (3,8) (3,9) (4,13) (4,5) (4,17) (4,16) (4,14) (4,8) (5,17) (5,16) (5,14) (6,12) (6,19) (6,20) (6,7) (7,18) (8,15) (8,17) (8,16) (8,14) (8,9) (9,13) (9,11) (9,17) (9,16) (9,14) (10,11) (10,15) (10,17) (10,16) (10,14) (11,13) (11,15) (11,16) (12,18) (12,19) (12,20) (13,17) (13,14) (14,15) (14,17) (14,16) (15,17) (16,17) (18,19) (18,20) (19,20)\nQ: Is there a path between node 0 and node 16?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "144"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,4) (1,13) (2,11) (3,4) (3,6) (3,19) (4,20) (4,12) (4,16) (5,14) (5,9) (6,18) (6,8) (7,13) (7,8) (7,19) (7,15) (8,18) (8,20) (8,15) (11,14) (12,20) (12,13) (12,19) (12,16) (13,18) (13,15) (15,18) (15,19) (18,20) (18,19)\nQ: Is there a path between node 15 and node 14?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "145"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,13) (0,8) (0,18) (0,25) (0,14) (0,17) (0,21) (1,13) (1,26) (1,14) (1,20) (1,17) (1,24) (1,6) (2,8) (2,18) (2,9) (2,26) (2,14) (2,10) (2,15) (3,16) (3,12) (4,13) (4,8) (4,18) (4,25) (4,6) (5,19) (5,13) (5,10) (5,20) (5,22) (5,17) (5,6) (6,8) (6,18) (6,9) (6,26) (6,14) (6,17) (6,21) (6,15) (6,23) (7,25) (7,14) (7,22) (7,24) (7,15) (7,23) (8,13) (8,25) (8,24) (8,23) (9,25) (9,27) (9,26) (9,14) (9,17) (9,24) (9,23) (10,19) (10,13) (10,25) (10,22) (11,12) (12,16) (13,19) (13,18) (13,21) (14,19) (14,18) (14,22) (15,19) (15,25) (15,23) (17,25) (17,22) (17,21) (17,24) (18,21) (18,24) (19,26) (19,22) (19,24) (19,23) (20,25) (20,26) (20,24) (20,23) (21,27) (21,23) (22,25) (22,26) (22,23) (25,27) (25,26)\nQ: Is there a path between node 13 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "146"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,7) (0,13) (0,24) (0,19) (0,5) (0,10) (0,4) (0,2) (0,21) (0,17) (0,23) (0,9) (0,20) (0,15) (0,22) (1,3) (1,18) (1,6) (1,14) (1,8) (1,11) (2,12) (2,7) (2,13) (2,24) (2,19) (2,5) (2,10) (2,4) (2,21) (2,17) (2,23) (2,9) (2,20) (2,15) (2,22) (3,18) (3,6) (3,14) (3,8) (3,11) (4,12) (4,7) (4,13) (4,24) (4,19) (4,5) (4,10) (4,21) (4,17) (4,23) (4,9) (4,20) (4,15) (4,22) (5,12) (5,7) (5,13) (5,24) (5,19) (5,10) (5,21) (5,17) (5,23) (5,9) (5,20) (5,15) (5,22) (6,18) (6,14) (6,8) (6,11) (7,12) (7,13) (7,24) (7,19) (7,10) (7,21) (7,17) (7,23) (7,9) (7,20) (7,15) (7,22) (8,18) (8,14) (8,11) (9,12) (9,13) (9,24) (9,19) (9,10) (9,21) (9,17) (9,23) (9,20) (9,15) (9,22) (10,12) (10,13) (10,24) (10,19) (10,21) (10,17) (10,23) (10,20) (10,15) (10,22) (11,18) (11,14) (12,13) (12,24) (12,19) (12,21) (12,17) (12,23) (12,20) (12,15) (12,22) (13,24) (13,19) (13,21) (13,17) (13,23) (13,20) (13,15) (13,22) (14,18) (15,24) (15,19) (15,21) (15,17) (15,23) (15,20) (15,22) (17,24) (17,19) (17,21) (17,23) (17,20) (17,22) (19,24) (19,21) (19,23) (19,20) (19,22) (20,24) (20,21) (20,23) (20,22) (21,24) (21,23) (21,22) (22,24) (22,23) (23,24)\nQ: Is there a path between node 2 and node 19?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "147"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,24) (0,2) (0,7) (0,15) (0,14) (0,22) (0,10) (0,18) (0,5) (0,9) (0,4) (0,11) (0,8) (0,20) (0,13) (1,2) (1,7) (1,15) (1,14) (1,18) (1,5) (1,16) (1,9) (1,4) (1,11) (1,8) (1,13) (2,24) (2,7) (2,15) (2,14) (2,22) (2,18) (2,16) (2,9) (2,4) (2,11) (2,8) (2,20) (2,23) (3,21) (4,7) (4,14) (4,22) (4,18) (4,16) (4,13) (4,23) (5,24) (5,7) (5,15) (5,14) (5,22) (5,10) (5,18) (5,20) (5,23) (6,12) (7,24) (7,15) (7,14) (7,10) (7,18) (7,16) (7,9) (7,11) (7,8) (7,20) (7,13) (7,23) (8,24) (8,14) (8,10) (8,18) (8,9) (8,13) (8,23) (9,24) (9,15) (9,14) (9,22) (9,10) (9,16) (9,20) (9,23) (10,24) (10,15) (10,14) (10,22) (10,18) (10,16) (10,20) (11,15) (11,14) (11,18) (11,16) (11,20) (11,13) (11,23) (13,24) (13,15) (13,18) (13,16) (13,23) (14,24) (14,15) (14,22) (14,18) (14,16) (14,23) (15,24) (15,22) (15,18) (15,16) (15,20) (15,23) (16,24) (16,20) (16,23) (18,22) (18,20) (18,23) (19,21) (20,22) (22,24) (22,23) (23,24)\nQ: Is there a path between node 4 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "148"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,4) (0,9) (0,12) (0,11) (0,5) (1,6) (1,17) (1,8) (1,15) (1,3) (1,2) (1,18) (1,19) (1,13) (1,14) (1,10) (2,6) (2,17) (2,8) (2,15) (2,3) (2,18) (2,19) (2,13) (2,14) (2,10) (3,6) (3,17) (3,8) (3,15) (3,18) (3,19) (3,13) (3,14) (3,10) (4,7) (4,9) (4,12) (4,11) (4,5) (5,7) (5,9) (5,12) (5,11) (6,17) (6,8) (6,15) (6,18) (6,19) (6,13) (6,14) (6,10) (7,9) (7,12) (7,11) (8,17) (8,15) (8,18) (8,19) (8,13) (8,14) (8,10) (9,12) (9,11) (10,17) (10,15) (10,18) (10,19) (10,13) (10,14) (11,12) (13,17) (13,15) (13,18) (13,19) (13,14) (14,17) (14,15) (14,18) (14,19) (15,17) (15,18) (15,19) (17,18) (17,19) (18,19)\nQ: Is there a path between node 6 and node 13?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "149"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,17) (0,13) (0,12) (0,4) (0,1) (1,3) (1,17) (1,16) (1,14) (1,4) (2,5) (2,7) (2,9) (2,11) (2,8) (3,15) (3,13) (3,16) (3,12) (3,14) (3,6) (4,15) (4,13) (4,16) (4,12) (4,6) (5,9) (5,11) (5,10) (6,17) (6,13) (6,12) (7,11) (7,10) (7,8) (8,9) (8,11) (9,10) (10,11) (12,15) (12,17) (12,16) (12,14) (13,17) (13,16) (14,15) (14,17) (15,17) (15,16) (16,17)\nQ: Is there a path between node 14 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "150"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,12) (1,25) (1,2) (1,10) (1,12) (1,3) (2,8) (2,22) (2,25) (2,26) (2,19) (2,11) (2,12) (2,7) (2,21) (3,25) (3,26) (3,10) (3,27) (3,21) (5,24) (5,6) (6,23) (6,9) (7,22) (7,25) (7,11) (8,20) (8,22) (8,25) (8,26) (8,27) (9,24) (10,14) (10,25) (10,13) (10,27) (10,21) (11,22) (11,12) (11,17) (11,21) (12,19) (12,18) (12,17) (12,27) (12,21) (13,17) (13,21) (14,17) (14,21) (15,23) (15,24) (16,22) (17,22) (17,25) (17,19) (18,20) (18,26) (18,21) (19,22) (19,26) (19,27) (20,27) (22,25) (25,26)\nQ: Is there a path between node 5 and node 24?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "151"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,1) (0,15) (0,6) (0,9) (0,4) (0,16) (0,19) (1,20) (1,15) (1,6) (1,9) (1,4) (1,16) (1,19) (2,14) (2,10) (2,3) (2,11) (2,7) (2,18) (2,5) (2,12) (2,17) (2,8) (3,14) (3,10) (3,11) (3,7) (3,18) (3,5) (3,12) (3,17) (3,8) (4,20) (4,15) (4,6) (4,9) (4,16) (4,19) (5,14) (5,10) (5,11) (5,7) (5,18) (5,12) (5,17) (5,8) (6,20) (6,15) (6,9) (6,16) (6,19) (7,14) (7,10) (7,11) (7,18) (7,12) (7,17) (7,8) (8,14) (8,10) (8,11) (8,18) (8,12) (8,17) (9,20) (9,15) (9,16) (9,19) (10,14) (10,11) (10,18) (10,12) (10,17) (11,14) (11,18) (11,12) (11,17) (12,14) (12,18) (12,17) (14,18) (14,17) (15,20) (15,16) (15,19) (16,20) (16,19) (17,18) (19,20)\nQ: Is there a path between node 4 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "152"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,10) (0,17) (0,4) (0,21) (0,1) (0,2) (0,18) (0,7) (0,19) (0,11) (0,3) (0,5) (0,14) (1,6) (1,10) (1,17) (1,21) (1,16) (1,18) (1,7) (1,8) (1,11) (2,6) (2,10) (2,17) (2,4) (2,21) (2,16) (2,13) (2,18) (2,7) (2,8) (2,19) (2,3) (2,5) (3,6) (3,10) (3,17) (3,4) (3,21) (3,16) (3,13) (3,18) (3,7) (3,19) (4,10) (4,16) (4,18) (4,7) (4,8) (4,19) (4,5) (5,6) (5,16) (5,13) (5,18) (5,7) (5,8) (5,19) (5,14) (6,10) (6,17) (6,21) (6,16) (6,13) (6,18) (6,7) (6,19) (6,11) (6,14) (7,10) (7,17) (7,21) (7,16) (7,13) (7,18) (7,8) (7,19) (7,11) (7,14) (8,10) (8,17) (8,21) (8,16) (8,13) (8,18) (8,19) (8,11) (9,20) (10,17) (10,21) (10,13) (10,18) (10,19) (10,11) (10,14) (11,17) (11,16) (11,13) (11,18) (11,19) (12,15) (13,21) (13,16) (13,18) (13,19) (13,14) (14,17) (14,21) (14,16) (14,18) (14,19) (16,17) (16,21) (16,18) (17,18) (18,21) (18,19) (19,21)\nQ: Is there a path between node 0 and node 19?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "153"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,15) (1,3) (1,20) (2,11) (3,12) (3,6) (3,16) (3,20) (5,14) (5,7) (6,20) (6,21) (7,13) (7,18) (8,14) (8,13) (9,12) (9,16) (9,21) (10,21) (11,17) (12,16) (14,18) (15,16) (15,21) (16,20) (20,21)\nQ: Is there a path between node 20 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "154"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,34) (0,4) (0,7) (0,28) (0,8) (0,15) (0,23) (0,13) (0,22) (0,32) (0,11) (0,18) (1,7) (1,2) (1,13) (1,27) (1,26) (1,9) (2,14) (2,31) (2,15) (2,23) (2,13) (2,9) (2,22) (2,17) (2,32) (2,18) (3,24) (4,7) (4,27) (4,17) (5,16) (5,12) (5,29) (5,20) (6,34) (6,7) (6,14) (6,31) (6,10) (6,23) (6,26) (6,21) (6,17) (6,18) (7,33) (7,14) (7,28) (7,15) (7,26) (7,19) (8,14) (8,28) (8,31) (8,10) (8,13) (8,25) (8,30) (8,18) (9,14) (9,21) (9,25) (9,22) (9,11) (10,31) (10,15) (10,27) (10,25) (10,17) (10,32) (11,28) (11,31) (11,15) (11,13) (11,27) (11,21) (11,25) (11,22) (12,16) (13,33) (13,14) (13,28) (13,26) (13,21) (13,17) (13,32) (13,18) (14,33) (14,31) (14,23) (14,27) (14,25) (15,34) (15,30) (15,17) (15,19) (16,24) (17,23) (17,26) (17,19) (18,34) (18,21) (18,30) (19,33) (19,21) (19,25) (19,30) (21,33) (21,28) (21,25) (21,30) (22,33) (22,23) (22,26) (22,25) (23,34) (23,25) (25,33) (25,32) (26,33) (26,28) (26,31) (26,32) (27,33) (27,32) (32,33)\nQ: Is there a path between node 29 and node 14?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "155"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (1,24) (1,13) (1,7) (2,24) (2,15) (2,18) (2,8) (2,13) (2,7) (3,23) (3,6) (5,20) (5,14) (6,11) (6,23) (7,12) (7,10) (7,21) (7,8) (7,13) (8,10) (8,15) (8,18) (8,22) (8,13) (9,21) (9,13) (10,12) (10,15) (10,13) (12,24) (13,24) (13,22) (14,20) (15,24) (17,24) (19,20) (21,24)\nQ: Is there a path between node 18 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "156"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,13) (0,19) (0,11) (0,16) (0,20) (0,8) (0,5) (0,3) (0,2) (0,7) (0,6) (0,17) (0,14) (0,12) (0,1) (0,18) (0,10) (0,23) (0,9) (1,4) (1,13) (1,19) (1,11) (1,16) (1,20) (1,8) (1,5) (1,3) (1,2) (1,7) (1,6) (1,17) (1,14) (1,12) (1,18) (1,10) (1,23) (1,9) (2,4) (2,13) (2,19) (2,11) (2,16) (2,20) (2,8) (2,5) (2,3) (2,7) (2,6) (2,17) (2,14) (2,12) (2,18) (2,10) (2,23) (2,9) (3,4) (3,13) (3,19) (3,11) (3,16) (3,20) (3,8) (3,5) (3,7) (3,6) (3,17) (3,14) (3,12) (3,18) (3,10) (3,23) (3,9) (4,13) (4,19) (4,11) (4,16) (4,20) (4,8) (4,5) (4,7) (4,6) (4,17) (4,14) (4,12) (4,18) (4,10) (4,23) (4,9) (5,13) (5,19) (5,11) (5,16) (5,20) (5,8) (5,7) (5,6) (5,17) (5,14) (5,12) (5,18) (5,10) (5,23) (5,9) (6,13) (6,19) (6,11) (6,16) (6,20) (6,8) (6,7) (6,17) (6,14) (6,12) (6,18) (6,10) (6,23) (6,9) (7,13) (7,19) (7,11) (7,16) (7,20) (7,8) (7,17) (7,14) (7,12) (7,18) (7,10) (7,23) (7,9) (8,13) (8,19) (8,11) (8,16) (8,20) (8,17) (8,14) (8,12) (8,18) (8,10) (8,23) (8,9) (9,13) (9,19) (9,11) (9,16) (9,20) (9,17) (9,14) (9,12) (9,18) (9,10) (9,23) (10,13) (10,19) (10,11) (10,16) (10,20) (10,17) (10,14) (10,12) (10,18) (10,23) (11,13) (11,19) (11,16) (11,20) (11,17) (11,14) (11,12) (11,18) (11,23) (12,13) (12,19) (12,16) (12,20) (12,17) (12,14) (12,18) (12,23) (13,19) (13,16) (13,20) (13,17) (13,14) (13,18) (13,23) (14,19) (14,16) (14,20) (14,17) (14,18) (14,23) (15,21) (15,22) (16,19) (16,20) (16,17) (16,18) (16,23) (17,19) (17,20) (17,18) (17,23) (18,19) (18,20) (18,23) (19,20) (19,23) (20,23) (21,22)\nQ: Is there a path between node 15 and node 19?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "157"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,11) (0,13) (0,3) (0,15) (0,4) (0,2) (1,7) (1,8) (2,14) (2,23) (2,21) (2,6) (2,10) (3,9) (3,17) (3,13) (3,5) (3,19) (3,4) (3,16) (3,10) (4,9) (4,22) (4,6) (5,11) (5,18) (5,23) (6,9) (6,14) (6,17) (6,20) (6,15) (6,21) (7,8) (9,17) (9,15) (9,21) (10,18) (10,12) (10,16) (11,17) (11,15) (11,22) (11,16) (12,15) (12,22) (13,23) (13,16) (14,17) (14,18) (14,20) (14,21) (14,22) (14,16) (15,20) (17,20) (17,19) (17,23) (18,19) (18,23) (19,20) (19,23) (21,23) (21,22)\nQ: Is there a path between node 11 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "158"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,4) (0,12) (0,11) (0,10) (0,3) (0,17) (0,21) (0,27) (0,15) (0,23) (0,31) (0,29) (0,2) (0,8) (0,9) (0,14) (0,18) (1,5) (1,26) (1,13) (1,20) (1,32) (1,7) (2,19) (2,4) (2,28) (2,22) (2,16) (2,12) (2,10) (2,3) (2,17) (2,21) (2,27) (2,15) (2,23) (2,31) (2,29) (2,8) (2,9) (2,14) (2,18) (3,4) (3,22) (3,16) (3,12) (3,10) (3,17) (3,21) (3,27) (3,23) (3,31) (3,29) (3,6) (3,9) (3,14) (3,18) (4,16) (4,12) (4,11) (4,17) (4,21) (4,15) (4,30) (4,23) (4,29) (4,6) (4,8) (4,9) (4,18) (5,26) (5,13) (5,25) (5,24) (5,32) (5,7) (6,19) (6,22) (6,12) (6,11) (6,10) (6,17) (6,21) (6,27) (6,15) (6,30) (6,23) (6,31) (6,29) (6,9) (6,14) (7,26) (7,25) (7,32) (8,19) (8,28) (8,10) (8,17) (8,27) (8,15) (8,30) (8,23) (9,19) (9,28) (9,22) (9,16) (9,12) (9,10) (9,17) (9,21) (9,15) (9,30) (9,23) (9,29) (9,18) (10,19) (10,28) (10,22) (10,12) (10,11) (10,17) (10,21) (10,27) (10,15) (10,30) (10,23) (10,31) (10,29) (10,14) (10,18) (11,16) (11,12) (11,17) (11,21) (11,27) (11,15) (11,30) (11,31) (11,29) (11,14) (11,18) (12,19) (12,28) (12,22) (12,17) (12,27) (12,15) (12,30) (12,23) (12,31) (12,29) (12,14) (12,18) (13,26) (13,25) (13,20) (13,32) (14,28) (14,16) (14,17) (14,21) (14,27) (14,15) (14,31) (14,29) (14,18) (15,19) (15,22) (15,16) (15,17) (15,21) (15,27) (15,30) (15,23) (15,31) (15,29) (15,18) (16,19) (16,28) (16,22) (16,17) (16,21) (16,27) (16,30) (16,31) (16,18) (17,22) (17,21) (17,30) (17,31) (17,29) (17,18) (18,19) (18,28) (18,22) (18,21) (18,27) (18,29) (19,28) (19,22) (19,21) (19,30) (19,31) (19,29) (20,32) (21,28) (21,22) (21,27) (21,29) (22,28) (22,30) (22,23) (22,31) (22,29) (23,28) (23,27) (23,30) (23,31) (23,29) (24,26) (24,25) (25,26) (25,32) (26,32) (27,28) (27,30) (27,29) (28,30) (28,31) (28,29) (29,30) (29,31)\nQ: Is there a path between node 27 and node 18?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "159"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,6) (0,4) (1,3) (1,7) (1,2) (2,3) (3,9) (4,6) (5,9) (6,8) (7,9)\nQ: Is there a path between node 9 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "160"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,6) (1,2) (3,7) (3,5)\nQ: Is there a path between node 2 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "161"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,13) (0,30) (0,1) (0,4) (0,2) (0,22) (1,30) (1,17) (1,5) (1,4) (1,25) (1,29) (2,3) (2,5) (2,23) (3,28) (3,24) (3,4) (3,6) (3,8) (3,12) (4,15) (4,24) (4,25) (4,7) (4,6) (4,29) (5,21) (5,23) (5,7) (5,12) (6,20) (6,28) (6,23) (7,13) (7,15) (7,16) (7,8) (7,12) (8,20) (8,30) (8,24) (8,17) (8,23) (10,19) (11,19) (11,26) (12,20) (12,16) (12,25) (12,18) (13,28) (13,18) (14,20) (15,28) (15,24) (15,23) (16,20) (16,30) (16,24) (16,29) (17,21) (17,28) (17,25) (18,21) (18,23) (18,29) (20,24) (20,23) (20,22) (20,29) (21,25) (21,23) (21,22) (22,25) (23,24) (23,29) (24,28) (24,29) (25,28) (26,27) (29,30)\nQ: Is there a path between node 22 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "162"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,5) (3,5)\nQ: Is there a path between node 5 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "163"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (1,17) (2,9) (3,16) (5,18) (5,11) (5,21) (6,21) (6,15) (7,19) (7,21) (8,10) (8,12) (8,16) (10,16) (14,23) (15,21) (16,19) (17,20) (18,19) (20,23)\nQ: Is there a path between node 23 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "164"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,8) (1,5) (2,3) (3,5) (3,11) (4,8) (5,9) (5,7) (5,10) (6,11)\nQ: Is there a path between node 3 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "165"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,12) (0,1) (0,13) (0,14) (0,11) (0,20) (0,7) (0,21) (1,4) (1,13) (1,14) (1,16) (1,7) (1,21) (2,5) (2,22) (2,8) (2,15) (2,25) (2,9) (2,17) (2,26) (3,11) (3,20) (3,7) (4,13) (4,14) (4,11) (4,20) (4,21) (5,22) (5,18) (5,15) (5,23) (5,25) (5,17) (5,26) (5,24) (6,19) (7,12) (7,13) (7,14) (7,11) (7,20) (7,21) (8,22) (8,15) (8,23) (8,9) (8,17) (8,24) (9,18) (9,15) (9,23) (9,25) (9,17) (11,13) (11,14) (11,16) (11,20) (12,13) (12,14) (12,16) (12,20) (12,21) (13,16) (13,20) (14,16) (14,20) (14,21) (15,22) (15,18) (15,23) (15,25) (15,26) (15,24) (16,21) (17,22) (17,18) (17,23) (17,25) (18,25) (18,24) (20,21) (22,23) (22,25) (22,26) (22,24) (23,26) (23,24) (24,25) (25,26)\nQ: Is there a path between node 9 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "166"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (3,7) (4,6) (5,6)\nQ: Is there a path between node 7 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "167"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,17) (0,13) (0,12) (0,4) (0,1) (1,3) (1,17) (1,16) (1,14) (1,4) (2,5) (2,7) (2,9) (2,11) (2,8) (3,15) (3,13) (3,16) (3,12) (3,14) (3,6) (4,15) (4,13) (4,16) (4,12) (4,6) (5,9) (5,11) (5,10) (6,17) (6,13) (6,12) (7,11) (7,10) (7,8) (8,9) (8,11) (9,10) (10,11) (12,15) (12,17) (12,16) (12,14) (13,17) (13,16) (14,15) (14,17) (15,17) (15,16) (16,17)\nQ: Is there a path between node 12 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "168"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,7) (0,6) (0,8) (0,4) (0,1) (1,2) (1,7) (1,6) (1,8) (1,4) (2,7) (2,6) (2,8) (2,4) (3,5) (4,7) (4,6) (4,8) (6,7) (6,8) (7,8)\nQ: Is there a path between node 5 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "169"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (1,15) (1,16) (2,18) (2,17) (2,7) (3,14) (3,7) (5,11) (6,13) (7,17) (8,15) (8,13) (9,17) (10,17) (13,15) (13,16) (16,19)\nQ: Is there a path between node 18 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "170"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (1,4) (1,11) (2,21) (2,20) (2,24) (3,24) (4,13) (4,15) (4,8) (5,19) (5,24) (6,20) (6,24) (7,25) (7,21) (8,17) (8,15) (8,12) (9,13) (9,12) (10,16) (11,13) (11,18) (11,23) (11,14) (11,12) (13,17) (14,23) (15,18) (15,23) (18,23) (19,25) (19,24) (20,21) (21,25) (24,25)\nQ: Is there a path between node 8 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "171"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,4) (1,13) (2,11) (3,4) (3,6) (3,19) (4,20) (4,12) (4,16) (5,14) (5,9) (6,18) (6,8) (7,13) (7,8) (7,19) (7,15) (8,18) (8,20) (8,15) (11,14) (12,20) (12,13) (12,19) (12,16) (13,18) (13,15) (15,18) (15,19) (18,20) (18,19)\nQ: Is there a path between node 8 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "172"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,4) (0,3) (0,6) (0,2) (0,8) (0,5) (0,11) (1,4) (1,3) (1,6) (1,2) (1,8) (1,5) (1,11) (2,4) (2,3) (2,6) (2,8) (2,5) (2,11) (3,4) (3,6) (3,8) (3,5) (3,11) (4,6) (4,8) (4,5) (4,11) (5,6) (5,8) (5,11) (6,8) (6,11) (7,9) (7,10) (8,11) (9,10)\nQ: Is there a path between node 5 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "173"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,17) (0,23) (0,22) (0,1) (0,9) (0,11) (0,14) (0,19) (0,12) (0,18) (0,8) (0,4) (0,16) (0,15) (0,10) (0,6) (1,20) (1,17) (1,23) (1,22) (1,9) (1,11) (1,14) (1,19) (1,12) (1,18) (1,8) (1,4) (1,16) (1,15) (1,10) (1,6) (2,13) (2,5) (2,3) (2,21) (2,7) (3,13) (3,5) (3,21) (3,7) (4,20) (4,17) (4,23) (4,22) (4,9) (4,11) (4,14) (4,19) (4,12) (4,18) (4,8) (4,16) (4,15) (4,10) (4,6) (5,13) (5,21) (5,7) (6,20) (6,17) (6,23) (6,22) (6,9) (6,11) (6,14) (6,19) (6,12) (6,18) (6,8) (6,16) (6,15) (6,10) (7,13) (7,21) (8,20) (8,17) (8,23) (8,22) (8,9) (8,11) (8,14) (8,19) (8,12) (8,18) (8,16) (8,15) (8,10) (9,20) (9,17) (9,23) (9,22) (9,11) (9,14) (9,19) (9,12) (9,18) (9,16) (9,15) (9,10) (10,20) (10,17) (10,23) (10,22) (10,11) (10,14) (10,19) (10,12) (10,18) (10,16) (10,15) (11,20) (11,17) (11,23) (11,22) (11,14) (11,19) (11,12) (11,18) (11,16) (11,15) (12,20) (12,17) (12,23) (12,22) (12,14) (12,19) (12,18) (12,16) (12,15) (13,21) (14,20) (14,17) (14,23) (14,22) (14,19) (14,18) (14,16) (14,15) (15,20) (15,17) (15,23) (15,22) (15,19) (15,18) (15,16) (16,20) (16,17) (16,23) (16,22) (16,19) (16,18) (17,20) (17,23) (17,22) (17,19) (17,18) (18,20) (18,23) (18,22) (18,19) (19,20) (19,23) (19,22) (20,23) (20,22) (22,23)\nQ: Is there a path between node 4 and node 23?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "174"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,8) (0,5) (0,4) (0,25) (0,22) (0,16) (0,24) (0,21) (2,15) (2,23) (2,26) (2,10) (2,3) (2,11) (2,6) (2,27) (3,15) (3,23) (3,14) (3,26) (3,10) (3,11) (3,27) (4,8) (4,13) (4,5) (4,20) (4,18) (4,7) (4,22) (4,16) (4,24) (5,8) (5,13) (5,20) (5,7) (5,22) (5,24) (5,21) (6,15) (6,23) (6,14) (6,26) (6,10) (6,11) (6,27) (7,12) (7,20) (7,25) (7,16) (7,21) (8,12) (8,20) (8,25) (8,16) (8,24) (10,15) (10,23) (10,14) (10,26) (10,19) (10,11) (10,27) (11,15) (11,23) (11,26) (11,27) (12,16) (12,24) (12,21) (13,20) (13,18) (13,25) (13,22) (13,16) (13,24) (13,21) (14,15) (14,26) (15,26) (15,27) (16,22) (16,24) (16,21) (18,25) (18,22) (18,21) (19,23) (19,26) (19,27) (20,25) (20,24) (21,25) (21,24) (22,25) (22,24) (23,26) (23,27) (24,25) (26,27)\nQ: Is there a path between node 23 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "175"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,28) (0,1) (0,22) (0,20) (0,15) (0,18) (0,2) (0,5) (0,10) (0,8) (0,14) (0,6) (1,27) (1,12) (1,19) (1,28) (1,25) (1,29) (1,22) (1,4) (1,7) (1,15) (1,18) (1,3) (1,2) (1,24) (1,5) (1,11) (1,14) (1,13) (1,6) (2,12) (2,19) (2,28) (2,29) (2,4) (2,15) (2,16) (2,18) (2,3) (2,10) (2,13) (2,21) (2,6) (3,27) (3,19) (3,28) (3,20) (3,4) (3,7) (3,16) (3,18) (3,9) (3,24) (3,5) (3,11) (3,10) (3,8) (3,14) (3,23) (3,21) (3,6) (4,27) (4,12) (4,19) (4,28) (4,25) (4,20) (4,7) (4,15) (4,16) (4,5) (4,8) (4,14) (4,13) (4,21) (4,6) (5,27) (5,12) (5,19) (5,28) (5,25) (5,29) (5,22) (5,20) (5,7) (5,15) (5,16) (5,24) (5,11) (5,10) (5,8) (5,14) (5,23) (5,13) (5,21) (5,6) (6,27) (6,12) (6,28) (6,25) (6,29) (6,22) (6,20) (6,7) (6,16) (6,18) (6,9) (6,24) (6,8) (6,14) (6,21) (7,19) (7,25) (7,29) (7,22) (7,20) (7,15) (7,16) (7,24) (7,11) (7,10) (7,14) (7,23) (7,21) (8,27) (8,12) (8,19) (8,29) (8,22) (8,20) (8,15) (8,16) (8,9) (8,24) (8,11) (8,10) (8,14) (8,13) (9,12) (9,19) (9,25) (9,22) (9,20) (9,18) (9,24) (9,11) (9,10) (9,14) (9,23) (9,13) (9,21) (10,27) (10,12) (10,19) (10,28) (10,25) (10,29) (10,16) (10,18) (10,24) (10,14) (10,23) (10,13) (10,21) (11,27) (11,12) (11,25) (11,22) (11,20) (11,18) (11,24) (12,19) (12,28) (12,29) (12,22) (12,15) (12,16) (12,18) (12,14) (12,23) (12,13) (12,21) (13,27) (13,28) (13,25) (13,29) (13,22) (13,20) (13,15) (13,18) (13,24) (14,19) (14,28) (14,25) (14,29) (14,15) (14,16) (14,18) (14,24) (14,23) (15,27) (15,28) (15,25) (15,29) (15,20) (15,18) (15,23) (15,21) (16,27) (16,19) (16,28) (16,25) (16,29) (16,22) (16,20) (16,18) (16,24) (16,21) (18,19) (18,28) (18,29) (18,22) (18,20) (18,24) (18,23) (18,21) (19,27) (19,28) (19,25) (19,29) (19,22) (19,20) (19,24) (19,23) (19,21) (20,27) (20,28) (20,29) (20,22) (20,23) (20,21) (21,27) (21,28) (21,24) (21,23) (22,27) (22,28) (22,29) (22,23) (23,27) (23,28) (23,25) (23,29) (24,27) (24,28) (24,25) (24,29) (25,27) (25,29) (27,28) (27,29)\nQ: Is there a path between node 17 and node 27?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "176"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,15) (0,6) (0,17) (0,4) (0,12) (0,16) (0,9) (1,14) (1,23) (1,18) (1,19) (1,3) (1,21) (2,14) (2,5) (2,11) (2,23) (2,22) (2,8) (2,18) (2,19) (2,3) (2,20) (3,14) (3,5) (3,23) (3,22) (3,8) (3,18) (3,19) (3,20) (3,21) (4,7) (4,15) (4,6) (4,17) (4,13) (4,10) (4,16) (5,14) (5,8) (5,18) (5,19) (5,21) (6,13) (6,10) (6,16) (6,9) (7,15) (7,13) (7,9) (8,14) (8,11) (8,23) (8,22) (8,18) (8,19) (8,20) (8,21) (9,15) (9,13) (9,12) (9,16) (10,15) (10,17) (10,13) (10,12) (11,14) (11,23) (11,22) (11,18) (11,19) (12,17) (12,16) (13,17) (13,16) (14,23) (14,19) (15,17) (16,17) (18,23) (18,22) (18,19) (18,21) (19,23) (19,22) (19,20) (20,23) (20,21) (21,23) (22,23)\nQ: Is there a path between node 17 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "177"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,15) (0,18) (0,27) (0,9) (0,13) (0,25) (0,3) (1,8) (1,5) (1,26) (1,12) (1,2) (1,16) (1,14) (2,8) (2,26) (2,12) (2,16) (2,14) (3,7) (3,4) (3,15) (3,18) (3,27) (3,13) (4,7) (4,15) (4,18) (4,27) (4,13) (5,8) (5,12) (5,11) (5,16) (5,14) (5,20) (6,17) (6,21) (6,29) (6,28) (7,15) (7,18) (7,27) (7,9) (7,13) (8,26) (8,23) (8,16) (8,14) (9,15) (10,29) (10,24) (11,12) (11,16) (11,14) (11,20) (12,22) (12,23) (12,14) (12,20) (13,18) (13,27) (14,26) (14,22) (14,23) (14,20) (15,18) (15,27) (15,25) (16,26) (16,22) (16,23) (16,20) (17,21) (17,19) (17,24) (17,28) (19,21) (19,29) (19,24) (19,28) (20,26) (20,22) (20,23) (21,29) (21,24) (22,26) (22,23) (24,29) (24,28) (25,27)\nQ: Is there a path between node 2 and node 22?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "178"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (0,1) (0,19) (0,15) (0,20) (0,9) (0,21) (0,3) (0,22) (0,32) (0,24) (0,14) (0,11) (0,17) (0,5) (0,34) (0,4) (0,26) (0,10) (0,8) (1,27) (1,23) (1,30) (1,6) (1,19) (1,20) (1,2) (1,9) (1,21) (1,3) (1,22) (1,24) (1,14) (1,11) (1,17) (1,5) (1,4) (1,26) (1,8) (2,27) (2,30) (2,6) (2,19) (2,20) (2,9) (2,21) (2,3) (2,22) (2,32) (2,7) (2,11) (2,17) (2,5) (2,34) (2,4) (2,26) (2,12) (2,10) (3,27) (3,23) (3,30) (3,6) (3,19) (3,15) (3,20) (3,9) (3,22) (3,24) (3,14) (3,34) (3,4) (3,12) (3,10) (3,8) (3,28) (4,27) (4,23) (4,30) (4,19) (4,15) (4,20) (4,9) (4,21) (4,32) (4,24) (4,14) (4,7) (4,11) (4,17) (4,5) (4,26) (4,12) (4,8) (4,28) (5,30) (5,19) (5,9) (5,21) (5,24) (5,7) (5,11) (5,17) (5,34) (5,12) (6,27) (6,23) (6,30) (6,19) (6,20) (6,9) (6,21) (6,22) (6,32) (6,24) (6,14) (6,7) (6,11) (6,17) (6,34) (6,26) (6,8) (6,28) (7,23) (7,30) (7,19) (7,15) (7,20) (7,21) (7,32) (7,24) (7,11) (7,17) (7,34) (7,12) (7,10) (7,8) (7,28) (8,23) (8,15) (8,20) (8,24) (8,14) (8,11) (8,17) (8,34) (8,26) (8,12) (8,10) (8,28) (9,30) (9,19) (9,15) (9,20) (9,22) (9,32) (9,24) (9,11) (9,34) (9,12) (9,10) (9,28) (10,27) (10,23) (10,30) (10,19) (10,21) (10,32) (10,24) (10,26) (10,12) (11,27) (11,30) (11,19) (11,20) (11,21) (11,22) (11,32) (11,24) (11,14) (11,17) (11,34) (11,12) (12,27) (12,30) (12,19) (12,20) (12,22) (12,32) (12,24) (12,14) (12,17) (12,34) (12,28) (14,27) (14,23) (14,30) (14,19) (14,15) (14,21) (14,22) (14,32) (14,17) (14,34) (14,28) (15,19) (15,20) (15,21) (15,22) (15,32) (15,24) (15,34) (15,26) (15,28) (16,33) (16,29) (16,18) (16,31) (17,27) (17,23) (17,30) (17,19) (17,20) (17,21) (17,22) (17,32) (17,24) (17,34) (17,28) (18,33) (18,31) (18,25) (19,27) (19,23) (19,30) (19,20) (19,22) (19,32) (19,34) (19,26) (19,28) (20,23) (20,30) (20,21) (20,22) (20,32) (20,24) (20,34) (20,26) (21,27) (21,23) (21,30) (21,22) (21,32) (21,24) (21,34) (21,26) (21,28) (22,27) (22,23) (22,24) (22,34) (22,26) (22,28) (23,32) (23,26) (23,28) (24,27) (24,32) (24,34) (24,26) (25,33) (26,30) (26,32) (26,34) (27,30) (27,32) (27,28) (28,30) (28,32) (28,34) (29,33) (29,31) (31,33) (32,34)\nQ: Is there a path between node 19 and node 32?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "179"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,2) (2,3)\nQ: Is there a path between node 3 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "180"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,3) (0,5) (1,2) (1,8) (1,7) (2,8) (2,7) (3,11) (3,9) (3,13) (5,11) (5,12) (10,11) (11,12) (12,13)\nQ: Is there a path between node 10 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "181"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,23) (1,6) (1,19) (1,7) (2,17) (2,24) (2,10) (2,20) (3,22) (3,27) (4,17) (4,15) (5,19) (5,12) (5,25) (6,19) (6,7) (7,18) (7,23) (8,16) (8,13) (9,27) (9,13) (10,21) (10,15) (10,11) (11,17) (11,26) (11,24) (11,14) (12,25) (12,23) (14,17) (14,26) (15,21) (17,26) (17,21) (17,24) (20,21) (20,24) (21,26) (21,24) (23,25)\nQ: Is there a path between node 20 and node 26?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "182"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,3) (0,4) (1,3) (1,4) (3,4)\nQ: Is there a path between node 4 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "183"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (3,8) (3,9) (4,5) (8,9)\nQ: Is there a path between node 6 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "184"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,18) (0,25) (0,19) (0,16) (0,22) (0,8) (0,10) (0,31) (0,13) (0,5) (0,14) (0,24) (0,27) (0,1) (0,15) (0,23) (1,9) (1,30) (1,25) (1,19) (1,16) (1,17) (1,22) (1,8) (1,21) (1,4) (1,31) (1,13) (1,14) (1,24) (1,12) (1,27) (1,15) (2,11) (2,28) (2,29) (2,7) (3,9) (3,18) (3,25) (3,19) (3,16) (3,22) (3,10) (3,4) (3,31) (3,13) (3,5) (3,14) (3,24) (3,12) (3,20) (3,27) (3,15) (3,23) (4,18) (4,30) (4,19) (4,22) (4,8) (4,21) (4,31) (4,5) (4,24) (4,12) (4,27) (4,23) (5,18) (5,30) (5,25) (5,19) (5,17) (5,10) (5,21) (5,31) (5,12) (5,20) (5,15) (5,23) (6,28) (6,29) (6,7) (6,26) (7,28) (8,9) (8,25) (8,19) (8,16) (8,22) (8,10) (8,13) (8,14) (8,24) (8,12) (8,27) (8,15) (8,23) (9,18) (9,30) (9,19) (9,16) (9,17) (9,22) (9,10) (9,31) (9,13) (9,27) (9,15) (9,23) (10,18) (10,30) (10,25) (10,16) (10,22) (10,21) (10,31) (10,14) (10,24) (10,12) (10,20) (10,15) (11,28) (11,26) (12,19) (12,22) (12,21) (12,13) (12,24) (12,15) (12,23) (13,25) (13,19) (13,16) (13,17) (13,22) (13,31) (13,14) (13,27) (14,30) (14,25) (14,16) (14,17) (14,22) (14,31) (14,24) (14,20) (14,15) (14,23) (15,18) (15,30) (15,25) (15,19) (15,16) (15,22) (15,31) (15,24) (16,18) (16,30) (16,22) (16,21) (16,31) (16,20) (16,27) (17,18) (17,30) (17,25) (17,19) (17,22) (17,21) (17,31) (17,24) (17,27) (17,23) (18,30) (18,25) (18,19) (18,22) (18,21) (18,31) (18,24) (18,27) (18,23) (19,30) (19,25) (19,21) (19,24) (19,20) (19,27) (19,23) (20,21) (20,31) (20,24) (20,27) (20,23) (21,25) (21,22) (21,31) (21,24) (21,27) (21,23) (22,30) (22,31) (22,24) (22,23) (23,30) (23,25) (23,24) (23,27) (24,30) (24,25) (24,31) (24,27) (25,30) (25,27) (26,28) (27,30) (27,31) (28,29) (30,31)\nQ: Is there a path between node 20 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "185"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,6) (0,21) (0,18) (1,24) (1,3) (3,24) (3,14) (4,6) (4,5) (4,23) (6,14) (6,21) (6,23) (7,11) (8,19) (8,13) (9,15) (9,19) (10,11) (10,12) (10,16) (10,17) (11,12) (11,16) (12,17) (13,15) (13,22) (14,23) (15,22) (16,17) (18,24) (18,21)\nQ: Is there a path between node 6 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "186"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (1,4) (2,4)\nQ: Is there a path between node 3 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "187"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,7) (0,8) (0,10) (0,3) (1,4) (1,11) (1,9) (1,6) (1,12) (1,2) (2,4) (2,11) (2,9) (2,6) (2,12) (3,5) (3,7) (3,8) (3,10) (4,11) (4,9) (4,6) (4,12) (5,7) (5,8) (5,10) (6,11) (6,9) (6,12) (7,8) (7,10) (8,10) (9,11) (9,12) (11,12)\nQ: Is there a path between node 10 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "188"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,11) (0,5) (0,9) (0,6) (1,2) (1,7) (1,3) (1,10) (1,8) (2,7) (2,3) (2,10) (2,8) (3,7) (3,10) (3,8) (4,11) (4,5) (4,9) (4,6) (5,11) (5,9) (5,6) (6,11) (6,9) (7,10) (7,8) (8,10) (9,11)\nQ: Is there a path between node 11 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "189"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,11) (3,15) (3,8) (5,18) (5,7) (6,17) (6,7) (7,13) (7,8) (7,14) (8,18) (8,12) (9,11) (9,15) (9,13) (9,17) (10,18) (11,13) (11,17) (12,18) (12,17) (12,14) (13,17) (14,17) (17,18)\nQ: Is there a path between node 7 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "190"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (1,17) (2,9) (3,16) (5,18) (5,11) (5,21) (6,21) (6,15) (7,19) (7,21) (8,10) (8,12) (8,16) (10,16) (14,23) (15,21) (16,19) (17,20) (18,19) (20,23)\nQ: Is there a path between node 15 and node 18?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "191"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,12) (0,1) (0,13) (0,14) (0,11) (0,20) (0,7) (0,21) (1,4) (1,13) (1,14) (1,16) (1,7) (1,21) (2,5) (2,22) (2,8) (2,15) (2,25) (2,9) (2,17) (2,26) (3,11) (3,20) (3,7) (4,13) (4,14) (4,11) (4,20) (4,21) (5,22) (5,18) (5,15) (5,23) (5,25) (5,17) (5,26) (5,24) (6,19) (7,12) (7,13) (7,14) (7,11) (7,20) (7,21) (8,22) (8,15) (8,23) (8,9) (8,17) (8,24) (9,18) (9,15) (9,23) (9,25) (9,17) (11,13) (11,14) (11,16) (11,20) (12,13) (12,14) (12,16) (12,20) (12,21) (13,16) (13,20) (14,16) (14,20) (14,21) (15,22) (15,18) (15,23) (15,25) (15,26) (15,24) (16,21) (17,22) (17,18) (17,23) (17,25) (18,25) (18,24) (20,21) (22,23) (22,25) (22,26) (22,24) (23,26) (23,24) (24,25) (25,26)\nQ: Is there a path between node 24 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "192"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (1,12) (1,19) (2,13) (3,20) (3,11) (4,7) (4,16) (4,18) (5,17) (5,7) (6,15) (6,20) (6,11) (7,20) (7,11) (8,12) (8,13) (8,19) (11,17) (11,15) (12,19) (16,17) (16,20) (17,20) (18,20)\nQ: Is there a path between node 14 and node 19?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "193"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,18) (0,12) (0,2) (0,11) (0,8) (0,13) (1,4) (1,10) (1,17) (1,5) (1,14) (1,7) (1,6) (1,15) (2,3) (2,18) (2,12) (2,11) (2,8) (2,13) (3,18) (3,12) (3,11) (3,8) (3,13) (4,10) (4,17) (4,5) (4,14) (4,7) (4,6) (4,15) (5,10) (5,17) (5,14) (5,7) (5,6) (5,15) (6,10) (6,17) (6,14) (6,7) (6,15) (7,10) (7,17) (7,14) (7,15) (8,18) (8,12) (8,11) (8,13) (9,16) (10,17) (10,14) (10,15) (11,18) (11,12) (11,13) (12,18) (12,13) (13,18) (14,17) (14,15) (15,17)\nQ: Is there a path between node 11 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "194"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,6) (0,1) (0,7) (0,4) (1,5) (1,6) (1,7) (1,4) (2,3) (4,5) (4,6) (4,7) (5,6) (5,7) (6,7)\nQ: Is there a path between node 1 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "195"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,17) (0,10) (0,28) (0,30) (0,29) (0,3) (1,14) (1,2) (2,25) (2,20) (2,7) (2,32) (2,22) (3,24) (3,19) (3,23) (3,4) (3,12) (3,29) (4,26) (4,24) (4,23) (4,8) (4,13) (5,26) (5,19) (5,23) (5,8) (5,15) (5,21) (6,14) (7,32) (8,16) (8,12) (8,29) (9,26) (9,13) (9,18) (9,29) (9,31) (10,17) (10,11) (10,30) (10,23) (10,13) (11,16) (11,17) (11,19) (11,28) (11,23) (12,26) (12,24) (12,21) (13,26) (13,17) (13,19) (13,30) (13,31) (14,25) (14,22) (15,16) (15,17) (15,23) (15,18) (15,29) (16,26) (16,24) (16,18) (16,21) (17,24) (17,19) (17,28) (17,30) (17,23) (18,24) (18,21) (19,26) (19,24) (19,28) (19,23) (20,32) (22,32) (22,27) (24,26) (24,30) (26,29) (28,29)\nQ: Is there a path between node 24 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "196"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,17) (0,13) (0,12) (0,4) (0,1) (1,3) (1,17) (1,16) (1,14) (1,4) (2,5) (2,7) (2,9) (2,11) (2,8) (3,15) (3,13) (3,16) (3,12) (3,14) (3,6) (4,15) (4,13) (4,16) (4,12) (4,6) (5,9) (5,11) (5,10) (6,17) (6,13) (6,12) (7,11) (7,10) (7,8) (8,9) (8,11) (9,10) (10,11) (12,15) (12,17) (12,16) (12,14) (13,17) (13,16) (14,15) (14,17) (15,17) (15,16) (16,17)\nQ: Is there a path between node 14 and node 12?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "197"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,18) (0,15) (0,12) (0,5) (1,24) (2,21) (2,23) (2,9) (2,15) (2,19) (3,23) (3,15) (3,8) (3,16) (5,21) (5,22) (5,6) (5,19) (5,8) (5,10) (5,16) (6,14) (6,22) (6,9) (6,12) (6,17) (9,23) (9,22) (9,20) (9,10) (10,22) (10,18) (10,19) (11,24) (12,14) (13,14) (13,21) (13,23) (13,18) (13,15) (14,21) (14,18) (14,15) (14,16) (15,20) (15,17) (17,23) (17,22) (17,18) (17,20) (17,19) (18,19) (19,20) (21,23)\nQ: Is there a path between node 15 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "198"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,10) (0,17) (0,5) (0,13) (0,15) (0,16) (0,3) (0,7) (0,11) (0,1) (0,4) (0,14) (1,12) (1,10) (1,17) (1,5) (1,13) (1,15) (1,16) (1,3) (1,7) (1,11) (1,4) (1,14) (2,8) (2,6) (3,12) (3,10) (3,17) (3,5) (3,13) (3,15) (3,16) (3,7) (3,11) (3,4) (3,14) (4,12) (4,10) (4,17) (4,5) (4,13) (4,15) (4,16) (4,7) (4,11) (4,14) (5,12) (5,10) (5,17) (5,13) (5,15) (5,16) (5,7) (5,11) (5,14) (6,8) (7,12) (7,10) (7,17) (7,13) (7,15) (7,16) (7,11) (7,14) (10,12) (10,17) (10,13) (10,15) (10,16) (10,11) (10,14) (11,12) (11,17) (11,13) (11,15) (11,16) (11,14) (12,17) (12,13) (12,15) (12,16) (12,14) (13,17) (13,15) (13,16) (13,14) (14,17) (14,15) (14,16) (15,17) (15,16) (16,17)\nQ: Is there a path between node 1 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "199"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,6) (0,4) (1,3) (1,7) (1,2) (2,3) (3,9) (4,6) (5,9) (6,8) (7,9)\nQ: Is there a path between node 7 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "200"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,8) (0,4) (0,5) (0,13) (0,2) (0,17) (1,15) (1,8) (1,3) (1,4) (1,5) (1,13) (1,17) (2,15) (2,8) (2,3) (2,4) (2,5) (2,13) (3,8) (3,5) (3,17) (4,15) (4,13) (4,17) (5,15) (5,8) (5,17) (6,14) (6,7) (6,10) (6,16) (6,9) (6,12) (7,14) (7,16) (7,9) (8,13) (9,14) (9,10) (9,11) (9,16) (9,12) (10,14) (10,12) (11,14) (11,12) (12,14) (12,16) (13,17) (15,17)\nQ: Is there a path between node 2 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "201"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (1,2)\nQ: Is there a path between node 1 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "202"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (1,15) (1,16) (2,18) (2,17) (2,7) (3,14) (3,7) (5,11) (6,13) (7,17) (8,15) (8,13) (9,17) (10,17) (13,15) (13,16) (16,19)\nQ: Is there a path between node 17 and node 18?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "203"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,21) (0,8) (0,11) (0,16) (0,13) (0,10) (0,20) (0,6) (0,4) (1,14) (1,17) (1,18) (1,5) (1,19) (1,2) (2,22) (2,14) (2,5) (3,8) (3,11) (3,10) (3,12) (3,6) (4,11) (4,13) (4,20) (4,12) (5,22) (5,14) (5,17) (5,18) (5,9) (5,19) (6,8) (6,11) (6,16) (6,13) (6,10) (6,20) (6,12) (7,15) (8,11) (8,13) (8,10) (8,20) (8,12) (9,22) (9,14) (9,17) (9,18) (9,19) (10,21) (10,13) (11,16) (11,13) (11,20) (11,12) (12,21) (12,16) (12,13) (12,20) (13,21) (13,16) (13,20) (14,22) (14,18) (16,21) (16,20) (17,22) (17,18) (17,19) (18,19) (20,21)\nQ: Is there a path between node 5 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "204"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,10) (0,13) (0,12) (0,9) (0,18) (0,24) (0,5) (0,20) (0,21) (0,7) (0,3) (0,23) (1,2) (1,13) (1,16) (1,12) (1,18) (1,24) (1,20) (1,4) (1,7) (1,3) (1,19) (1,23) (2,13) (2,16) (2,12) (2,9) (2,11) (2,18) (2,24) (2,5) (2,20) (2,4) (2,21) (2,7) (2,3) (2,23) (3,13) (3,16) (3,12) (3,9) (3,11) (3,24) (3,5) (3,20) (3,21) (3,7) (3,19) (3,23) (4,10) (4,16) (4,12) (4,11) (4,18) (4,24) (4,5) (4,20) (4,21) (4,7) (4,19) (4,23) (5,13) (5,12) (5,11) (5,18) (5,24) (5,20) (5,21) (5,7) (5,23) (6,15) (6,25) (6,22) (6,8) (7,13) (7,12) (7,9) (7,11) (7,18) (7,20) (7,21) (7,19) (8,17) (8,15) (8,22) (8,14) (9,10) (9,13) (9,16) (9,11) (9,18) (9,21) (9,19) (9,23) (10,13) (10,12) (10,11) (10,24) (10,20) (10,21) (10,19) (10,23) (11,13) (11,16) (11,24) (11,20) (11,21) (11,19) (11,23) (12,13) (12,16) (12,18) (12,24) (12,20) (12,21) (12,19) (12,23) (13,16) (13,24) (13,21) (13,23) (14,17) (14,15) (14,22) (15,17) (15,25) (15,22) (16,18) (16,24) (16,21) (16,23) (17,25) (17,22) (18,20) (18,21) (18,19) (18,23) (19,20) (19,23) (20,24) (20,21) (21,23) (22,25) (23,24)\nQ: Is there a path between node 25 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "205"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,17) (0,13) (0,12) (0,4) (0,1) (1,3) (1,17) (1,16) (1,14) (1,4) (2,5) (2,7) (2,9) (2,11) (2,8) (3,15) (3,13) (3,16) (3,12) (3,14) (3,6) (4,15) (4,13) (4,16) (4,12) (4,6) (5,9) (5,11) (5,10) (6,17) (6,13) (6,12) (7,11) (7,10) (7,8) (8,9) (8,11) (9,10) (10,11) (12,15) (12,17) (12,16) (12,14) (13,17) (13,16) (14,15) (14,17) (15,17) (15,16) (16,17)\nQ: Is there a path between node 5 and node 17?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "206"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,11) (0,2) (0,7) (0,8) (0,16) (0,15) (1,11) (1,2) (1,7) (1,8) (1,16) (1,15) (1,14) (2,4) (2,11) (2,5) (2,7) (2,12) (2,16) (2,15) (3,13) (3,10) (4,6) (4,5) (4,7) (4,8) (4,12) (4,16) (4,15) (4,14) (5,6) (5,7) (5,8) (5,12) (5,16) (5,14) (6,11) (6,7) (6,8) (6,12) (6,16) (6,15) (6,14) (7,11) (7,8) (7,16) (7,14) (8,11) (8,12) (8,16) (11,12) (11,16) (11,15) (11,14) (12,14) (14,16) (14,15)\nQ: Is there a path between node 4 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "207"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,23) (1,6) (1,19) (1,7) (2,17) (2,24) (2,10) (2,20) (3,22) (3,27) (4,17) (4,15) (5,19) (5,12) (5,25) (6,19) (6,7) (7,18) (7,23) (8,16) (8,13) (9,27) (9,13) (10,21) (10,15) (10,11) (11,17) (11,26) (11,24) (11,14) (12,25) (12,23) (14,17) (14,26) (15,21) (17,26) (17,21) (17,24) (20,21) (20,24) (21,26) (21,24) (23,25)\nQ: Is there a path between node 11 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "208"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,13) (1,6) (1,8) (1,3) (1,4) (2,5) (2,9) (3,12) (3,9) (3,13) (4,6) (4,10) (5,6) (5,9) (6,12) (6,8) (8,9) (9,10) (12,13)\nQ: Is there a path between node 1 and node 13?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "209"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,14) (0,5) (0,9) (0,8) (0,6) (0,21) (1,4) (1,15) (1,18) (1,11) (1,10) (1,12) (2,20) (2,14) (2,5) (2,9) (2,22) (2,6) (2,16) (3,9) (3,23) (3,22) (3,6) (3,21) (4,15) (4,11) (4,19) (4,13) (5,20) (5,14) (5,9) (5,8) (5,6) (5,21) (6,20) (6,14) (6,9) (6,23) (6,8) (6,16) (7,18) (7,11) (7,10) (7,12) (7,19) (7,13) (8,20) (8,14) (8,23) (8,21) (9,20) (9,23) (9,22) (9,21) (10,15) (10,18) (10,11) (10,12) (10,19) (10,13) (11,15) (11,13) (12,18) (12,19) (13,18) (13,19) (14,23) (14,22) (14,21) (15,19) (16,23) (16,22) (20,21) (22,23)\nQ: Is there a path between node 20 and node 22?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "210"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,11) (1,9) (1,19) (1,31) (1,20) (2,15) (2,11) (2,27) (2,29) (2,16) (2,31) (3,8) (3,4) (3,12) (3,18) (3,17) (3,10) (3,25) (3,31) (3,20) (4,30) (4,24) (4,19) (5,26) (5,23) (6,13) (7,15) (7,9) (7,30) (7,12) (7,16) (7,19) (7,10) (7,25) (8,15) (8,11) (8,30) (8,24) (8,10) (8,31) (9,11) (9,30) (9,27) (9,29) (9,10) (10,15) (10,30) (10,12) (10,18) (10,19) (10,17) (10,14) (11,30) (11,29) (11,19) (12,15) (12,19) (12,14) (12,20) (13,28) (14,27) (14,24) (14,20) (15,27) (15,18) (15,25) (15,20) (16,29) (16,24) (16,19) (17,29) (17,19) (17,31) (18,30) (18,24) (18,19) (18,31) (19,30) (19,25) (21,28) (21,23) (22,23) (25,27) (25,31) (26,28) (29,31)\nQ: Is there a path between node 7 and node 23?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "211"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,2) (3,5)\nQ: Is there a path between node 2 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "212"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (0,13) (0,22) (1,12) (1,6) (2,20) (2,14) (2,11) (3,5) (3,23) (3,6) (5,17) (6,19) (7,23) (8,13) (8,15) (9,21) (9,18) (12,24) (12,17) (12,19) (13,21) (13,18) (13,25) (13,15) (13,16) (15,16) (16,21) (16,25) (17,23) (17,19) (19,26) (21,22) (22,25)\nQ: Is there a path between node 16 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "213"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,19) (0,25) (0,2) (0,13) (0,1) (1,17) (1,24) (1,25) (1,11) (2,17) (2,25) (2,16) (2,13) (3,17) (4,23) (4,7) (4,14) (4,8) (5,18) (5,16) (6,18) (6,16) (6,21) (7,14) (7,15) (7,10) (8,23) (8,10) (9,14) (9,10) (10,23) (10,20) (11,17) (11,18) (11,25) (11,16) (11,13) (12,16) (13,17) (13,24) (13,25) (13,21) (14,15) (16,21) (17,19) (17,18) (17,25) (19,25) (19,21) (21,25)\nQ: Is there a path between node 19 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "214"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,3) (0,14) (1,8) (1,6) (1,14) (2,6) (2,12) (2,18) (3,8) (3,6) (3,12) (3,18) (4,12) (4,9) (4,14) (5,15) (5,16) (5,7) (6,8) (6,12) (6,14) (7,10) (9,11) (9,18) (15,17) (15,16)\nQ: Is there a path between node 12 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "215"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,13) (0,17) (0,10) (0,5) (0,4) (0,16) (0,19) (0,20) (0,7) (0,8) (0,15) (0,1) (0,18) (0,9) (0,12) (1,13) (1,17) (1,10) (1,5) (1,4) (1,16) (1,19) (1,20) (1,7) (1,8) (1,15) (1,18) (1,9) (1,12) (2,11) (2,21) (2,3) (2,14) (3,11) (3,21) (3,14) (4,13) (4,17) (4,10) (4,5) (4,16) (4,19) (4,20) (4,7) (4,8) (4,15) (4,18) (4,9) (4,12) (5,13) (5,17) (5,10) (5,16) (5,19) (5,20) (5,7) (5,8) (5,15) (5,18) (5,9) (5,12) (7,13) (7,17) (7,10) (7,16) (7,19) (7,20) (7,8) (7,15) (7,18) (7,9) (7,12) (8,13) (8,17) (8,10) (8,16) (8,19) (8,20) (8,15) (8,18) (8,9) (8,12) (9,13) (9,17) (9,10) (9,16) (9,19) (9,20) (9,15) (9,18) (9,12) (10,13) (10,17) (10,16) (10,19) (10,20) (10,15) (10,18) (10,12) (11,21) (11,14) (12,13) (12,17) (12,16) (12,19) (12,20) (12,15) (12,18) (13,17) (13,16) (13,19) (13,20) (13,15) (13,18) (14,21) (15,17) (15,16) (15,19) (15,20) (15,18) (16,17) (16,19) (16,20) (16,18) (17,19) (17,20) (17,18) (18,19) (18,20) (19,20)\nQ: Is there a path between node 14 and node 17?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "216"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,1) (0,13) (0,15) (0,16) (0,9) (0,14) (0,3) (0,12) (0,17) (0,2) (0,18) (1,11) (1,13) (1,15) (1,16) (1,9) (1,8) (1,14) (1,3) (1,4) (1,17) (1,18) (2,11) (2,13) (2,15) (2,9) (2,8) (2,14) (2,3) (2,12) (2,17) (2,18) (3,11) (3,13) (3,15) (3,16) (3,9) (3,8) (3,14) (3,12) (3,17) (3,18) (4,13) (4,15) (4,16) (4,8) (4,14) (4,12) (4,18) (5,6) (5,7) (5,10) (6,7) (6,10) (7,10) (8,11) (8,15) (8,16) (8,18) (9,11) (9,13) (9,15) (9,16) (9,14) (9,12) (9,17) (9,18) (11,13) (11,16) (11,17) (11,18) (12,15) (12,16) (12,17) (12,18) (13,15) (13,18) (14,15) (14,17) (15,16) (16,17) (16,18) (17,18)\nQ: Is there a path between node 17 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "217"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (1,12) (1,19) (2,13) (3,20) (3,11) (4,7) (4,16) (4,18) (5,17) (5,7) (6,15) (6,20) (6,11) (7,20) (7,11) (8,12) (8,13) (8,19) (11,17) (11,15) (12,19) (16,17) (16,20) (17,20) (18,20)\nQ: Is there a path between node 14 and node 20?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "218"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,6) (1,4) (1,3) (1,2) (1,7) (2,10) (2,4) (2,8) (3,10) (3,6) (3,4) (3,8) (3,5) (4,6) (4,8) (4,5) (4,7) (5,10) (5,8) (6,10) (6,8) (7,10)\nQ: Is there a path between node 10 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "219"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (1,14) (1,3) (1,9) (1,10) (1,4) (1,7) (1,6) (1,13) (1,12) (1,11) (2,15) (3,14) (3,8) (3,9) (3,10) (3,4) (3,12) (3,11) (4,8) (4,9) (4,10) (4,7) (4,5) (4,11) (5,9) (5,7) (5,13) (5,12) (5,11) (6,14) (6,8) (6,7) (6,13) (6,11) (7,8) (7,9) (7,10) (7,11) (8,14) (8,10) (8,12) (8,11) (9,14) (9,10) (9,13) (9,12) (10,14) (10,13) (10,12) (11,14) (11,13) (11,12) (12,14)\nQ: Is there a path between node 6 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "220"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,18) (0,17) (0,10) (1,7) (1,24) (1,27) (2,4) (2,8) (2,13) (2,19) (2,27) (3,16) (3,28) (3,9) (4,18) (4,6) (4,10) (4,11) (4,27) (6,20) (6,8) (6,7) (6,27) (7,8) (7,18) (7,17) (7,23) (7,24) (7,10) (7,13) (7,19) (7,11) (7,14) (8,17) (8,22) (8,24) (8,10) (8,11) (10,18) (10,17) (10,12) (10,11) (10,27) (11,17) (11,12) (12,20) (12,18) (12,17) (12,14) (13,20) (13,18) (13,24) (13,27) (13,26) (14,18) (15,28) (15,25) (16,25) (17,20) (17,18) (17,26) (18,22) (18,23) (18,19) (18,27) (19,23) (19,27) (19,26) (20,24) (22,23) (22,24) (22,26) (26,27)\nQ: Is there a path between node 1 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "221"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,9) (0,13) (0,3) (0,1) (0,2) (0,7) (0,8) (0,11) (1,14) (1,13) (1,8) (1,10) (1,11) (1,5) (2,9) (2,13) (2,3) (2,7) (2,8) (2,10) (3,14) (3,9) (3,13) (3,8) (3,11) (3,5) (4,6) (4,12) (5,14) (5,9) (5,7) (5,8) (5,10) (5,11) (6,12) (7,14) (7,13) (7,8) (7,10) (8,14) (8,9) (8,10) (9,14) (9,13) (10,14) (10,13) (11,14) (13,14)\nQ: Is there a path between node 14 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "222"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,18) (0,24) (0,5) (0,12) (0,26) (0,14) (0,16) (0,21) (0,9) (0,1) (0,28) (0,25) (1,3) (1,18) (1,24) (1,5) (1,12) (1,26) (1,14) (1,16) (1,21) (1,2) (1,23) (1,20) (1,28) (1,25) (2,3) (2,18) (2,10) (2,24) (2,5) (2,12) (2,26) (2,14) (2,16) (2,9) (2,23) (2,20) (2,28) (2,7) (2,25) (2,22) (2,13) (3,18) (3,24) (3,12) (3,26) (3,16) (3,9) (3,19) (3,7) (3,25) (3,22) (4,11) (4,27) (4,17) (4,15) (4,8) (5,18) (5,24) (5,12) (5,26) (5,14) (5,16) (5,21) (5,9) (5,23) (5,19) (5,20) (5,7) (5,13) (6,11) (6,27) (6,29) (6,15) (6,8) (7,18) (7,10) (7,12) (7,26) (7,14) (7,16) (7,21) (7,9) (7,20) (7,25) (7,22) (7,13) (8,11) (8,27) (8,29) (8,17) (8,15) (9,18) (9,10) (9,24) (9,16) (9,21) (9,19) (9,20) (9,28) (9,25) (9,13) (10,18) (10,24) (10,12) (10,26) (10,14) (10,16) (10,23) (10,20) (10,28) (10,25) (10,22) (10,13) (11,27) (11,29) (12,18) (12,24) (12,16) (12,21) (12,23) (12,20) (12,28) (12,22) (12,13) (13,18) (13,24) (13,26) (13,14) (13,16) (13,21) (13,23) (13,20) (13,28) (13,25) (13,22) (14,26) (14,16) (14,21) (14,23) (14,19) (14,20) (14,28) (14,25) (15,27) (15,17) (16,18) (16,24) (16,26) (16,20) (16,25) (16,22) (17,29) (18,24) (18,26) (18,23) (18,19) (18,20) (18,25) (18,22) (19,21) (19,23) (19,28) (19,25) (20,26) (20,23) (20,28) (20,25) (20,22) (21,26) (21,23) (21,28) (21,22) (22,26) (22,23) (22,25) (23,24) (23,26) (24,26) (24,28) (25,26)\nQ: Is there a path between node 3 and node 17?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "223"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,8) (0,4) (0,5) (0,13) (0,2) (0,17) (1,15) (1,8) (1,3) (1,4) (1,5) (1,13) (1,17) (2,15) (2,8) (2,3) (2,4) (2,5) (2,13) (3,8) (3,5) (3,17) (4,15) (4,13) (4,17) (5,15) (5,8) (5,17) (6,14) (6,7) (6,10) (6,16) (6,9) (6,12) (7,14) (7,16) (7,9) (8,13) (9,14) (9,10) (9,11) (9,16) (9,12) (10,14) (10,12) (11,14) (11,12) (12,14) (12,16) (13,17) (15,17)\nQ: Is there a path between node 11 and node 12?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "224"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,4) (0,9) (0,1) (0,11) (0,2) (1,10) (1,6) (1,9) (1,15) (1,13) (2,12) (2,9) (2,17) (2,15) (3,4) (3,6) (3,11) (4,12) (4,9) (4,11) (6,10) (6,12) (6,9) (6,15) (6,13) (8,12) (8,9) (8,15) (8,13) (9,10) (9,11) (10,13) (10,11) (11,13) (12,13) (14,16)\nQ: Is there a path between node 16 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "225"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,14) (1,21) (1,3) (1,15) (1,7) (3,12) (4,10) (5,10) (6,22) (7,21) (7,15) (9,12) (11,13) (11,21) (14,20) (15,17) (15,21) (16,18) (18,22)\nQ: Is there a path between node 5 and node 14?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "226"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,10) (0,13) (0,12) (0,9) (0,18) (0,24) (0,5) (0,20) (0,21) (0,7) (0,3) (0,23) (1,2) (1,13) (1,16) (1,12) (1,18) (1,24) (1,20) (1,4) (1,7) (1,3) (1,19) (1,23) (2,13) (2,16) (2,12) (2,9) (2,11) (2,18) (2,24) (2,5) (2,20) (2,4) (2,21) (2,7) (2,3) (2,23) (3,13) (3,16) (3,12) (3,9) (3,11) (3,24) (3,5) (3,20) (3,21) (3,7) (3,19) (3,23) (4,10) (4,16) (4,12) (4,11) (4,18) (4,24) (4,5) (4,20) (4,21) (4,7) (4,19) (4,23) (5,13) (5,12) (5,11) (5,18) (5,24) (5,20) (5,21) (5,7) (5,23) (6,15) (6,25) (6,22) (6,8) (7,13) (7,12) (7,9) (7,11) (7,18) (7,20) (7,21) (7,19) (8,17) (8,15) (8,22) (8,14) (9,10) (9,13) (9,16) (9,11) (9,18) (9,21) (9,19) (9,23) (10,13) (10,12) (10,11) (10,24) (10,20) (10,21) (10,19) (10,23) (11,13) (11,16) (11,24) (11,20) (11,21) (11,19) (11,23) (12,13) (12,16) (12,18) (12,24) (12,20) (12,21) (12,19) (12,23) (13,16) (13,24) (13,21) (13,23) (14,17) (14,15) (14,22) (15,17) (15,25) (15,22) (16,18) (16,24) (16,21) (16,23) (17,25) (17,22) (18,20) (18,21) (18,19) (18,23) (19,20) (19,23) (20,24) (20,21) (21,23) (22,25) (23,24)\nQ: Is there a path between node 7 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "227"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,4) (0,9) (0,12) (0,11) (0,5) (1,6) (1,17) (1,8) (1,15) (1,3) (1,2) (1,18) (1,19) (1,13) (1,14) (1,10) (2,6) (2,17) (2,8) (2,15) (2,3) (2,18) (2,19) (2,13) (2,14) (2,10) (3,6) (3,17) (3,8) (3,15) (3,18) (3,19) (3,13) (3,14) (3,10) (4,7) (4,9) (4,12) (4,11) (4,5) (5,7) (5,9) (5,12) (5,11) (6,17) (6,8) (6,15) (6,18) (6,19) (6,13) (6,14) (6,10) (7,9) (7,12) (7,11) (8,17) (8,15) (8,18) (8,19) (8,13) (8,14) (8,10) (9,12) (9,11) (10,17) (10,15) (10,18) (10,19) (10,13) (10,14) (11,12) (13,17) (13,15) (13,18) (13,19) (13,14) (14,17) (14,15) (14,18) (14,19) (15,17) (15,18) (15,19) (17,18) (17,19) (18,19)\nQ: Is there a path between node 4 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "228"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,24) (0,1) (0,6) (0,14) (1,10) (2,25) (2,5) (2,20) (2,18) (3,22) (3,6) (3,19) (3,23) (4,9) (4,18) (5,15) (5,25) (5,17) (5,20) (6,11) (6,24) (6,14) (6,7) (6,21) (7,24) (8,25) (8,17) (8,20) (8,18) (9,25) (10,24) (10,22) (10,21) (11,22) (11,19) (11,23) (12,15) (12,16) (12,17) (13,19) (13,14) (14,22) (14,19) (15,16) (15,18) (16,17) (17,20) (18,25) (19,24) (19,22) (20,25) (21,23) (22,24) (22,23)\nQ: Is there a path between node 7 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "229"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,28) (0,1) (0,22) (0,20) (0,15) (0,18) (0,2) (0,5) (0,10) (0,8) (0,14) (0,6) (1,27) (1,12) (1,19) (1,28) (1,25) (1,29) (1,22) (1,4) (1,7) (1,15) (1,18) (1,3) (1,2) (1,24) (1,5) (1,11) (1,14) (1,13) (1,6) (2,12) (2,19) (2,28) (2,29) (2,4) (2,15) (2,16) (2,18) (2,3) (2,10) (2,13) (2,21) (2,6) (3,27) (3,19) (3,28) (3,20) (3,4) (3,7) (3,16) (3,18) (3,9) (3,24) (3,5) (3,11) (3,10) (3,8) (3,14) (3,23) (3,21) (3,6) (4,27) (4,12) (4,19) (4,28) (4,25) (4,20) (4,7) (4,15) (4,16) (4,5) (4,8) (4,14) (4,13) (4,21) (4,6) (5,27) (5,12) (5,19) (5,28) (5,25) (5,29) (5,22) (5,20) (5,7) (5,15) (5,16) (5,24) (5,11) (5,10) (5,8) (5,14) (5,23) (5,13) (5,21) (5,6) (6,27) (6,12) (6,28) (6,25) (6,29) (6,22) (6,20) (6,7) (6,16) (6,18) (6,9) (6,24) (6,8) (6,14) (6,21) (7,19) (7,25) (7,29) (7,22) (7,20) (7,15) (7,16) (7,24) (7,11) (7,10) (7,14) (7,23) (7,21) (8,27) (8,12) (8,19) (8,29) (8,22) (8,20) (8,15) (8,16) (8,9) (8,24) (8,11) (8,10) (8,14) (8,13) (9,12) (9,19) (9,25) (9,22) (9,20) (9,18) (9,24) (9,11) (9,10) (9,14) (9,23) (9,13) (9,21) (10,27) (10,12) (10,19) (10,28) (10,25) (10,29) (10,16) (10,18) (10,24) (10,14) (10,23) (10,13) (10,21) (11,27) (11,12) (11,25) (11,22) (11,20) (11,18) (11,24) (12,19) (12,28) (12,29) (12,22) (12,15) (12,16) (12,18) (12,14) (12,23) (12,13) (12,21) (13,27) (13,28) (13,25) (13,29) (13,22) (13,20) (13,15) (13,18) (13,24) (14,19) (14,28) (14,25) (14,29) (14,15) (14,16) (14,18) (14,24) (14,23) (15,27) (15,28) (15,25) (15,29) (15,20) (15,18) (15,23) (15,21) (16,27) (16,19) (16,28) (16,25) (16,29) (16,22) (16,20) (16,18) (16,24) (16,21) (18,19) (18,28) (18,29) (18,22) (18,20) (18,24) (18,23) (18,21) (19,27) (19,28) (19,25) (19,29) (19,22) (19,20) (19,24) (19,23) (19,21) (20,27) (20,28) (20,29) (20,22) (20,23) (20,21) (21,27) (21,28) (21,24) (21,23) (22,27) (22,28) (22,29) (22,23) (23,27) (23,28) (23,25) (23,29) (24,27) (24,28) (24,25) (24,29) (25,27) (25,29) (27,28) (27,29)\nQ: Is there a path between node 24 and node 23?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "230"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,18) (0,15) (0,12) (0,5) (1,24) (2,21) (2,23) (2,9) (2,15) (2,19) (3,23) (3,15) (3,8) (3,16) (5,21) (5,22) (5,6) (5,19) (5,8) (5,10) (5,16) (6,14) (6,22) (6,9) (6,12) (6,17) (9,23) (9,22) (9,20) (9,10) (10,22) (10,18) (10,19) (11,24) (12,14) (13,14) (13,21) (13,23) (13,18) (13,15) (14,21) (14,18) (14,15) (14,16) (15,20) (15,17) (17,23) (17,22) (17,18) (17,20) (17,19) (18,19) (19,20) (21,23)\nQ: Is there a path between node 12 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "231"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,6) (0,1) (0,5) (1,7) (1,6) (1,8) (1,5) (2,7) (2,8) (2,5) (3,4) (5,7) (5,6) (5,8)\nQ: Is there a path between node 4 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "232"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (1,14) (1,3) (1,9) (1,10) (1,4) (1,7) (1,6) (1,13) (1,12) (1,11) (2,15) (3,14) (3,8) (3,9) (3,10) (3,4) (3,12) (3,11) (4,8) (4,9) (4,10) (4,7) (4,5) (4,11) (5,9) (5,7) (5,13) (5,12) (5,11) (6,14) (6,8) (6,7) (6,13) (6,11) (7,8) (7,9) (7,10) (7,11) (8,14) (8,10) (8,12) (8,11) (9,14) (9,10) (9,13) (9,12) (10,14) (10,13) (10,12) (11,14) (11,13) (11,12) (12,14)\nQ: Is there a path between node 6 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "233"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,13) (1,6) (1,8) (1,3) (1,4) (2,5) (2,9) (3,12) (3,9) (3,13) (4,6) (4,10) (5,6) (5,9) (6,12) (6,8) (8,9) (9,10) (12,13)\nQ: Is there a path between node 11 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "234"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (1,2) (1,5) (5,6)\nQ: Is there a path between node 6 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "235"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,10) (0,17) (0,5) (0,13) (0,15) (0,16) (0,3) (0,7) (0,11) (0,1) (0,4) (0,14) (1,12) (1,10) (1,17) (1,5) (1,13) (1,15) (1,16) (1,3) (1,7) (1,11) (1,4) (1,14) (2,8) (2,6) (3,12) (3,10) (3,17) (3,5) (3,13) (3,15) (3,16) (3,7) (3,11) (3,4) (3,14) (4,12) (4,10) (4,17) (4,5) (4,13) (4,15) (4,16) (4,7) (4,11) (4,14) (5,12) (5,10) (5,17) (5,13) (5,15) (5,16) (5,7) (5,11) (5,14) (6,8) (7,12) (7,10) (7,17) (7,13) (7,15) (7,16) (7,11) (7,14) (10,12) (10,17) (10,13) (10,15) (10,16) (10,11) (10,14) (11,12) (11,17) (11,13) (11,15) (11,16) (11,14) (12,17) (12,13) (12,15) (12,16) (12,14) (13,17) (13,15) (13,16) (13,14) (14,17) (14,15) (14,16) (15,17) (15,16) (16,17)\nQ: Is there a path between node 0 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "236"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,18) (0,17) (0,10) (1,7) (1,24) (1,27) (2,4) (2,8) (2,13) (2,19) (2,27) (3,16) (3,28) (3,9) (4,18) (4,6) (4,10) (4,11) (4,27) (6,20) (6,8) (6,7) (6,27) (7,8) (7,18) (7,17) (7,23) (7,24) (7,10) (7,13) (7,19) (7,11) (7,14) (8,17) (8,22) (8,24) (8,10) (8,11) (10,18) (10,17) (10,12) (10,11) (10,27) (11,17) (11,12) (12,20) (12,18) (12,17) (12,14) (13,20) (13,18) (13,24) (13,27) (13,26) (14,18) (15,28) (15,25) (16,25) (17,20) (17,18) (17,26) (18,22) (18,23) (18,19) (18,27) (19,23) (19,27) (19,26) (20,24) (22,23) (22,24) (22,26) (26,27)\nQ: Is there a path between node 28 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "237"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,1) (0,14) (0,18) (1,17) (1,14) (1,18) (2,19) (2,7) (2,10) (2,3) (2,12) (2,16) (2,11) (2,5) (2,9) (2,15) (2,6) (2,20) (2,8) (2,4) (2,13) (3,19) (3,7) (3,10) (3,12) (3,16) (3,11) (3,5) (3,9) (3,15) (3,6) (3,20) (3,8) (3,4) (3,13) (4,19) (4,7) (4,10) (4,12) (4,16) (4,11) (4,5) (4,9) (4,15) (4,6) (4,20) (4,8) (4,13) (5,19) (5,7) (5,10) (5,12) (5,16) (5,11) (5,9) (5,15) (5,6) (5,20) (5,8) (5,13) (6,19) (6,7) (6,10) (6,12) (6,16) (6,11) (6,9) (6,15) (6,20) (6,8) (6,13) (7,19) (7,10) (7,12) (7,16) (7,11) (7,9) (7,15) (7,20) (7,8) (7,13) (8,19) (8,10) (8,12) (8,16) (8,11) (8,9) (8,15) (8,20) (8,13) (9,19) (9,10) (9,12) (9,16) (9,11) (9,15) (9,20) (9,13) (10,19) (10,12) (10,16) (10,11) (10,15) (10,20) (10,13) (11,19) (11,12) (11,16) (11,15) (11,20) (11,13) (12,19) (12,16) (12,15) (12,20) (12,13) (13,19) (13,16) (13,15) (13,20) (14,17) (14,18) (15,19) (15,16) (15,20) (16,19) (16,20) (17,18) (19,20)\nQ: Is there a path between node 10 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "238"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,11) (0,15) (0,25) (0,31) (0,23) (0,14) (1,28) (1,20) (1,12) (1,21) (1,19) (1,24) (1,27) (1,13) (1,6) (2,20) (2,22) (2,21) (2,19) (2,13) (2,6) (3,15) (3,4) (3,25) (3,23) (4,9) (4,15) (4,14) (5,8) (5,17) (5,10) (5,26) (5,7) (5,16) (6,20) (6,21) (6,19) (6,27) (6,13) (7,17) (7,16) (7,29) (8,17) (9,11) (9,15) (9,31) (9,23) (9,14) (10,17) (11,15) (11,30) (11,23) (11,14) (12,20) (12,22) (12,19) (12,27) (12,13) (12,18) (13,28) (13,22) (13,21) (13,24) (13,27) (13,18) (14,15) (14,25) (14,31) (14,23) (15,25) (15,30) (15,23) (16,26) (17,26) (17,29) (18,28) (18,20) (18,22) (18,21) (18,19) (18,24) (18,27) (19,22) (19,21) (19,24) (19,27) (20,28) (20,22) (20,21) (20,24) (20,27) (21,28) (21,22) (21,24) (22,24) (22,27) (23,30) (23,31) (24,28) (25,31) (27,28) (30,31)\nQ: Is there a path between node 19 and node 20?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "239"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,6) (2,7) (2,6) (2,4) (5,7) (6,8)\nQ: Is there a path between node 2 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "240"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,19) (1,11) (2,4) (2,13) (3,17) (3,10) (3,11) (5,8) (5,13) (6,10) (6,12) (7,18) (7,9) (10,17) (10,12) (11,12) (12,17) (13,16) (13,15) (14,18)\nQ: Is there a path between node 10 and node 17?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "241"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,3) (0,4) (1,3) (1,4) (3,4)\nQ: Is there a path between node 4 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "242"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,11) (0,5) (0,9) (0,6) (1,2) (1,7) (1,3) (1,10) (1,8) (2,7) (2,3) (2,10) (2,8) (3,7) (3,10) (3,8) (4,11) (4,5) (4,9) (4,6) (5,11) (5,9) (5,6) (6,11) (6,9) (7,10) (7,8) (8,10) (9,11)\nQ: Is there a path between node 9 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "243"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,7) (0,8) (0,10) (0,3) (1,4) (1,11) (1,9) (1,6) (1,12) (1,2) (2,4) (2,11) (2,9) (2,6) (2,12) (3,5) (3,7) (3,8) (3,10) (4,11) (4,9) (4,6) (4,12) (5,7) (5,8) (5,10) (6,11) (6,9) (6,12) (7,8) (7,10) (8,10) (9,11) (9,12) (11,12)\nQ: Is there a path between node 1 and node 12?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "244"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,1) (0,14) (0,18) (1,17) (1,14) (1,18) (2,19) (2,7) (2,10) (2,3) (2,12) (2,16) (2,11) (2,5) (2,9) (2,15) (2,6) (2,20) (2,8) (2,4) (2,13) (3,19) (3,7) (3,10) (3,12) (3,16) (3,11) (3,5) (3,9) (3,15) (3,6) (3,20) (3,8) (3,4) (3,13) (4,19) (4,7) (4,10) (4,12) (4,16) (4,11) (4,5) (4,9) (4,15) (4,6) (4,20) (4,8) (4,13) (5,19) (5,7) (5,10) (5,12) (5,16) (5,11) (5,9) (5,15) (5,6) (5,20) (5,8) (5,13) (6,19) (6,7) (6,10) (6,12) (6,16) (6,11) (6,9) (6,15) (6,20) (6,8) (6,13) (7,19) (7,10) (7,12) (7,16) (7,11) (7,9) (7,15) (7,20) (7,8) (7,13) (8,19) (8,10) (8,12) (8,16) (8,11) (8,9) (8,15) (8,20) (8,13) (9,19) (9,10) (9,12) (9,16) (9,11) (9,15) (9,20) (9,13) (10,19) (10,12) (10,16) (10,11) (10,15) (10,20) (10,13) (11,19) (11,12) (11,16) (11,15) (11,20) (11,13) (12,19) (12,16) (12,15) (12,20) (12,13) (13,19) (13,16) (13,15) (13,20) (14,17) (14,18) (15,19) (15,16) (15,20) (16,19) (16,20) (17,18) (19,20)\nQ: Is there a path between node 8 and node 18?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "245"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,28) (0,1) (0,22) (0,20) (0,15) (0,18) (0,2) (0,5) (0,10) (0,8) (0,14) (0,6) (1,27) (1,12) (1,19) (1,28) (1,25) (1,29) (1,22) (1,4) (1,7) (1,15) (1,18) (1,3) (1,2) (1,24) (1,5) (1,11) (1,14) (1,13) (1,6) (2,12) (2,19) (2,28) (2,29) (2,4) (2,15) (2,16) (2,18) (2,3) (2,10) (2,13) (2,21) (2,6) (3,27) (3,19) (3,28) (3,20) (3,4) (3,7) (3,16) (3,18) (3,9) (3,24) (3,5) (3,11) (3,10) (3,8) (3,14) (3,23) (3,21) (3,6) (4,27) (4,12) (4,19) (4,28) (4,25) (4,20) (4,7) (4,15) (4,16) (4,5) (4,8) (4,14) (4,13) (4,21) (4,6) (5,27) (5,12) (5,19) (5,28) (5,25) (5,29) (5,22) (5,20) (5,7) (5,15) (5,16) (5,24) (5,11) (5,10) (5,8) (5,14) (5,23) (5,13) (5,21) (5,6) (6,27) (6,12) (6,28) (6,25) (6,29) (6,22) (6,20) (6,7) (6,16) (6,18) (6,9) (6,24) (6,8) (6,14) (6,21) (7,19) (7,25) (7,29) (7,22) (7,20) (7,15) (7,16) (7,24) (7,11) (7,10) (7,14) (7,23) (7,21) (8,27) (8,12) (8,19) (8,29) (8,22) (8,20) (8,15) (8,16) (8,9) (8,24) (8,11) (8,10) (8,14) (8,13) (9,12) (9,19) (9,25) (9,22) (9,20) (9,18) (9,24) (9,11) (9,10) (9,14) (9,23) (9,13) (9,21) (10,27) (10,12) (10,19) (10,28) (10,25) (10,29) (10,16) (10,18) (10,24) (10,14) (10,23) (10,13) (10,21) (11,27) (11,12) (11,25) (11,22) (11,20) (11,18) (11,24) (12,19) (12,28) (12,29) (12,22) (12,15) (12,16) (12,18) (12,14) (12,23) (12,13) (12,21) (13,27) (13,28) (13,25) (13,29) (13,22) (13,20) (13,15) (13,18) (13,24) (14,19) (14,28) (14,25) (14,29) (14,15) (14,16) (14,18) (14,24) (14,23) (15,27) (15,28) (15,25) (15,29) (15,20) (15,18) (15,23) (15,21) (16,27) (16,19) (16,28) (16,25) (16,29) (16,22) (16,20) (16,18) (16,24) (16,21) (18,19) (18,28) (18,29) (18,22) (18,20) (18,24) (18,23) (18,21) (19,27) (19,28) (19,25) (19,29) (19,22) (19,20) (19,24) (19,23) (19,21) (20,27) (20,28) (20,29) (20,22) (20,23) (20,21) (21,27) (21,28) (21,24) (21,23) (22,27) (22,28) (22,29) (22,23) (23,27) (23,28) (23,25) (23,29) (24,27) (24,28) (24,25) (24,29) (25,27) (25,29) (27,28) (27,29)\nQ: Is there a path between node 2 and node 19?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "246"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,7) (0,6) (0,8) (0,4) (0,1) (1,2) (1,7) (1,6) (1,8) (1,4) (2,7) (2,6) (2,8) (2,4) (3,5) (4,7) (4,6) (4,8) (6,7) (6,8) (7,8)\nQ: Is there a path between node 2 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "247"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,32) (0,29) (0,7) (0,15) (1,30) (1,10) (1,8) (2,27) (2,18) (2,20) (2,7) (2,26) (3,14) (3,9) (4,18) (4,11) (4,13) (4,15) (5,30) (5,21) (6,14) (6,21) (6,17) (7,18) (7,22) (7,31) (7,29) (7,26) (8,14) (8,10) (9,21) (10,12) (10,21) (10,17) (11,19) (11,22) (11,28) (11,32) (11,29) (11,15) (11,26) (12,30) (12,21) (13,27) (13,20) (13,28) (13,31) (14,17) (15,20) (15,31) (15,26) (16,27) (16,32) (17,30) (18,27) (18,28) (18,32) (18,26) (18,24) (18,23) (19,27) (19,20) (19,31) (19,29) (19,26) (19,24) (20,25) (20,28) (20,32) (20,26) (22,31) (22,23) (23,27) (23,28) (23,26) (25,26) (26,27) (26,28) (26,29) (28,32) (28,31) (29,31)\nQ: Is there a path between node 11 and node 22?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "248"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,13) (0,2) (0,15) (0,6) (0,17) (0,8) (0,16) (0,18) (0,9) (0,12) (0,11) (1,10) (1,14) (1,7) (1,5) (1,4) (2,3) (2,13) (2,15) (2,6) (2,17) (2,8) (2,16) (2,18) (2,9) (2,12) (2,11) (3,13) (3,15) (3,6) (3,17) (3,8) (3,16) (3,18) (3,9) (3,12) (3,11) (4,10) (4,14) (4,7) (4,5) (5,10) (5,14) (5,7) (6,13) (6,15) (6,17) (6,8) (6,16) (6,18) (6,9) (6,12) (6,11) (7,10) (7,14) (8,13) (8,15) (8,17) (8,16) (8,18) (8,9) (8,12) (8,11) (9,13) (9,15) (9,17) (9,16) (9,18) (9,12) (9,11) (10,14) (11,13) (11,15) (11,17) (11,16) (11,18) (11,12) (12,13) (12,15) (12,17) (12,16) (12,18) (13,15) (13,17) (13,16) (13,18) (15,17) (15,16) (15,18) (16,17) (16,18) (17,18)\nQ: Is there a path between node 6 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "249"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,3) (0,2) (0,9) (0,8) (1,6) (1,4) (2,7) (2,10) (2,3) (2,8) (2,5) (3,10) (3,9) (3,8) (4,6) (5,7) (5,10) (5,9) (7,8) (8,9)\nQ: Is there a path between node 9 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "250"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,11) (0,2) (0,7) (0,8) (0,16) (0,15) (1,11) (1,2) (1,7) (1,8) (1,16) (1,15) (1,14) (2,4) (2,11) (2,5) (2,7) (2,12) (2,16) (2,15) (3,13) (3,10) (4,6) (4,5) (4,7) (4,8) (4,12) (4,16) (4,15) (4,14) (5,6) (5,7) (5,8) (5,12) (5,16) (5,14) (6,11) (6,7) (6,8) (6,12) (6,16) (6,15) (6,14) (7,11) (7,8) (7,16) (7,14) (8,11) (8,12) (8,16) (11,12) (11,16) (11,15) (11,14) (12,14) (14,16) (14,15)\nQ: Is there a path between node 9 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "251"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,13) (0,12) (0,14) (0,8) (0,3) (0,6) (0,2) (0,9) (0,5) (1,10) (1,7) (1,11) (2,4) (2,13) (2,12) (2,14) (2,8) (2,3) (2,6) (2,9) (2,5) (3,4) (3,13) (3,12) (3,14) (3,8) (3,6) (3,9) (3,5) (4,13) (4,12) (4,14) (4,8) (4,6) (4,9) (4,5) (5,13) (5,12) (5,14) (5,8) (5,6) (5,9) (6,13) (6,12) (6,14) (6,8) (6,9) (7,10) (7,11) (8,13) (8,12) (8,14) (8,9) (9,13) (9,12) (9,14) (10,11) (12,13) (12,14) (13,14)\nQ: Is there a path between node 3 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "252"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (2,3) (2,5) (3,5) (4,6)\nQ: Is there a path between node 3 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "253"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,7) (0,6) (0,8) (0,4) (0,1) (1,2) (1,7) (1,6) (1,8) (1,4) (2,7) (2,6) (2,8) (2,4) (3,5) (4,7) (4,6) (4,8) (6,7) (6,8) (7,8)\nQ: Is there a path between node 0 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "254"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,27) (0,13) (0,10) (0,15) (0,2) (0,17) (1,5) (1,22) (1,8) (1,19) (1,26) (1,24) (1,18) (1,16) (1,14) (1,12) (1,4) (1,9) (2,7) (2,27) (2,13) (2,3) (2,6) (2,10) (2,11) (2,17) (3,7) (3,27) (3,20) (3,6) (3,10) (3,15) (3,21) (3,17) (4,5) (4,8) (4,19) (4,26) (4,25) (4,18) (4,14) (4,12) (5,8) (5,26) (5,18) (5,16) (5,14) (5,12) (6,7) (6,13) (6,10) (6,21) (7,20) (7,13) (7,10) (7,15) (7,11) (8,19) (8,26) (8,18) (8,16) (8,14) (8,9) (9,22) (9,19) (9,26) (9,25) (9,16) (9,14) (9,12) (10,13) (10,21) (10,17) (11,27) (11,13) (11,15) (11,21) (11,17) (12,22) (12,19) (12,26) (12,24) (12,25) (12,16) (12,14) (13,27) (13,15) (14,22) (14,19) (14,26) (15,27) (15,20) (15,21) (15,17) (16,22) (16,19) (16,24) (16,25) (16,18) (17,27) (17,20) (17,21) (18,22) (18,19) (18,26) (18,24) (19,26) (19,25) (20,27) (20,21) (21,27) (22,26) (22,24) (24,26)\nQ: Is there a path between node 5 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "255"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,12) (0,2) (0,3) (1,13) (1,22) (1,7) (1,11) (1,19) (1,6) (1,8) (2,14) (2,20) (2,3) (3,14) (3,20) (4,21) (4,18) (4,5) (4,17) (4,9) (4,15) (4,10) (5,21) (5,17) (5,9) (5,15) (5,10) (6,16) (6,13) (6,22) (6,7) (6,11) (6,19) (6,8) (7,16) (7,13) (7,22) (7,8) (8,16) (8,13) (8,11) (8,19) (9,18) (9,17) (9,15) (9,10) (10,21) (10,18) (11,16) (11,13) (11,22) (11,19) (12,14) (12,20) (13,16) (13,19) (14,20) (15,21) (15,18) (15,17) (16,22) (17,21) (17,18) (19,22)\nQ: Is there a path between node 7 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "256"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,14) (0,20) (0,13) (1,2) (1,8) (1,9) (2,9) (4,10) (4,20) (5,21) (5,17) (5,9) (6,10) (6,14) (6,13) (7,21) (7,22) (8,9) (10,19) (10,18) (10,12) (10,13) (11,16) (11,18) (12,16) (12,19) (12,18) (13,19) (14,19) (16,18) (17,22) (18,19)\nQ: Is there a path between node 14 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "257"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,1) (0,15) (0,6) (0,9) (0,4) (0,16) (0,19) (1,20) (1,15) (1,6) (1,9) (1,4) (1,16) (1,19) (2,14) (2,10) (2,3) (2,11) (2,7) (2,18) (2,5) (2,12) (2,17) (2,8) (3,14) (3,10) (3,11) (3,7) (3,18) (3,5) (3,12) (3,17) (3,8) (4,20) (4,15) (4,6) (4,9) (4,16) (4,19) (5,14) (5,10) (5,11) (5,7) (5,18) (5,12) (5,17) (5,8) (6,20) (6,15) (6,9) (6,16) (6,19) (7,14) (7,10) (7,11) (7,18) (7,12) (7,17) (7,8) (8,14) (8,10) (8,11) (8,18) (8,12) (8,17) (9,20) (9,15) (9,16) (9,19) (10,14) (10,11) (10,18) (10,12) (10,17) (11,14) (11,18) (11,12) (11,17) (12,14) (12,18) (12,17) (14,18) (14,17) (15,20) (15,16) (15,19) (16,20) (16,19) (17,18) (19,20)\nQ: Is there a path between node 3 and node 15?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "258"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,13) (1,6) (1,8) (1,3) (1,4) (2,5) (2,9) (3,12) (3,9) (3,13) (4,6) (4,10) (5,6) (5,9) (6,12) (6,8) (8,9) (9,10) (12,13)\nQ: Is there a path between node 4 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "259"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,2) (1,5) (1,2) (2,5) (2,10) (3,10) (3,4) (3,8) (4,5) (5,10) (5,8) (7,11) (8,10) (9,11)\nQ: Is there a path between node 6 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "260"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,5) (0,2) (0,3) (0,10) (0,6) (0,1) (0,4) (0,9) (0,7) (0,12) (1,8) (1,5) (1,2) (1,3) (1,10) (1,6) (1,4) (1,9) (1,7) (1,12) (2,8) (2,5) (2,3) (2,10) (2,6) (2,4) (2,9) (2,7) (2,12) (3,8) (3,5) (3,10) (3,6) (3,4) (3,9) (3,7) (3,12) (4,8) (4,5) (4,10) (4,6) (4,9) (4,7) (4,12) (5,8) (5,10) (5,6) (5,9) (5,7) (5,12) (6,8) (6,10) (6,9) (6,7) (6,12) (7,8) (7,10) (7,9) (7,12) (8,10) (8,9) (8,12) (9,10) (9,12) (10,12) (11,13)\nQ: Is there a path between node 12 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "261"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,17) (0,10) (0,28) (0,30) (0,29) (0,3) (1,14) (1,2) (2,25) (2,20) (2,7) (2,32) (2,22) (3,24) (3,19) (3,23) (3,4) (3,12) (3,29) (4,26) (4,24) (4,23) (4,8) (4,13) (5,26) (5,19) (5,23) (5,8) (5,15) (5,21) (6,14) (7,32) (8,16) (8,12) (8,29) (9,26) (9,13) (9,18) (9,29) (9,31) (10,17) (10,11) (10,30) (10,23) (10,13) (11,16) (11,17) (11,19) (11,28) (11,23) (12,26) (12,24) (12,21) (13,26) (13,17) (13,19) (13,30) (13,31) (14,25) (14,22) (15,16) (15,17) (15,23) (15,18) (15,29) (16,26) (16,24) (16,18) (16,21) (17,24) (17,19) (17,28) (17,30) (17,23) (18,24) (18,21) (19,26) (19,24) (19,28) (19,23) (20,32) (22,32) (22,27) (24,26) (24,30) (26,29) (28,29)\nQ: Is there a path between node 22 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "262"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,1) (2,3) (4,6) (5,6) (5,7)\nQ: Is there a path between node 7 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "263"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (0,13) (0,3) (0,14) (0,15) (0,19) (0,7) (0,9) (0,10) (1,5) (1,18) (1,12) (1,13) (1,14) (1,6) (1,17) (1,16) (1,9) (1,10) (1,11) (2,18) (2,12) (2,13) (2,6) (2,15) (2,19) (2,7) (2,17) (2,16) (2,9) (2,10) (2,11) (3,18) (3,12) (3,13) (3,14) (3,6) (3,19) (3,17) (3,9) (3,10) (3,11) (5,18) (5,12) (5,13) (5,14) (5,6) (5,15) (5,19) (5,7) (5,16) (5,11) (6,18) (6,12) (6,7) (6,17) (6,16) (6,9) (6,10) (7,18) (7,12) (7,13) (7,15) (7,19) (7,17) (7,16) (7,10) (7,11) (9,18) (9,13) (9,15) (9,19) (9,16) (9,10) (10,18) (10,13) (10,14) (10,19) (10,17) (10,11) (11,12) (11,13) (11,14) (11,15) (11,19) (11,17) (11,16) (12,14) (12,19) (12,17) (12,16) (13,18) (13,15) (13,19) (13,17) (14,18) (14,15) (14,19) (14,17) (14,16) (15,18) (15,19) (15,16) (16,18) (17,18) (17,19) (18,19)\nQ: Is there a path between node 4 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "264"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,14) (0,10) (0,24) (0,2) (0,12) (0,19) (0,3) (0,17) (0,25) (0,23) (0,15) (1,18) (1,11) (1,8) (2,14) (2,10) (2,24) (2,7) (2,3) (2,21) (2,25) (2,23) (2,6) (3,14) (3,24) (3,12) (3,19) (3,17) (3,25) (3,23) (3,6) (3,15) (4,18) (4,8) (5,18) (5,11) (5,8) (6,16) (6,14) (6,10) (6,12) (6,7) (6,19) (6,21) (6,25) (6,23) (6,9) (6,15) (7,16) (7,10) (7,24) (7,12) (7,19) (7,17) (7,25) (7,9) (7,15) (8,18) (8,11) (9,16) (9,14) (9,10) (9,24) (9,12) (9,19) (9,17) (9,21) (9,23) (9,15) (10,16) (10,14) (10,19) (10,21) (10,25) (10,23) (10,15) (11,18) (12,16) (12,14) (12,24) (12,19) (12,17) (12,21) (12,25) (12,23) (12,15) (13,20) (14,16) (14,24) (14,17) (14,21) (14,25) (14,23) (14,15) (15,16) (15,24) (15,23) (16,21) (16,25) (16,23) (17,21) (17,23) (19,21) (19,25) (21,24) (21,25) (21,23) (23,25) (24,25)\nQ: Is there a path between node 13 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "265"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,4) (1,5)\nQ: Is there a path between node 6 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "266"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,12) (1,25) (1,2) (1,10) (1,12) (1,3) (2,8) (2,22) (2,25) (2,26) (2,19) (2,11) (2,12) (2,7) (2,21) (3,25) (3,26) (3,10) (3,27) (3,21) (5,24) (5,6) (6,23) (6,9) (7,22) (7,25) (7,11) (8,20) (8,22) (8,25) (8,26) (8,27) (9,24) (10,14) (10,25) (10,13) (10,27) (10,21) (11,22) (11,12) (11,17) (11,21) (12,19) (12,18) (12,17) (12,27) (12,21) (13,17) (13,21) (14,17) (14,21) (15,23) (15,24) (16,22) (17,22) (17,25) (17,19) (18,20) (18,26) (18,21) (19,22) (19,26) (19,27) (20,27) (22,25) (25,26)\nQ: Is there a path between node 5 and node 17?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "267"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,4) (0,9) (0,5) (0,13) (1,14) (1,15) (1,12) (1,5) (1,7) (2,4) (2,6) (2,9) (2,12) (2,13) (4,11) (4,6) (4,15) (4,7) (4,8) (4,13) (5,11) (5,10) (5,14) (5,6) (5,9) (5,15) (5,12) (5,7) (5,13) (6,14) (7,14) (7,8) (9,13) (10,14) (12,15)\nQ: Is there a path between node 3 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "268"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,8) (0,10) (0,12) (0,13) (1,10) (2,5) (2,16) (3,13) (4,16) (5,7) (5,14) (6,7) (7,16) (7,14) (9,13) (10,15) (11,12) (12,15)\nQ: Is there a path between node 2 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "269"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,5) (0,7) (0,6) (0,2) (0,4) (0,8) (0,9) (1,10) (2,3) (2,5) (2,7) (2,6) (2,4) (2,8) (2,9) (2,11) (3,5) (3,4) (3,8) (3,11) (4,5) (4,6) (4,9) (4,11) (5,6) (5,8) (5,9) (6,7) (6,8) (6,9) (6,11) (7,8) (7,11) (8,9) (9,11)\nQ: Is there a path between node 10 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "270"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (1,14) (1,3) (1,9) (1,10) (1,4) (1,7) (1,6) (1,13) (1,12) (1,11) (2,15) (3,14) (3,8) (3,9) (3,10) (3,4) (3,12) (3,11) (4,8) (4,9) (4,10) (4,7) (4,5) (4,11) (5,9) (5,7) (5,13) (5,12) (5,11) (6,14) (6,8) (6,7) (6,13) (6,11) (7,8) (7,9) (7,10) (7,11) (8,14) (8,10) (8,12) (8,11) (9,14) (9,10) (9,13) (9,12) (10,14) (10,13) (10,12) (11,14) (11,13) (11,12) (12,14)\nQ: Is there a path between node 8 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "271"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,1) (0,14) (0,18) (1,17) (1,14) (1,18) (2,19) (2,7) (2,10) (2,3) (2,12) (2,16) (2,11) (2,5) (2,9) (2,15) (2,6) (2,20) (2,8) (2,4) (2,13) (3,19) (3,7) (3,10) (3,12) (3,16) (3,11) (3,5) (3,9) (3,15) (3,6) (3,20) (3,8) (3,4) (3,13) (4,19) (4,7) (4,10) (4,12) (4,16) (4,11) (4,5) (4,9) (4,15) (4,6) (4,20) (4,8) (4,13) (5,19) (5,7) (5,10) (5,12) (5,16) (5,11) (5,9) (5,15) (5,6) (5,20) (5,8) (5,13) (6,19) (6,7) (6,10) (6,12) (6,16) (6,11) (6,9) (6,15) (6,20) (6,8) (6,13) (7,19) (7,10) (7,12) (7,16) (7,11) (7,9) (7,15) (7,20) (7,8) (7,13) (8,19) (8,10) (8,12) (8,16) (8,11) (8,9) (8,15) (8,20) (8,13) (9,19) (9,10) (9,12) (9,16) (9,11) (9,15) (9,20) (9,13) (10,19) (10,12) (10,16) (10,11) (10,15) (10,20) (10,13) (11,19) (11,12) (11,16) (11,15) (11,20) (11,13) (12,19) (12,16) (12,15) (12,20) (12,13) (13,19) (13,16) (13,15) (13,20) (14,17) (14,18) (15,19) (15,16) (15,20) (16,19) (16,20) (17,18) (19,20)\nQ: Is there a path between node 11 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "272"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,17) (1,4) (2,10) (3,19) (3,30) (3,13) (3,25) (3,8) (4,31) (5,16) (6,29) (6,11) (6,32) (7,14) (7,17) (8,21) (8,30) (8,13) (8,28) (9,20) (9,25) (11,29) (11,26) (11,22) (13,21) (13,15) (13,28) (13,23) (15,31) (15,16) (15,28) (15,23) (16,21) (16,25) (16,23) (18,29) (18,24) (20,31) (20,30) (20,25) (21,25) (22,24) (23,25) (23,28) (24,29) (24,32) (25,30) (26,32) (28,30)\nQ: Is there a path between node 10 and node 22?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "273"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (1,24) (1,13) (1,7) (2,24) (2,15) (2,18) (2,8) (2,13) (2,7) (3,23) (3,6) (5,20) (5,14) (6,11) (6,23) (7,12) (7,10) (7,21) (7,8) (7,13) (8,10) (8,15) (8,18) (8,22) (8,13) (9,21) (9,13) (10,12) (10,15) (10,13) (12,24) (13,24) (13,22) (14,20) (15,24) (17,24) (19,20) (21,24)\nQ: Is there a path between node 16 and node 19?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "274"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,4) (0,9) (0,12) (0,11) (0,5) (1,6) (1,17) (1,8) (1,15) (1,3) (1,2) (1,18) (1,19) (1,13) (1,14) (1,10) (2,6) (2,17) (2,8) (2,15) (2,3) (2,18) (2,19) (2,13) (2,14) (2,10) (3,6) (3,17) (3,8) (3,15) (3,18) (3,19) (3,13) (3,14) (3,10) (4,7) (4,9) (4,12) (4,11) (4,5) (5,7) (5,9) (5,12) (5,11) (6,17) (6,8) (6,15) (6,18) (6,19) (6,13) (6,14) (6,10) (7,9) (7,12) (7,11) (8,17) (8,15) (8,18) (8,19) (8,13) (8,14) (8,10) (9,12) (9,11) (10,17) (10,15) (10,18) (10,19) (10,13) (10,14) (11,12) (13,17) (13,15) (13,18) (13,19) (13,14) (14,17) (14,15) (14,18) (14,19) (15,17) (15,18) (15,19) (17,18) (17,19) (18,19)\nQ: Is there a path between node 17 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "275"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,13) (0,8) (0,18) (0,25) (0,14) (0,17) (0,21) (1,13) (1,26) (1,14) (1,20) (1,17) (1,24) (1,6) (2,8) (2,18) (2,9) (2,26) (2,14) (2,10) (2,15) (3,16) (3,12) (4,13) (4,8) (4,18) (4,25) (4,6) (5,19) (5,13) (5,10) (5,20) (5,22) (5,17) (5,6) (6,8) (6,18) (6,9) (6,26) (6,14) (6,17) (6,21) (6,15) (6,23) (7,25) (7,14) (7,22) (7,24) (7,15) (7,23) (8,13) (8,25) (8,24) (8,23) (9,25) (9,27) (9,26) (9,14) (9,17) (9,24) (9,23) (10,19) (10,13) (10,25) (10,22) (11,12) (12,16) (13,19) (13,18) (13,21) (14,19) (14,18) (14,22) (15,19) (15,25) (15,23) (17,25) (17,22) (17,21) (17,24) (18,21) (18,24) (19,26) (19,22) (19,24) (19,23) (20,25) (20,26) (20,24) (20,23) (21,27) (21,23) (22,25) (22,26) (22,23) (25,27) (25,26)\nQ: Is there a path between node 22 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "276"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,14) (0,5) (0,9) (0,8) (0,6) (0,21) (1,4) (1,15) (1,18) (1,11) (1,10) (1,12) (2,20) (2,14) (2,5) (2,9) (2,22) (2,6) (2,16) (3,9) (3,23) (3,22) (3,6) (3,21) (4,15) (4,11) (4,19) (4,13) (5,20) (5,14) (5,9) (5,8) (5,6) (5,21) (6,20) (6,14) (6,9) (6,23) (6,8) (6,16) (7,18) (7,11) (7,10) (7,12) (7,19) (7,13) (8,20) (8,14) (8,23) (8,21) (9,20) (9,23) (9,22) (9,21) (10,15) (10,18) (10,11) (10,12) (10,19) (10,13) (11,15) (11,13) (12,18) (12,19) (13,18) (13,19) (14,23) (14,22) (14,21) (15,19) (16,23) (16,22) (20,21) (22,23)\nQ: Is there a path between node 11 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "277"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,13) (0,11) (0,21) (0,8) (0,18) (0,3) (0,7) (0,15) (0,20) (0,17) (0,10) (0,22) (0,1) (0,9) (0,6) (0,19) (1,23) (1,14) (1,5) (1,13) (1,11) (1,12) (1,21) (1,8) (1,18) (1,3) (1,25) (1,7) (1,28) (1,15) (1,20) (1,17) (1,10) (1,22) (1,9) (1,6) (1,16) (1,19) (3,27) (3,14) (3,5) (3,13) (3,4) (3,21) (3,18) (3,25) (3,28) (3,15) (3,20) (3,17) (3,22) (3,6) (3,16) (3,19) (4,27) (4,23) (4,5) (4,13) (4,11) (4,12) (4,8) (4,28) (4,15) (4,20) (4,17) (4,10) (4,24) (4,6) (5,27) (5,23) (5,14) (5,13) (5,11) (5,12) (5,21) (5,8) (5,18) (5,25) (5,7) (5,15) (5,10) (5,22) (5,24) (5,9) (5,6) (5,16) (5,19) (6,27) (6,14) (6,11) (6,12) (6,18) (6,25) (6,7) (6,20) (6,17) (6,10) (6,22) (6,24) (6,9) (6,16) (6,19) (7,23) (7,14) (7,13) (7,12) (7,21) (7,8) (7,25) (7,28) (7,20) (7,10) (7,22) (7,16) (7,19) (8,27) (8,13) (8,18) (8,25) (8,15) (8,17) (8,10) (8,22) (8,24) (8,9) (8,16) (8,19) (9,27) (9,23) (9,11) (9,21) (9,25) (9,28) (9,15) (9,20) (9,17) (9,10) (9,22) (9,24) (9,16) (9,19) (10,27) (10,14) (10,11) (10,12) (10,25) (10,28) (10,15) (10,20) (10,17) (10,24) (10,16) (10,19) (11,23) (11,21) (11,18) (11,25) (11,28) (11,15) (11,17) (11,22) (11,24) (11,19) (12,27) (12,23) (12,13) (12,21) (12,18) (12,25) (12,28) (12,15) (12,17) (12,22) (12,24) (12,16) (13,27) (13,14) (13,21) (13,18) (13,28) (13,15) (13,17) (13,24) (13,16) (13,19) (14,27) (14,25) (14,28) (14,15) (14,17) (14,22) (14,24) (14,16) (15,23) (15,21) (15,18) (15,25) (15,20) (15,24) (16,27) (16,23) (16,17) (16,24) (16,19) (17,27) (17,23) (17,18) (17,25) (17,28) (17,20) (17,22) (17,24) (17,19) (18,23) (18,21) (18,25) (18,28) (18,20) (18,22) (18,24) (18,19) (19,27) (19,23) (19,21) (19,25) (19,24) (20,27) (20,23) (20,21) (20,25) (20,24) (21,23) (21,22) (23,27) (23,24) (25,27) (25,28) (27,28)\nQ: Is there a path between node 10 and node 25?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "278"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,13) (0,30) (0,1) (0,4) (0,2) (0,22) (1,30) (1,17) (1,5) (1,4) (1,25) (1,29) (2,3) (2,5) (2,23) (3,28) (3,24) (3,4) (3,6) (3,8) (3,12) (4,15) (4,24) (4,25) (4,7) (4,6) (4,29) (5,21) (5,23) (5,7) (5,12) (6,20) (6,28) (6,23) (7,13) (7,15) (7,16) (7,8) (7,12) (8,20) (8,30) (8,24) (8,17) (8,23) (10,19) (11,19) (11,26) (12,20) (12,16) (12,25) (12,18) (13,28) (13,18) (14,20) (15,28) (15,24) (15,23) (16,20) (16,30) (16,24) (16,29) (17,21) (17,28) (17,25) (18,21) (18,23) (18,29) (20,24) (20,23) (20,22) (20,29) (21,25) (21,23) (21,22) (22,25) (23,24) (23,29) (24,28) (24,29) (25,28) (26,27) (29,30)\nQ: Is there a path between node 8 and node 27?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "279"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,12) (0,2) (0,3) (1,13) (1,22) (1,7) (1,11) (1,19) (1,6) (1,8) (2,14) (2,20) (2,3) (3,14) (3,20) (4,21) (4,18) (4,5) (4,17) (4,9) (4,15) (4,10) (5,21) (5,17) (5,9) (5,15) (5,10) (6,16) (6,13) (6,22) (6,7) (6,11) (6,19) (6,8) (7,16) (7,13) (7,22) (7,8) (8,16) (8,13) (8,11) (8,19) (9,18) (9,17) (9,15) (9,10) (10,21) (10,18) (11,16) (11,13) (11,22) (11,19) (12,14) (12,20) (13,16) (13,19) (14,20) (15,21) (15,18) (15,17) (16,22) (17,21) (17,18) (19,22)\nQ: Is there a path between node 5 and node 17?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "280"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,5) (0,1) (0,9) (0,3) (0,4) (1,6) (1,5) (1,9) (1,3) (1,4) (2,7) (2,8) (2,10) (3,6) (3,5) (3,9) (3,4) (4,6) (4,5) (4,9) (5,6) (5,9) (6,9) (7,8) (7,10) (8,10)\nQ: Is there a path between node 1 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "281"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,7) (0,6) (0,8) (0,4) (0,1) (1,2) (1,7) (1,6) (1,8) (1,4) (2,7) (2,6) (2,8) (2,4) (3,5) (4,7) (4,6) (4,8) (6,7) (6,8) (7,8)\nQ: Is there a path between node 2 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "282"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,20) (0,8) (0,31) (0,22) (1,4) (1,24) (1,19) (1,16) (1,5) (1,2) (1,8) (1,18) (1,27) (2,4) (2,19) (2,12) (2,17) (2,21) (2,31) (2,22) (3,25) (3,20) (3,14) (3,31) (3,22) (3,27) (4,7) (4,21) (4,26) (4,27) (5,11) (5,24) (5,20) (5,19) (5,12) (5,16) (5,17) (5,21) (5,9) (5,22) (6,15) (7,24) (7,20) (7,19) (7,16) (7,29) (7,17) (7,21) (7,14) (7,9) (7,8) (7,18) (7,22) (7,30) (8,20) (8,12) (8,14) (9,20) (9,16) (9,14) (9,18) (9,26) (9,23) (10,15) (11,25) (11,28) (11,20) (11,21) (11,26) (12,28) (12,24) (12,20) (12,29) (12,14) (12,18) (12,26) (12,22) (12,27) (12,23) (14,24) (14,16) (14,18) (14,31) (16,25) (16,26) (16,31) (16,23) (17,31) (17,27) (18,25) (18,28) (18,24) (18,21) (18,26) (18,27) (19,29) (19,21) (19,22) (20,25) (20,21) (20,26) (21,24) (21,29) (21,31) (21,23) (22,29) (22,26) (22,23) (23,25) (23,26) (24,25) (24,26) (24,30) (25,29) (25,31) (26,29) (26,31) (27,28) (27,31) (28,29) (29,31) (29,30) (30,31)\nQ: Is there a path between node 6 and node 27?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "283"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,2) (0,4) (0,5) (0,15) (0,7) (1,9) (1,13) (1,12) (1,3) (2,14) (2,10) (2,4) (2,8) (2,15) (2,7) (3,9) (3,13) (3,12) (3,11) (4,14) (4,6) (4,10) (4,8) (4,15) (5,6) (5,8) (5,7) (6,14) (6,8) (6,15) (7,14) (7,10) (7,8) (7,15) (8,14) (8,10) (8,15) (9,13) (9,12) (9,11) (10,14) (10,15) (11,13) (11,12) (12,13) (14,15)\nQ: Is there a path between node 7 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "284"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,11) (0,5) (0,9) (0,6) (1,2) (1,7) (1,3) (1,10) (1,8) (2,7) (2,3) (2,10) (2,8) (3,7) (3,10) (3,8) (4,11) (4,5) (4,9) (4,6) (5,11) (5,9) (5,6) (6,11) (6,9) (7,10) (7,8) (8,10) (9,11)\nQ: Is there a path between node 4 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "285"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,13) (0,2) (0,14) (0,23) (0,8) (0,1) (0,25) (0,27) (0,10) (1,29) (1,13) (1,19) (1,28) (1,23) (1,30) (1,25) (1,24) (2,12) (2,5) (2,14) (2,17) (2,23) (3,7) (3,12) (3,19) (3,23) (3,8) (3,30) (3,25) (3,24) (4,33) (5,20) (5,23) (5,30) (6,15) (6,11) (7,32) (7,17) (7,23) (7,8) (7,10) (8,29) (8,12) (8,32) (8,20) (8,19) (8,17) (8,30) (9,29) (9,28) (9,30) (9,24) (10,13) (10,20) (10,14) (10,22) (11,31) (12,13) (12,23) (12,27) (12,26) (13,29) (13,32) (13,14) (13,28) (13,30) (13,24) (14,17) (14,30) (14,22) (14,27) (15,16) (15,31) (15,33) (17,32) (17,20) (17,19) (17,27) (17,24) (17,26) (18,21) (20,28) (20,30) (20,25) (21,31) (22,32) (22,28) (22,30) (23,28) (23,25) (23,27) (24,29) (24,28) (24,26) (25,32) (26,29) (26,27) (27,32) (27,30) (28,32) (28,30)\nQ: Is there a path between node 16 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "286"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (3,8) (3,9) (4,5) (8,9)\nQ: Is there a path between node 8 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "287"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (0,13) (0,3) (0,14) (0,15) (0,19) (0,7) (0,9) (0,10) (1,5) (1,18) (1,12) (1,13) (1,14) (1,6) (1,17) (1,16) (1,9) (1,10) (1,11) (2,18) (2,12) (2,13) (2,6) (2,15) (2,19) (2,7) (2,17) (2,16) (2,9) (2,10) (2,11) (3,18) (3,12) (3,13) (3,14) (3,6) (3,19) (3,17) (3,9) (3,10) (3,11) (5,18) (5,12) (5,13) (5,14) (5,6) (5,15) (5,19) (5,7) (5,16) (5,11) (6,18) (6,12) (6,7) (6,17) (6,16) (6,9) (6,10) (7,18) (7,12) (7,13) (7,15) (7,19) (7,17) (7,16) (7,10) (7,11) (9,18) (9,13) (9,15) (9,19) (9,16) (9,10) (10,18) (10,13) (10,14) (10,19) (10,17) (10,11) (11,12) (11,13) (11,14) (11,15) (11,19) (11,17) (11,16) (12,14) (12,19) (12,17) (12,16) (13,18) (13,15) (13,19) (13,17) (14,18) (14,15) (14,19) (14,17) (14,16) (15,18) (15,19) (15,16) (16,18) (17,18) (17,19) (18,19)\nQ: Is there a path between node 17 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "288"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,13) (0,17) (0,10) (0,5) (0,4) (0,16) (0,19) (0,20) (0,7) (0,8) (0,15) (0,1) (0,18) (0,9) (0,12) (1,13) (1,17) (1,10) (1,5) (1,4) (1,16) (1,19) (1,20) (1,7) (1,8) (1,15) (1,18) (1,9) (1,12) (2,11) (2,21) (2,3) (2,14) (3,11) (3,21) (3,14) (4,13) (4,17) (4,10) (4,5) (4,16) (4,19) (4,20) (4,7) (4,8) (4,15) (4,18) (4,9) (4,12) (5,13) (5,17) (5,10) (5,16) (5,19) (5,20) (5,7) (5,8) (5,15) (5,18) (5,9) (5,12) (7,13) (7,17) (7,10) (7,16) (7,19) (7,20) (7,8) (7,15) (7,18) (7,9) (7,12) (8,13) (8,17) (8,10) (8,16) (8,19) (8,20) (8,15) (8,18) (8,9) (8,12) (9,13) (9,17) (9,10) (9,16) (9,19) (9,20) (9,15) (9,18) (9,12) (10,13) (10,17) (10,16) (10,19) (10,20) (10,15) (10,18) (10,12) (11,21) (11,14) (12,13) (12,17) (12,16) (12,19) (12,20) (12,15) (12,18) (13,17) (13,16) (13,19) (13,20) (13,15) (13,18) (14,21) (15,17) (15,16) (15,19) (15,20) (15,18) (16,17) (16,19) (16,20) (16,18) (17,19) (17,20) (17,18) (18,19) (18,20) (19,20)\nQ: Is there a path between node 19 and node 18?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "289"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,15) (1,3) (1,20) (2,11) (3,12) (3,6) (3,16) (3,20) (5,14) (5,7) (6,20) (6,21) (7,13) (7,18) (8,14) (8,13) (9,12) (9,16) (9,21) (10,21) (11,17) (12,16) (14,18) (15,16) (15,21) (16,20) (20,21)\nQ: Is there a path between node 6 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "290"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,3) (0,7) (0,10) (0,13) (0,12) (0,16) (1,14) (1,2) (1,5) (1,9) (1,8) (1,15) (1,4) (1,6) (2,14) (2,5) (2,9) (2,8) (2,15) (2,4) (2,6) (3,11) (3,7) (3,10) (3,13) (3,12) (3,16) (4,14) (4,5) (4,9) (4,8) (4,15) (4,6) (5,14) (5,9) (5,8) (5,15) (5,6) (6,14) (6,9) (6,8) (6,15) (7,11) (7,10) (7,13) (7,12) (7,16) (8,14) (8,9) (8,15) (9,14) (9,15) (10,11) (10,13) (10,12) (10,16) (11,13) (11,12) (11,16) (12,13) (12,16) (13,16) (14,15)\nQ: Is there a path between node 2 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "291"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,34) (0,1) (0,10) (0,12) (1,12) (2,24) (3,31) (3,30) (3,25) (4,19) (4,6) (5,8) (7,26) (10,20) (10,28) (10,17) (10,18) (12,20) (12,32) (12,17) (13,14) (13,15) (13,21) (13,26) (13,23) (14,15) (14,21) (15,26) (15,23) (16,21) (16,30) (17,20) (17,27) (17,32) (18,27) (18,34) (19,33) (20,27) (21,31) (21,22) (22,26) (22,31) (23,31) (26,31) (28,34) (30,31)\nQ: Is there a path between node 18 and node 28?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "292"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,11) (1,9) (1,19) (1,31) (1,20) (2,15) (2,11) (2,27) (2,29) (2,16) (2,31) (3,8) (3,4) (3,12) (3,18) (3,17) (3,10) (3,25) (3,31) (3,20) (4,30) (4,24) (4,19) (5,26) (5,23) (6,13) (7,15) (7,9) (7,30) (7,12) (7,16) (7,19) (7,10) (7,25) (8,15) (8,11) (8,30) (8,24) (8,10) (8,31) (9,11) (9,30) (9,27) (9,29) (9,10) (10,15) (10,30) (10,12) (10,18) (10,19) (10,17) (10,14) (11,30) (11,29) (11,19) (12,15) (12,19) (12,14) (12,20) (13,28) (14,27) (14,24) (14,20) (15,27) (15,18) (15,25) (15,20) (16,29) (16,24) (16,19) (17,29) (17,19) (17,31) (18,30) (18,24) (18,19) (18,31) (19,30) (19,25) (21,28) (21,23) (22,23) (25,27) (25,31) (26,28) (29,31)\nQ: Is there a path between node 28 and node 24?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "293"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,1) (3,4)\nQ: Is there a path between node 3 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "294"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,6) (0,3) (0,18) (0,1) (0,15) (0,12) (0,14) (0,9) (0,16) (0,8) (0,2) (0,11) (0,19) (1,7) (1,6) (1,3) (1,18) (1,15) (1,9) (1,8) (1,2) (1,20) (2,7) (2,3) (2,18) (2,15) (2,12) (2,14) (2,9) (2,16) (2,8) (2,11) (2,19) (2,20) (3,18) (3,15) (3,12) (3,9) (3,16) (3,8) (3,19) (3,20) (4,13) (4,17) (5,17) (6,7) (6,18) (6,15) (6,14) (6,9) (6,16) (6,11) (6,19) (6,20) (7,15) (7,12) (7,14) (7,9) (7,16) (8,18) (8,12) (8,14) (8,9) (8,16) (8,11) (8,19) (8,20) (9,18) (9,15) (9,12) (9,11) (9,19) (9,20) (10,13) (11,18) (11,12) (11,14) (11,16) (11,19) (11,20) (12,18) (12,15) (12,14) (12,19) (12,20) (13,17) (14,19) (16,18) (16,19) (18,20)\nQ: Is there a path between node 0 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "295"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,1) (2,3) (4,6) (5,6) (5,7)\nQ: Is there a path between node 9 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "296"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,13) (0,12) (0,14) (0,8) (0,3) (0,6) (0,2) (0,9) (0,5) (1,10) (1,7) (1,11) (2,4) (2,13) (2,12) (2,14) (2,8) (2,3) (2,6) (2,9) (2,5) (3,4) (3,13) (3,12) (3,14) (3,8) (3,6) (3,9) (3,5) (4,13) (4,12) (4,14) (4,8) (4,6) (4,9) (4,5) (5,13) (5,12) (5,14) (5,8) (5,6) (5,9) (6,13) (6,12) (6,14) (6,8) (6,9) (7,10) (7,11) (8,13) (8,12) (8,14) (8,9) (9,13) (9,12) (9,14) (10,11) (12,13) (12,14) (13,14)\nQ: Is there a path between node 0 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "297"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,1) (1,12) (1,15) (2,9) (2,6) (3,10) (3,17) (3,15) (5,7) (6,10) (6,9) (6,11) (7,13) (8,17) (8,16) (10,15) (11,12) (15,17)\nQ: Is there a path between node 12 and node 17?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "298"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,13) (0,1) (0,9) (0,5) (0,7) (0,3) (0,10) (0,23) (0,26) (0,27) (0,8) (0,14) (0,22) (0,20) (0,15) (0,4) (0,2) (1,25) (1,11) (1,21) (1,13) (1,9) (1,3) (1,10) (1,23) (1,26) (1,27) (1,14) (1,20) (1,15) (1,2) (1,28) (2,25) (2,11) (2,16) (2,21) (2,6) (2,13) (2,9) (2,7) (2,23) (2,26) (2,8) (2,20) (2,15) (3,25) (3,6) (3,13) (3,9) (3,10) (3,27) (3,20) (3,15) (3,4) (3,28) (4,11) (4,16) (4,6) (4,13) (4,10) (4,23) (4,26) (4,27) (4,8) (4,14) (4,22) (4,15) (4,28) (5,25) (5,16) (5,21) (5,6) (5,13) (5,9) (5,7) (5,26) (5,8) (5,22) (5,15) (5,28) (6,11) (6,16) (6,21) (6,13) (6,9) (6,7) (6,10) (6,27) (6,22) (6,20) (6,15) (7,25) (7,16) (7,21) (7,9) (7,10) (7,27) (7,8) (7,14) (7,22) (7,20) (7,15) (7,28) (8,25) (8,13) (8,23) (8,26) (8,27) (8,14) (8,20) (8,28) (9,25) (9,11) (9,16) (9,21) (9,10) (9,23) (9,26) (9,27) (9,22) (9,20) (9,28) (10,11) (10,16) (10,21) (10,13) (10,23) (10,26) (10,27) (10,14) (10,22) (10,20) (10,15) (10,28) (11,25) (11,16) (11,21) (11,13) (11,23) (11,26) (11,27) (11,14) (11,22) (11,20) (12,24) (12,19) (13,25) (13,16) (13,14) (13,22) (13,15) (13,28) (14,25) (14,21) (14,23) (14,26) (14,20) (14,15) (15,16) (15,21) (15,26) (15,27) (15,22) (15,28) (16,21) (16,23) (16,26) (16,27) (16,28) (17,18) (20,25) (20,23) (20,26) (20,27) (20,22) (20,28) (21,25) (21,23) (21,26) (21,22) (22,25) (22,23) (22,27) (23,25) (23,26) (23,27) (23,28) (25,26) (25,27) (26,27) (27,28)\nQ: Is there a path between node 27 and node 19?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "299"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,6) (0,21) (0,18) (1,24) (1,3) (3,24) (3,14) (4,6) (4,5) (4,23) (6,14) (6,21) (6,23) (7,11) (8,19) (8,13) (9,15) (9,19) (10,11) (10,12) (10,16) (10,17) (11,12) (11,16) (12,17) (13,15) (13,22) (14,23) (15,22) (16,17) (18,24) (18,21)\nQ: Is there a path between node 21 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "300"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,16) (0,22) (0,4) (0,15) (0,9) (1,8) (1,17) (1,12) (1,3) (1,5) (1,21) (1,6) (1,13) (1,19) (2,20) (2,16) (2,22) (2,4) (2,9) (3,8) (3,17) (3,14) (3,6) (3,10) (3,19) (4,20) (4,16) (4,22) (4,15) (4,9) (5,8) (5,17) (5,12) (5,14) (5,13) (5,10) (5,19) (6,17) (6,12) (6,14) (6,21) (6,13) (6,10) (6,19) (8,17) (8,12) (8,13) (8,19) (9,20) (9,22) (9,15) (10,17) (10,14) (10,21) (11,18) (11,23) (12,17) (12,21) (12,13) (12,19) (13,17) (13,14) (13,21) (15,20) (16,22) (17,21) (18,23)\nQ: Is there a path between node 21 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "301"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,11) (0,2) (0,7) (0,8) (0,16) (0,15) (1,11) (1,2) (1,7) (1,8) (1,16) (1,15) (1,14) (2,4) (2,11) (2,5) (2,7) (2,12) (2,16) (2,15) (3,13) (3,10) (4,6) (4,5) (4,7) (4,8) (4,12) (4,16) (4,15) (4,14) (5,6) (5,7) (5,8) (5,12) (5,16) (5,14) (6,11) (6,7) (6,8) (6,12) (6,16) (6,15) (6,14) (7,11) (7,8) (7,16) (7,14) (8,11) (8,12) (8,16) (11,12) (11,16) (11,15) (11,14) (12,14) (14,16) (14,15)\nQ: Is there a path between node 7 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "302"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,1) (0,15) (0,6) (0,9) (0,4) (0,16) (0,19) (1,20) (1,15) (1,6) (1,9) (1,4) (1,16) (1,19) (2,14) (2,10) (2,3) (2,11) (2,7) (2,18) (2,5) (2,12) (2,17) (2,8) (3,14) (3,10) (3,11) (3,7) (3,18) (3,5) (3,12) (3,17) (3,8) (4,20) (4,15) (4,6) (4,9) (4,16) (4,19) (5,14) (5,10) (5,11) (5,7) (5,18) (5,12) (5,17) (5,8) (6,20) (6,15) (6,9) (6,16) (6,19) (7,14) (7,10) (7,11) (7,18) (7,12) (7,17) (7,8) (8,14) (8,10) (8,11) (8,18) (8,12) (8,17) (9,20) (9,15) (9,16) (9,19) (10,14) (10,11) (10,18) (10,12) (10,17) (11,14) (11,18) (11,12) (11,17) (12,14) (12,18) (12,17) (14,18) (14,17) (15,20) (15,16) (15,19) (16,20) (16,19) (17,18) (19,20)\nQ: Is there a path between node 18 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "303"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,16) (0,22) (0,4) (0,15) (0,9) (1,8) (1,17) (1,12) (1,3) (1,5) (1,21) (1,6) (1,13) (1,19) (2,20) (2,16) (2,22) (2,4) (2,9) (3,8) (3,17) (3,14) (3,6) (3,10) (3,19) (4,20) (4,16) (4,22) (4,15) (4,9) (5,8) (5,17) (5,12) (5,14) (5,13) (5,10) (5,19) (6,17) (6,12) (6,14) (6,21) (6,13) (6,10) (6,19) (8,17) (8,12) (8,13) (8,19) (9,20) (9,22) (9,15) (10,17) (10,14) (10,21) (11,18) (11,23) (12,17) (12,21) (12,13) (12,19) (13,17) (13,14) (13,21) (15,20) (16,22) (17,21) (18,23)\nQ: Is there a path between node 12 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "304"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (1,27) (1,24) (1,21) (1,3) (2,10) (2,22) (2,6) (2,18) (2,25) (2,12) (3,19) (3,27) (3,24) (4,10) (4,6) (4,18) (4,25) (5,28) (5,16) (6,10) (6,13) (6,25) (6,12) (6,9) (7,28) (8,10) (8,14) (8,18) (8,29) (8,25) (8,23) (9,13) (9,14) (10,29) (10,25) (12,22) (12,18) (12,17) (13,29) (13,26) (14,20) (14,17) (15,19) (17,25) (18,20) (18,25) (20,29) (20,26) (20,23) (21,27) (21,24) (23,26) (23,25) (24,27) (26,29)\nQ: Is there a path between node 7 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "305"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,3) (0,11) (0,8) (0,2) (0,12) (0,9) (0,1) (1,4) (1,3) (1,6) (1,11) (1,8) (1,7) (1,10) (1,2) (1,12) (2,3) (2,6) (2,11) (2,8) (2,9) (3,6) (3,11) (3,8) (3,7) (3,10) (3,9) (4,6) (4,11) (4,8) (4,7) (4,10) (4,12) (4,9) (6,8) (6,10) (7,10) (7,12) (7,9) (8,11) (8,10) (8,12) (9,10) (10,12)\nQ: Is there a path between node 12 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "306"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,4) (1,2) (3,4)\nQ: Is there a path between node 0 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "307"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,8) (0,11) (0,17) (0,1) (0,2) (0,12) (0,6) (0,18) (0,7) (0,15) (1,19) (1,8) (1,9) (1,11) (1,2) (1,12) (1,6) (1,7) (1,15) (2,19) (2,4) (2,9) (2,11) (2,17) (2,12) (2,6) (2,18) (2,15) (3,5) (3,13) (3,10) (4,19) (4,8) (4,9) (4,11) (4,17) (4,12) (4,6) (4,7) (4,15) (5,13) (5,10) (6,9) (6,11) (6,12) (6,18) (7,19) (7,8) (7,9) (7,11) (7,17) (7,15) (8,19) (8,11) (8,17) (8,12) (9,17) (9,12) (9,18) (10,13) (11,17) (11,15) (12,19) (12,17) (12,18) (12,15) (14,20) (14,21) (15,17) (15,18) (17,19) (17,18) (18,19) (20,21)\nQ: Is there a path between node 21 and node 18?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "308"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,4) (1,2) (3,4)\nQ: Is there a path between node 4 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "309"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,3) (1,20) (1,21) (1,8) (1,5) (1,16) (1,17) (1,19) (1,6) (1,12) (1,14) (1,9) (1,13) (1,18) (1,7) (1,11) (1,15) (1,2) (1,10) (2,20) (2,21) (2,8) (2,5) (2,16) (2,17) (2,19) (2,6) (2,12) (2,14) (2,9) (2,13) (2,18) (2,7) (2,11) (2,15) (2,10) (3,4) (5,20) (5,21) (5,8) (5,16) (5,17) (5,19) (5,6) (5,12) (5,14) (5,9) (5,13) (5,18) (5,7) (5,11) (5,15) (5,10) (6,20) (6,21) (6,8) (6,16) (6,17) (6,19) (6,12) (6,14) (6,9) (6,13) (6,18) (6,7) (6,11) (6,15) (6,10) (7,20) (7,21) (7,8) (7,16) (7,17) (7,19) (7,12) (7,14) (7,9) (7,13) (7,18) (7,11) (7,15) (7,10) (8,20) (8,21) (8,16) (8,17) (8,19) (8,12) (8,14) (8,9) (8,13) (8,18) (8,11) (8,15) (8,10) (9,20) (9,21) (9,16) (9,17) (9,19) (9,12) (9,14) (9,13) (9,18) (9,11) (9,15) (9,10) (10,20) (10,21) (10,16) (10,17) (10,19) (10,12) (10,14) (10,13) (10,18) (10,11) (10,15) (11,20) (11,21) (11,16) (11,17) (11,19) (11,12) (11,14) (11,13) (11,18) (11,15) (12,20) (12,21) (12,16) (12,17) (12,19) (12,14) (12,13) (12,18) (12,15) (13,20) (13,21) (13,16) (13,17) (13,19) (13,14) (13,18) (13,15) (14,20) (14,21) (14,16) (14,17) (14,19) (14,18) (14,15) (15,20) (15,21) (15,16) (15,17) (15,19) (15,18) (16,20) (16,21) (16,17) (16,19) (16,18) (17,20) (17,21) (17,19) (17,18) (18,20) (18,21) (18,19) (19,20) (19,21) (20,21)\nQ: Is there a path between node 1 and node 12?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "310"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,10) (0,25) (0,16) (0,24) (0,4) (0,8) (0,27) (0,19) (1,5) (1,28) (2,15) (3,12) (3,13) (3,21) (3,24) (3,4) (3,8) (4,26) (4,20) (4,21) (4,11) (4,9) (6,13) (6,14) (6,22) (6,21) (6,7) (6,23) (6,11) (7,12) (7,26) (7,20) (7,17) (7,14) (7,10) (7,25) (7,24) (7,8) (7,11) (7,19) (7,9) (8,25) (8,27) (8,11) (9,17) (9,14) (9,21) (9,23) (9,27) (9,11) (10,26) (10,20) (10,14) (10,25) (10,23) (10,24) (11,13) (11,17) (11,21) (11,25) (11,23) (11,19) (12,20) (12,17) (12,24) (13,26) (13,20) (13,17) (13,22) (13,25) (13,24) (13,19) (14,20) (14,16) (15,28) (15,18) (16,26) (16,21) (16,23) (17,26) (17,22) (17,23) (17,27) (18,28) (19,22) (20,23) (20,24) (20,27) (21,26) (21,27) (23,25) (24,25) (24,27) (25,27)\nQ: Is there a path between node 7 and node 28?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "311"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,4) (0,1) (0,5) (0,24) (0,3) (0,21) (0,19) (0,9) (0,15) (0,20) (0,27) (0,13) (1,24) (1,21) (1,31) (1,10) (1,7) (1,20) (1,27) (1,13) (2,6) (2,5) (2,24) (2,3) (2,21) (2,19) (2,9) (2,31) (2,15) (2,7) (2,27) (2,13) (3,6) (3,4) (3,5) (3,22) (3,24) (3,21) (3,19) (3,9) (3,31) (3,18) (3,7) (3,20) (4,5) (4,21) (4,19) (4,9) (4,31) (4,7) (4,20) (4,27) (4,13) (5,6) (5,22) (5,24) (5,21) (5,9) (5,31) (5,10) (5,15) (5,18) (5,20) (5,27) (5,13) (6,22) (6,21) (6,19) (6,9) (6,31) (6,10) (6,15) (6,18) (6,7) (6,27) (6,13) (7,22) (7,9) (7,10) (7,15) (7,18) (7,20) (7,27) (7,13) (8,16) (8,11) (8,28) (8,12) (8,25) (8,30) (8,14) (8,32) (8,29) (9,22) (9,24) (9,21) (9,19) (9,31) (9,10) (9,15) (9,18) (9,20) (10,22) (10,19) (10,31) (10,15) (10,20) (10,27) (10,13) (11,16) (11,28) (11,26) (11,23) (11,30) (11,14) (11,32) (11,17) (12,16) (12,28) (12,23) (12,30) (12,14) (12,33) (12,32) (12,17) (12,29) (13,22) (13,24) (13,21) (13,19) (13,15) (13,18) (13,20) (14,28) (14,26) (14,23) (14,25) (14,33) (14,32) (14,29) (15,22) (15,24) (15,21) (15,19) (15,20) (15,27) (16,26) (16,25) (16,30) (16,33) (16,32) (16,17) (16,29) (17,28) (17,26) (17,25) (17,30) (17,33) (17,32) (17,29) (18,24) (18,19) (18,31) (19,22) (19,24) (19,31) (19,20) (19,27) (20,21) (20,31) (20,27) (21,31) (23,28) (23,26) (23,25) (23,30) (24,31) (24,27) (25,26) (25,30) (25,33) (25,32) (25,29) (26,28) (26,33) (26,32) (28,30) (28,29) (29,30) (29,33) (29,32) (30,32)\nQ: Is there a path between node 12 and node 25?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "312"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (1,12) (1,19) (2,13) (3,20) (3,11) (4,7) (4,16) (4,18) (5,17) (5,7) (6,15) (6,20) (6,11) (7,20) (7,11) (8,12) (8,13) (8,19) (11,17) (11,15) (12,19) (16,17) (16,20) (17,20) (18,20)\nQ: Is there a path between node 8 and node 12?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "313"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (1,4) (2,4)\nQ: Is there a path between node 1 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "314"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,9) (0,8) (0,19) (0,13) (0,11) (1,15) (1,6) (1,3) (1,12) (1,4) (1,2) (1,23) (1,5) (1,16) (1,22) (1,17) (1,18) (1,21) (1,24) (1,25) (2,15) (2,3) (2,4) (2,20) (2,23) (2,22) (2,27) (2,18) (2,21) (2,24) (3,15) (3,4) (3,26) (3,20) (3,23) (3,5) (3,16) (3,14) (3,22) (3,27) (3,18) (3,21) (3,24) (3,25) (4,15) (4,6) (4,12) (4,26) (4,20) (4,5) (4,22) (4,27) (4,17) (4,21) (4,25) (5,15) (5,6) (5,12) (5,20) (5,16) (5,14) (5,22) (5,27) (5,18) (5,21) (5,25) (6,15) (6,12) (6,27) (6,17) (6,21) (6,24) (6,25) (7,19) (7,13) (8,9) (8,19) (8,13) (9,19) (9,10) (10,19) (10,13) (10,11) (11,13) (12,15) (12,26) (12,20) (12,14) (12,22) (12,21) (12,24) (13,19) (14,15) (14,26) (14,20) (14,16) (14,22) (14,17) (14,21) (14,24) (14,25) (15,26) (15,20) (15,23) (15,16) (15,22) (15,17) (15,18) (15,24) (16,26) (16,27) (16,18) (16,25) (17,26) (17,23) (17,18) (17,21) (17,24) (17,25) (18,26) (18,20) (18,22) (18,27) (18,24) (18,25) (20,26) (20,23) (20,22) (20,27) (20,24) (20,25) (21,22) (21,27) (21,24) (21,25) (22,23) (22,27) (22,24) (22,25) (23,27) (23,25) (24,26) (24,27) (25,26) (25,27) (26,27)\nQ: Is there a path between node 9 and node 14?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "315"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (2,8) (2,4) (2,3) (3,8) (5,7) (6,7)\nQ: Is there a path between node 4 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "316"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,2) (0,1) (1,5) (1,6) (2,6) (3,7) (4,7) (5,6)\nQ: Is there a path between node 5 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "317"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,4) (0,1) (0,11) (0,9) (0,12) (1,2) (1,4) (1,11) (1,9) (1,13) (1,8) (1,12) (2,6) (2,3) (2,4) (2,11) (2,9) (2,13) (2,8) (3,6) (3,9) (3,13) (3,8) (3,12) (4,6) (4,11) (4,9) (4,13) (4,8) (4,12) (5,7) (5,10) (6,11) (6,9) (6,8) (6,12) (8,9) (8,12) (9,11) (9,12) (11,13) (12,13)\nQ: Is there a path between node 10 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "318"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (1,4) (1,11) (2,21) (2,20) (2,24) (3,24) (4,13) (4,15) (4,8) (5,19) (5,24) (6,20) (6,24) (7,25) (7,21) (8,17) (8,15) (8,12) (9,13) (9,12) (10,16) (11,13) (11,18) (11,23) (11,14) (11,12) (13,17) (14,23) (15,18) (15,23) (18,23) (19,25) (19,24) (20,21) (21,25) (24,25)\nQ: Is there a path between node 15 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "319"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,7) (0,4) (0,10) (0,5) (0,13) (0,12) (0,1) (0,2) (0,3) (0,15) (0,6) (0,8) (0,14) (1,11) (1,7) (1,4) (1,10) (1,5) (1,13) (1,12) (1,2) (1,3) (1,15) (1,6) (1,8) (1,14) (2,11) (2,7) (2,4) (2,10) (2,5) (2,13) (2,12) (2,3) (2,15) (2,6) (2,8) (2,14) (3,11) (3,7) (3,4) (3,10) (3,5) (3,13) (3,12) (3,15) (3,6) (3,8) (3,14) (4,11) (4,7) (4,10) (4,5) (4,13) (4,12) (4,15) (4,6) (4,8) (4,14) (5,11) (5,7) (5,10) (5,13) (5,12) (5,15) (5,6) (5,8) (5,14) (6,11) (6,7) (6,10) (6,13) (6,12) (6,15) (6,8) (6,14) (7,11) (7,10) (7,13) (7,12) (7,15) (7,8) (7,14) (8,11) (8,10) (8,13) (8,12) (8,15) (8,14) (10,11) (10,13) (10,12) (10,15) (10,14) (11,13) (11,12) (11,15) (11,14) (12,13) (12,15) (12,14) (13,15) (13,14) (14,15)\nQ: Is there a path between node 14 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "320"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,21) (0,17) (0,7) (0,29) (1,20) (2,32) (2,6) (2,13) (3,22) (3,23) (3,8) (4,30) (4,31) (6,23) (6,16) (6,32) (7,19) (8,14) (8,23) (8,16) (8,32) (8,13) (9,24) (9,17) (9,29) (13,14) (13,32) (14,16) (14,32) (16,20) (16,28) (17,24) (20,28) (21,29) (24,29) (27,30) (30,31)\nQ: Is there a path between node 21 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "321"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,4) (1,23) (1,7) (1,18) (1,24) (1,32) (1,31) (1,21) (1,27) (1,11) (1,6) (1,29) (1,17) (1,20) (2,23) (2,7) (2,18) (2,33) (2,24) (2,31) (2,21) (2,8) (2,27) (2,11) (2,29) (2,17) (2,26) (3,9) (3,22) (3,13) (3,5) (3,30) (3,28) (3,16) (3,14) (3,15) (4,19) (4,10) (5,9) (5,22) (5,13) (5,28) (5,16) (5,14) (6,18) (6,32) (6,25) (6,21) (6,8) (6,11) (6,17) (6,20) (6,26) (7,18) (7,33) (7,24) (7,32) (7,25) (7,31) (7,21) (7,17) (7,20) (7,26) (8,18) (8,33) (8,32) (8,25) (8,31) (8,27) (8,11) (8,29) (8,20) (8,26) (9,22) (9,13) (9,30) (9,28) (9,14) (9,15) (10,19) (10,12) (11,18) (11,33) (11,24) (11,25) (11,31) (11,27) (11,29) (11,26) (12,19) (13,28) (13,15) (14,30) (14,28) (14,16) (14,15) (15,22) (15,30) (15,16) (16,22) (17,23) (17,18) (17,33) (17,25) (17,31) (17,21) (17,27) (17,29) (17,20) (17,26) (18,23) (18,32) (18,25) (18,21) (18,29) (18,20) (18,26) (20,23) (20,33) (20,32) (20,25) (20,31) (20,21) (20,27) (20,29) (20,26) (21,23) (21,33) (21,24) (21,25) (21,29) (23,33) (23,24) (23,25) (23,31) (23,27) (23,29) (23,26) (24,33) (24,32) (24,25) (24,27) (24,29) (24,26) (25,32) (25,31) (25,27) (25,29) (25,26) (26,33) (26,31) (26,27) (27,31) (27,29) (28,30) (31,32) (32,33)\nQ: Is there a path between node 32 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "322"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,5) (0,2) (0,3) (0,10) (0,6) (0,1) (0,4) (0,9) (0,7) (0,12) (1,8) (1,5) (1,2) (1,3) (1,10) (1,6) (1,4) (1,9) (1,7) (1,12) (2,8) (2,5) (2,3) (2,10) (2,6) (2,4) (2,9) (2,7) (2,12) (3,8) (3,5) (3,10) (3,6) (3,4) (3,9) (3,7) (3,12) (4,8) (4,5) (4,10) (4,6) (4,9) (4,7) (4,12) (5,8) (5,10) (5,6) (5,9) (5,7) (5,12) (6,8) (6,10) (6,9) (6,7) (6,12) (7,8) (7,10) (7,9) (7,12) (8,10) (8,9) (8,12) (9,10) (9,12) (10,12) (11,13)\nQ: Is there a path between node 11 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "323"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,8) (1,5) (1,10) (1,8) (2,6) (2,7) (3,9) (3,10) (4,11) (4,8) (6,7) (8,9) (8,10) (11,12)\nQ: Is there a path between node 2 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "324"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,4) (0,3) (0,6) (0,2) (0,8) (0,5) (0,11) (1,4) (1,3) (1,6) (1,2) (1,8) (1,5) (1,11) (2,4) (2,3) (2,6) (2,8) (2,5) (2,11) (3,4) (3,6) (3,8) (3,5) (3,11) (4,6) (4,8) (4,5) (4,11) (5,6) (5,8) (5,11) (6,8) (6,11) (7,9) (7,10) (8,11) (9,10)\nQ: Is there a path between node 6 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "325"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (1,14) (1,3) (1,9) (1,10) (1,4) (1,7) (1,6) (1,13) (1,12) (1,11) (2,15) (3,14) (3,8) (3,9) (3,10) (3,4) (3,12) (3,11) (4,8) (4,9) (4,10) (4,7) (4,5) (4,11) (5,9) (5,7) (5,13) (5,12) (5,11) (6,14) (6,8) (6,7) (6,13) (6,11) (7,8) (7,9) (7,10) (7,11) (8,14) (8,10) (8,12) (8,11) (9,14) (9,10) (9,13) (9,12) (10,14) (10,13) (10,12) (11,14) (11,13) (11,12) (12,14)\nQ: Is there a path between node 7 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "326"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,11) (0,1) (0,25) (0,28) (0,16) (0,31) (0,2) (0,23) (1,20) (1,26) (1,24) (1,10) (1,31) (1,21) (2,26) (2,19) (2,11) (2,5) (2,15) (2,32) (2,33) (2,8) (2,16) (2,31) (2,21) (2,30) (3,12) (3,4) (4,18) (5,11) (5,24) (6,14) (6,12) (6,9) (6,13) (7,26) (7,25) (7,33) (7,8) (7,21) (8,26) (8,19) (8,32) (8,31) (9,12) (10,19) (10,11) (10,25) (11,33) (11,24) (12,14) (14,18) (15,19) (15,17) (15,32) (15,25) (15,31) (15,21) (16,26) (16,32) (17,20) (17,19) (17,23) (19,24) (19,31) (19,21) (19,30) (21,32) (21,25) (21,24) (21,31) (23,31) (24,28) (25,32) (25,33) (25,28) (26,32) (26,33) (26,28) (26,31) (26,30) (28,33) (28,30) (31,32)\nQ: Is there a path between node 25 and node 29?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "327"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,3) (0,2) (0,1) (1,6) (1,3) (1,2) (2,6) (2,3) (3,6) (4,5)\nQ: Is there a path between node 6 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "328"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,5) (0,7) (0,6) (0,2) (0,4) (0,8) (0,9) (1,10) (2,3) (2,5) (2,7) (2,6) (2,4) (2,8) (2,9) (2,11) (3,5) (3,4) (3,8) (3,11) (4,5) (4,6) (4,9) (4,11) (5,6) (5,8) (5,9) (6,7) (6,8) (6,9) (6,11) (7,8) (7,11) (8,9) (9,11)\nQ: Is there a path between node 5 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "329"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,2) (0,3) (1,5) (2,4) (2,3) (3,4)\nQ: Is there a path between node 2 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "330"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,10) (0,15) (0,21) (0,1) (0,7) (0,29) (0,24) (0,16) (0,23) (0,17) (1,26) (1,10) (1,15) (1,7) (1,28) (1,29) (1,12) (1,24) (1,16) (1,3) (1,23) (2,14) (2,27) (2,34) (3,26) (3,32) (3,15) (3,21) (3,7) (3,28) (3,29) (3,12) (3,24) (3,23) (3,17) (4,9) (4,14) (4,27) (4,31) (5,19) (5,22) (5,13) (5,20) (5,25) (5,30) (5,8) (5,33) (6,9) (6,27) (6,34) (6,31) (7,26) (7,32) (7,10) (7,15) (7,21) (7,29) (7,12) (7,24) (7,16) (7,23) (7,17) (8,19) (8,22) (8,13) (8,20) (8,25) (8,18) (8,30) (8,33) (9,14) (9,34) (10,32) (10,15) (10,21) (10,29) (10,24) (10,23) (10,17) (11,19) (11,22) (11,13) (11,25) (11,18) (11,30) (12,26) (12,32) (12,15) (12,21) (12,24) (12,16) (12,23) (13,19) (13,20) (13,25) (13,18) (13,33) (14,27) (14,31) (15,26) (15,21) (15,28) (15,24) (15,16) (15,23) (15,17) (16,26) (16,32) (16,23) (16,17) (17,26) (17,32) (17,21) (17,28) (17,24) (18,19) (18,22) (18,20) (18,30) (19,22) (19,20) (19,25) (19,30) (20,25) (20,30) (20,33) (21,26) (21,32) (21,28) (21,29) (22,25) (22,30) (22,33) (23,32) (23,28) (23,29) (23,24) (24,32) (24,28) (25,30) (25,33) (26,32) (26,28) (27,31) (28,29) (30,33)\nQ: Is there a path between node 14 and node 24?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "331"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,10) (0,17) (0,15) (0,4) (0,12) (0,24) (0,9) (0,3) (0,13) (0,23) (0,7) (0,19) (0,16) (0,6) (0,25) (0,8) (1,10) (1,17) (1,4) (1,12) (1,24) (1,3) (1,13) (1,23) (1,26) (1,22) (1,19) (1,6) (1,14) (1,25) (1,8) (1,20) (2,10) (2,17) (2,11) (2,4) (2,24) (2,9) (2,3) (2,13) (2,23) (2,26) (2,7) (2,22) (2,19) (2,6) (2,14) (2,25) (2,8) (3,10) (3,17) (3,11) (3,15) (3,4) (3,12) (3,24) (3,9) (3,13) (3,26) (3,7) (3,19) (3,16) (3,14) (3,25) (3,8) (3,20) (4,10) (4,17) (4,11) (4,15) (4,12) (4,24) (4,9) (4,7) (4,19) (4,16) (4,6) (4,25) (4,20) (5,18) (6,10) (6,17) (6,15) (6,12) (6,24) (6,9) (6,23) (6,7) (6,16) (6,25) (6,8) (7,10) (7,11) (7,15) (7,12) (7,13) (7,22) (7,19) (7,16) (7,25) (7,8) (7,20) (8,10) (8,17) (8,11) (8,15) (8,12) (8,24) (8,9) (8,23) (8,22) (8,19) (8,16) (8,14) (8,25) (8,20) (9,10) (9,17) (9,11) (9,12) (9,24) (9,13) (9,23) (9,26) (9,22) (9,19) (9,16) (9,20) (10,17) (10,11) (10,15) (10,12) (10,24) (10,13) (10,23) (10,26) (10,19) (10,14) (10,20) (11,15) (11,12) (11,24) (11,13) (11,23) (11,26) (11,19) (11,16) (11,14) (11,20) (12,15) (12,24) (12,23) (12,22) (12,19) (12,16) (12,14) (12,25) (12,20) (13,15) (13,24) (13,23) (13,19) (13,16) (13,14) (13,25) (13,20) (14,17) (14,15) (14,24) (14,23) (14,26) (14,22) (14,19) (14,16) (14,25) (14,20) (15,17) (15,24) (15,23) (15,26) (15,16) (15,20) (16,24) (16,23) (16,26) (16,19) (16,25) (16,20) (17,23) (17,20) (18,21) (19,23) (19,22) (19,25) (19,20) (20,24) (20,23) (20,22) (20,25) (22,26) (22,25) (23,24) (23,26) (23,25) (24,26) (24,25) (25,26)\nQ: Is there a path between node 20 and node 17?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "332"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,18) (0,19) (0,20) (0,23) (0,9) (0,10) (0,22) (0,13) (0,1) (0,12) (0,5) (0,7) (0,15) (0,4) (1,11) (1,18) (1,19) (1,20) (1,23) (1,9) (1,10) (1,22) (1,13) (1,12) (1,5) (1,7) (1,15) (1,4) (2,8) (2,6) (2,3) (2,24) (2,16) (2,21) (2,17) (2,14) (3,8) (3,6) (3,24) (3,16) (3,21) (3,17) (3,14) (4,11) (4,18) (4,19) (4,20) (4,23) (4,9) (4,10) (4,22) (4,13) (4,12) (4,5) (4,7) (4,15) (5,11) (5,18) (5,19) (5,20) (5,23) (5,9) (5,10) (5,22) (5,13) (5,12) (5,7) (5,15) (6,8) (6,24) (6,16) (6,21) (6,17) (6,14) (7,11) (7,18) (7,19) (7,20) (7,23) (7,9) (7,10) (7,22) (7,13) (7,12) (7,15) (8,24) (8,16) (8,21) (8,17) (8,14) (9,11) (9,18) (9,19) (9,20) (9,23) (9,10) (9,22) (9,13) (9,12) (9,15) (10,11) (10,18) (10,19) (10,20) (10,23) (10,22) (10,13) (10,12) (10,15) (11,18) (11,19) (11,20) (11,23) (11,22) (11,13) (11,12) (11,15) (12,18) (12,19) (12,20) (12,23) (12,22) (12,13) (12,15) (13,18) (13,19) (13,20) (13,23) (13,22) (13,15) (14,24) (14,16) (14,21) (14,17) (15,18) (15,19) (15,20) (15,23) (15,22) (16,24) (16,21) (16,17) (17,24) (17,21) (18,19) (18,20) (18,23) (18,22) (19,20) (19,23) (19,22) (20,23) (20,22) (21,24) (22,23)\nQ: Is there a path between node 4 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "333"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (1,15) (1,16) (2,18) (2,17) (2,7) (3,14) (3,7) (5,11) (6,13) (7,17) (8,15) (8,13) (9,17) (10,17) (13,15) (13,16) (16,19)\nQ: Is there a path between node 2 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "334"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,10) (2,9) (2,5) (3,12) (3,14) (3,4) (3,8) (3,18) (4,19) (4,16) (4,11) (5,20) (5,12) (5,14) (5,11) (6,18) (6,16) (7,15) (8,20) (8,12) (8,18) (8,16) (9,20) (9,14) (9,19) (9,11) (11,13) (11,12) (11,18) (11,16) (12,18) (13,19) (13,18) (14,19) (16,20) (18,19)\nQ: Is there a path between node 20 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "335"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (1,17) (2,9) (3,16) (5,18) (5,11) (5,21) (6,21) (6,15) (7,19) (7,21) (8,10) (8,12) (8,16) (10,16) (14,23) (15,21) (16,19) (17,20) (18,19) (20,23)\nQ: Is there a path between node 9 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "336"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,8) (1,5) (2,3) (3,5) (3,11) (4,8) (5,9) (5,7) (5,10) (6,11)\nQ: Is there a path between node 10 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "337"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,18) (0,24) (0,5) (0,12) (0,26) (0,14) (0,16) (0,21) (0,9) (0,1) (0,28) (0,25) (1,3) (1,18) (1,24) (1,5) (1,12) (1,26) (1,14) (1,16) (1,21) (1,2) (1,23) (1,20) (1,28) (1,25) (2,3) (2,18) (2,10) (2,24) (2,5) (2,12) (2,26) (2,14) (2,16) (2,9) (2,23) (2,20) (2,28) (2,7) (2,25) (2,22) (2,13) (3,18) (3,24) (3,12) (3,26) (3,16) (3,9) (3,19) (3,7) (3,25) (3,22) (4,11) (4,27) (4,17) (4,15) (4,8) (5,18) (5,24) (5,12) (5,26) (5,14) (5,16) (5,21) (5,9) (5,23) (5,19) (5,20) (5,7) (5,13) (6,11) (6,27) (6,29) (6,15) (6,8) (7,18) (7,10) (7,12) (7,26) (7,14) (7,16) (7,21) (7,9) (7,20) (7,25) (7,22) (7,13) (8,11) (8,27) (8,29) (8,17) (8,15) (9,18) (9,10) (9,24) (9,16) (9,21) (9,19) (9,20) (9,28) (9,25) (9,13) (10,18) (10,24) (10,12) (10,26) (10,14) (10,16) (10,23) (10,20) (10,28) (10,25) (10,22) (10,13) (11,27) (11,29) (12,18) (12,24) (12,16) (12,21) (12,23) (12,20) (12,28) (12,22) (12,13) (13,18) (13,24) (13,26) (13,14) (13,16) (13,21) (13,23) (13,20) (13,28) (13,25) (13,22) (14,26) (14,16) (14,21) (14,23) (14,19) (14,20) (14,28) (14,25) (15,27) (15,17) (16,18) (16,24) (16,26) (16,20) (16,25) (16,22) (17,29) (18,24) (18,26) (18,23) (18,19) (18,20) (18,25) (18,22) (19,21) (19,23) (19,28) (19,25) (20,26) (20,23) (20,28) (20,25) (20,22) (21,26) (21,23) (21,28) (21,22) (22,26) (22,23) (22,25) (23,24) (23,26) (24,26) (24,28) (25,26)\nQ: Is there a path between node 23 and node 28?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "338"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,13) (2,25) (2,28) (2,21) (2,5) (2,23) (3,22) (3,8) (3,6) (3,19) (3,21) (3,31) (3,15) (5,20) (5,16) (5,21) (5,23) (6,18) (6,17) (6,23) (7,10) (8,21) (9,24) (12,22) (12,18) (13,30) (13,27) (14,26) (15,16) (15,19) (15,31) (16,22) (16,20) (16,19) (17,20) (17,21) (17,31) (18,22) (18,25) (18,20) (18,21) (18,23) (19,25) (19,28) (20,28) (20,21) (21,25) (22,25) (22,28) (23,28) (27,29) (29,30) (30,32)\nQ: Is there a path between node 5 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "339"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,31) (1,4) (1,27) (1,25) (2,31) (2,24) (2,13) (2,10) (3,30) (3,32) (3,27) (3,15) (4,30) (4,6) (4,28) (4,8) (5,22) (6,27) (7,20) (7,11) (7,12) (8,15) (9,14) (10,17) (10,23) (10,13) (11,14) (12,18) (13,23) (14,22) (15,30) (15,27) (15,25) (15,16) (15,28) (17,23) (17,21) (18,22) (18,33) (20,22) (21,31) (23,24) (25,30) (25,27) (25,28) (26,31) (27,30) (27,32) (28,32)\nQ: Is there a path between node 9 and node 33?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "340"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,1) (0,12) (0,4) (1,13) (1,3) (1,6) (1,9) (2,15) (2,14) (2,11) (4,7) (5,16) (5,6) (5,9) (6,13) (6,8) (10,13) (10,12) (11,15) (11,14)\nQ: Is there a path between node 15 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "341"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,11) (0,1) (0,3) (0,10) (0,4) (1,11) (1,3) (1,10) (1,4) (2,7) (3,11) (3,4) (4,5) (4,11) (5,11) (6,9) (6,8) (7,9) (7,8) (8,9) (10,11)\nQ: Is there a path between node 10 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "342"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,6) (0,3) (0,18) (0,1) (0,15) (0,12) (0,14) (0,9) (0,16) (0,8) (0,2) (0,11) (0,19) (1,7) (1,6) (1,3) (1,18) (1,15) (1,9) (1,8) (1,2) (1,20) (2,7) (2,3) (2,18) (2,15) (2,12) (2,14) (2,9) (2,16) (2,8) (2,11) (2,19) (2,20) (3,18) (3,15) (3,12) (3,9) (3,16) (3,8) (3,19) (3,20) (4,13) (4,17) (5,17) (6,7) (6,18) (6,15) (6,14) (6,9) (6,16) (6,11) (6,19) (6,20) (7,15) (7,12) (7,14) (7,9) (7,16) (8,18) (8,12) (8,14) (8,9) (8,16) (8,11) (8,19) (8,20) (9,18) (9,15) (9,12) (9,11) (9,19) (9,20) (10,13) (11,18) (11,12) (11,14) (11,16) (11,19) (11,20) (12,18) (12,15) (12,14) (12,19) (12,20) (13,17) (14,19) (16,18) (16,19) (18,20)\nQ: Is there a path between node 4 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "343"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,1) (1,12) (1,15) (2,9) (2,6) (3,10) (3,17) (3,15) (5,7) (6,10) (6,9) (6,11) (7,13) (8,17) (8,16) (10,15) (11,12) (15,17)\nQ: Is there a path between node 6 and node 12?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "344"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (0,4) (1,32) (1,22) (1,34) (1,7) (1,5) (1,28) (1,11) (1,13) (1,30) (1,31) (1,26) (2,12) (2,3) (2,24) (2,15) (2,18) (2,8) (2,20) (2,25) (2,19) (2,17) (2,16) (3,10) (3,24) (3,15) (3,18) (3,8) (3,20) (3,14) (3,19) (3,21) (4,23) (4,6) (5,32) (5,22) (5,7) (5,33) (5,11) (5,13) (5,27) (5,31) (5,26) (6,23) (7,22) (7,34) (7,28) (7,13) (7,27) (7,30) (7,26) (7,29) (8,10) (8,24) (8,15) (8,18) (8,20) (8,14) (8,17) (8,21) (8,16) (9,32) (9,22) (9,34) (9,28) (9,13) (9,27) (9,31) (9,26) (9,29) (10,12) (10,24) (10,15) (10,18) (10,20) (10,25) (10,17) (11,32) (11,22) (11,34) (11,28) (11,13) (11,27) (11,30) (11,31) (11,26) (12,24) (12,25) (12,14) (12,17) (12,21) (12,16) (13,34) (13,33) (13,27) (13,30) (13,31) (13,29) (14,15) (14,18) (14,20) (14,25) (14,19) (14,17) (14,21) (14,16) (15,24) (15,18) (15,20) (15,17) (15,21) (16,24) (16,20) (16,19) (16,17) (17,24) (17,20) (17,21) (18,20) (18,25) (18,19) (20,24) (20,25) (20,21) (21,25) (22,32) (22,28) (22,27) (22,30) (22,31) (22,26) (24,25) (26,34) (26,33) (26,31) (27,34) (27,33) (27,28) (27,30) (27,31) (27,29) (28,32) (28,33) (28,30) (28,31) (28,29) (29,32) (29,33) (30,32) (31,32) (31,34) (32,34) (32,33) (33,34)\nQ: Is there a path between node 32 and node 18?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "345"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,15) (0,25) (0,14) (0,7) (0,2) (0,9) (0,5) (1,26) (1,15) (1,25) (1,7) (1,6) (1,2) (1,20) (1,22) (2,25) (2,19) (2,14) (2,4) (3,12) (3,16) (4,15) (4,7) (4,6) (4,8) (5,26) (5,20) (5,8) (5,9) (5,22) (5,13) (6,19) (6,17) (6,7) (6,20) (6,22) (7,19) (7,17) (7,9) (8,19) (9,26) (9,14) (9,24) (11,12) (12,21) (12,18) (12,16) (13,17) (13,22) (14,26) (14,22) (15,19) (15,20) (16,21) (18,23) (19,20) (19,22) (25,26)\nQ: Is there a path between node 2 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "346"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,4) (0,9) (0,1) (0,11) (0,2) (1,10) (1,6) (1,9) (1,15) (1,13) (2,12) (2,9) (2,17) (2,15) (3,4) (3,6) (3,11) (4,12) (4,9) (4,11) (6,10) (6,12) (6,9) (6,15) (6,13) (8,12) (8,9) (8,15) (8,13) (9,10) (9,11) (10,13) (10,11) (11,13) (12,13) (14,16)\nQ: Is there a path between node 8 and node 14?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "347"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,11) (0,6) (1,5) (1,8) (1,10) (1,15) (1,17) (1,13) (1,16) (2,5) (2,4) (2,8) (2,10) (2,14) (2,17) (2,13) (2,16) (3,9) (3,6) (3,12) (4,8) (4,15) (4,14) (4,17) (4,13) (5,8) (5,15) (5,17) (6,7) (6,9) (7,11) (7,9) (8,15) (8,17) (8,13) (8,16) (9,11) (10,15) (10,14) (10,17) (11,12) (13,15) (13,14) (13,16) (14,15) (14,17) (14,16) (15,17) (15,16) (16,17)\nQ: Is there a path between node 17 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "348"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,16) (0,9) (0,3) (0,4) (0,8) (0,17) (1,6) (1,12) (1,13) (1,18) (1,2) (1,4) (1,8) (1,17) (2,6) (2,12) (2,15) (2,9) (2,13) (2,18) (2,4) (2,8) (2,17) (3,6) (3,16) (3,12) (3,9) (3,13) (3,18) (3,8) (3,17) (3,5) (4,6) (4,16) (4,12) (4,9) (4,18) (4,17) (4,5) (5,6) (5,12) (5,15) (5,9) (5,17) (6,12) (6,15) (6,9) (6,13) (6,18) (6,8) (7,10) (7,11) (7,19) (8,16) (8,15) (8,9) (8,18) (9,16) (9,12) (9,15) (9,13) (9,18) (9,17) (10,19) (11,14) (11,19) (12,16) (12,15) (12,13) (12,17) (13,18) (14,19) (15,17) (16,17) (17,18)\nQ: Is there a path between node 0 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "349"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,20) (0,27) (0,29) (0,26) (0,17) (0,3) (0,1) (0,16) (1,6) (1,7) (1,20) (1,19) (1,3) (1,33) (1,4) (2,27) (2,34) (2,26) (2,19) (2,17) (2,3) (2,21) (2,4) (3,6) (3,7) (3,11) (3,28) (3,29) (4,6) (4,28) (4,27) (4,29) (4,26) (4,19) (4,33) (4,23) (5,7) (5,11) (5,28) (5,19) (5,33) (5,16) (6,7) (6,28) (6,27) (6,26) (6,21) (7,34) (8,13) (8,12) (8,22) (8,15) (9,24) (9,12) (9,10) (10,25) (11,16) (11,23) (12,32) (12,18) (12,22) (12,15) (13,14) (14,18) (14,15) (15,30) (15,18) (16,27) (16,17) (16,23) (17,29) (17,19) (17,33) (17,23) (18,31) (18,24) (19,28) (19,27) (19,34) (19,29) (19,33) (19,21) (20,21) (21,26) (21,33) (22,30) (22,25) (25,30) (25,31) (26,28) (26,34) (26,29) (27,28) (30,32) (31,32)\nQ: Is there a path between node 24 and node 19?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "350"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,28) (0,26) (0,7) (0,22) (0,6) (0,1) (0,30) (0,3) (1,16) (1,28) (1,26) (1,22) (1,10) (1,30) (2,4) (2,29) (2,24) (2,14) (2,21) (2,25) (2,13) (2,12) (2,31) (2,19) (2,33) (2,27) (2,23) (2,8) (2,18) (3,16) (3,28) (3,26) (3,9) (3,7) (3,10) (4,29) (4,32) (4,24) (4,21) (4,25) (4,15) (4,12) (4,31) (4,19) (4,33) (4,27) (4,17) (4,23) (4,18) (5,32) (5,14) (5,21) (5,15) (5,12) (5,19) (5,33) (5,27) (5,23) (5,8) (6,28) (6,26) (6,7) (6,22) (6,10) (7,16) (7,9) (7,22) (7,10) (8,29) (8,32) (8,24) (8,21) (8,15) (8,13) (8,33) (8,27) (8,23) (8,18) (9,16) (9,28) (9,26) (9,22) (9,10) (10,28) (10,22) (10,30) (12,29) (12,14) (12,21) (12,25) (12,15) (12,13) (12,31) (12,19) (12,33) (12,17) (12,23) (12,18) (13,20) (13,29) (13,24) (13,21) (13,25) (13,15) (13,31) (13,19) (13,33) (13,27) (13,17) (13,23) (13,18) (14,20) (14,29) (14,32) (14,24) (14,21) (14,15) (14,31) (14,19) (14,33) (14,17) (14,18) (15,20) (15,29) (15,32) (15,24) (15,21) (15,25) (15,31) (15,19) (15,33) (15,27) (15,17) (15,23) (15,18) (16,28) (16,26) (16,22) (16,30) (17,20) (17,29) (17,32) (17,24) (17,21) (17,25) (17,31) (17,19) (17,18) (18,20) (18,29) (18,32) (18,24) (18,21) (18,25) (18,31) (18,19) (18,27) (18,23) (19,32) (19,24) (19,33) (19,27) (19,23) (20,29) (20,32) (20,24) (20,21) (20,25) (20,31) (20,33) (20,27) (20,23) (21,32) (21,24) (21,25) (21,31) (21,33) (21,27) (21,23) (22,26) (22,30) (23,29) (23,32) (23,24) (23,25) (23,31) (23,33) (23,27) (24,32) (24,25) (24,31) (24,27) (25,29) (25,33) (25,27) (26,28) (26,30) (27,29) (27,31) (27,33) (28,30) (29,32) (29,31) (29,33) (31,32) (31,33) (32,33)\nQ: Is there a path between node 23 and node 29?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "351"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,11) (3,15) (3,8) (5,18) (5,7) (6,17) (6,7) (7,13) (7,8) (7,14) (8,18) (8,12) (9,11) (9,15) (9,13) (9,17) (10,18) (11,13) (11,17) (12,18) (12,17) (12,14) (13,17) (14,17) (17,18)\nQ: Is there a path between node 1 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "352"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,13) (0,17) (0,10) (0,5) (0,4) (0,16) (0,19) (0,20) (0,7) (0,8) (0,15) (0,1) (0,18) (0,9) (0,12) (1,13) (1,17) (1,10) (1,5) (1,4) (1,16) (1,19) (1,20) (1,7) (1,8) (1,15) (1,18) (1,9) (1,12) (2,11) (2,21) (2,3) (2,14) (3,11) (3,21) (3,14) (4,13) (4,17) (4,10) (4,5) (4,16) (4,19) (4,20) (4,7) (4,8) (4,15) (4,18) (4,9) (4,12) (5,13) (5,17) (5,10) (5,16) (5,19) (5,20) (5,7) (5,8) (5,15) (5,18) (5,9) (5,12) (7,13) (7,17) (7,10) (7,16) (7,19) (7,20) (7,8) (7,15) (7,18) (7,9) (7,12) (8,13) (8,17) (8,10) (8,16) (8,19) (8,20) (8,15) (8,18) (8,9) (8,12) (9,13) (9,17) (9,10) (9,16) (9,19) (9,20) (9,15) (9,18) (9,12) (10,13) (10,17) (10,16) (10,19) (10,20) (10,15) (10,18) (10,12) (11,21) (11,14) (12,13) (12,17) (12,16) (12,19) (12,20) (12,15) (12,18) (13,17) (13,16) (13,19) (13,20) (13,15) (13,18) (14,21) (15,17) (15,16) (15,19) (15,20) (15,18) (16,17) (16,19) (16,20) (16,18) (17,19) (17,20) (17,18) (18,19) (18,20) (19,20)\nQ: Is there a path between node 7 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "353"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,27) (0,23) (0,4) (0,20) (0,17) (0,6) (1,5) (1,22) (1,11) (1,19) (1,24) (1,2) (1,15) (1,8) (1,30) (1,9) (1,28) (1,18) (2,5) (2,22) (2,24) (2,15) (2,8) (2,30) (2,9) (2,28) (2,18) (3,26) (3,13) (4,21) (4,29) (4,23) (4,20) (4,17) (4,6) (5,22) (5,19) (5,24) (5,14) (5,30) (5,28) (5,18) (6,21) (6,29) (6,27) (6,23) (6,20) (6,17) (7,26) (7,10) (7,13) (7,16) (7,12) (8,11) (8,24) (8,14) (8,30) (8,9) (8,28) (8,18) (9,22) (9,11) (9,19) (9,15) (9,28) (10,16) (10,12) (11,15) (11,30) (11,28) (11,18) (12,13) (12,16) (13,26) (13,16) (13,25) (14,22) (14,19) (14,15) (14,30) (15,19) (15,30) (15,28) (15,18) (16,26) (16,25) (17,29) (17,23) (18,19) (18,24) (18,28) (19,30) (19,28) (20,21) (20,27) (21,29) (21,27) (21,23) (22,24) (22,28) (23,27) (24,30) (24,28) (25,26) (28,30)\nQ: Is there a path between node 15 and node 27?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "354"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (0,10) (0,23) (0,3) (0,9) (0,26) (1,8) (1,20) (1,6) (1,4) (1,19) (1,16) (1,13) (1,24) (2,8) (2,20) (2,4) (2,19) (2,16) (2,13) (2,24) (2,12) (3,10) (3,9) (3,21) (3,22) (4,6) (4,19) (4,13) (4,24) (4,12) (5,15) (5,25) (5,11) (5,7) (6,8) (6,20) (6,19) (6,16) (6,13) (6,24) (7,15) (7,25) (7,14) (8,19) (8,13) (8,24) (8,12) (9,18) (9,23) (10,18) (10,23) (10,21) (10,26) (11,15) (11,17) (11,25) (12,20) (12,19) (12,16) (12,24) (13,20) (13,19) (13,16) (13,24) (14,17) (14,25) (15,17) (15,25) (16,20) (16,24) (17,25) (18,21) (18,22) (19,20) (19,24) (20,24) (21,23) (22,23) (22,26) (23,26)\nQ: Is there a path between node 5 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "355"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,13) (0,30) (0,1) (0,4) (0,2) (0,22) (1,30) (1,17) (1,5) (1,4) (1,25) (1,29) (2,3) (2,5) (2,23) (3,28) (3,24) (3,4) (3,6) (3,8) (3,12) (4,15) (4,24) (4,25) (4,7) (4,6) (4,29) (5,21) (5,23) (5,7) (5,12) (6,20) (6,28) (6,23) (7,13) (7,15) (7,16) (7,8) (7,12) (8,20) (8,30) (8,24) (8,17) (8,23) (10,19) (11,19) (11,26) (12,20) (12,16) (12,25) (12,18) (13,28) (13,18) (14,20) (15,28) (15,24) (15,23) (16,20) (16,30) (16,24) (16,29) (17,21) (17,28) (17,25) (18,21) (18,23) (18,29) (20,24) (20,23) (20,22) (20,29) (21,25) (21,23) (21,22) (22,25) (23,24) (23,29) (24,28) (24,29) (25,28) (26,27) (29,30)\nQ: Is there a path between node 7 and node 27?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "356"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,23) (0,8) (1,6) (1,26) (1,11) (2,6) (2,11) (3,12) (3,19) (3,20) (4,13) (4,21) (4,17) (4,10) (4,6) (4,23) (4,8) (5,13) (5,7) (5,21) (5,17) (5,28) (5,6) (5,23) (5,8) (5,26) (5,24) (5,11) (6,13) (6,17) (6,10) (6,23) (6,24) (7,17) (7,28) (7,23) (8,21) (8,10) (9,15) (10,13) (10,21) (10,23) (10,11) (11,13) (11,17) (12,19) (12,14) (12,27) (12,15) (12,22) (13,17) (13,16) (14,22) (15,19) (16,17) (16,28) (16,24) (17,24) (18,19) (18,27) (19,27) (21,26) (21,24) (22,25) (23,28) (24,28) (25,27)\nQ: Is there a path between node 12 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "357"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,19) (0,25) (0,2) (0,13) (0,1) (1,17) (1,24) (1,25) (1,11) (2,17) (2,25) (2,16) (2,13) (3,17) (4,23) (4,7) (4,14) (4,8) (5,18) (5,16) (6,18) (6,16) (6,21) (7,14) (7,15) (7,10) (8,23) (8,10) (9,14) (9,10) (10,23) (10,20) (11,17) (11,18) (11,25) (11,16) (11,13) (12,16) (13,17) (13,24) (13,25) (13,21) (14,15) (16,21) (17,19) (17,18) (17,25) (19,25) (19,21) (21,25)\nQ: Is there a path between node 7 and node 18?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "358"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,12) (1,25) (1,2) (1,10) (1,12) (1,3) (2,8) (2,22) (2,25) (2,26) (2,19) (2,11) (2,12) (2,7) (2,21) (3,25) (3,26) (3,10) (3,27) (3,21) (5,24) (5,6) (6,23) (6,9) (7,22) (7,25) (7,11) (8,20) (8,22) (8,25) (8,26) (8,27) (9,24) (10,14) (10,25) (10,13) (10,27) (10,21) (11,22) (11,12) (11,17) (11,21) (12,19) (12,18) (12,17) (12,27) (12,21) (13,17) (13,21) (14,17) (14,21) (15,23) (15,24) (16,22) (17,22) (17,25) (17,19) (18,20) (18,26) (18,21) (19,22) (19,26) (19,27) (20,27) (22,25) (25,26)\nQ: Is there a path between node 14 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "359"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,9) (0,13) (0,3) (0,1) (0,2) (0,7) (0,8) (0,11) (1,14) (1,13) (1,8) (1,10) (1,11) (1,5) (2,9) (2,13) (2,3) (2,7) (2,8) (2,10) (3,14) (3,9) (3,13) (3,8) (3,11) (3,5) (4,6) (4,12) (5,14) (5,9) (5,7) (5,8) (5,10) (5,11) (6,12) (7,14) (7,13) (7,8) (7,10) (8,14) (8,9) (8,10) (9,14) (9,13) (10,14) (10,13) (11,14) (13,14)\nQ: Is there a path between node 13 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "360"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,4) (1,5)\nQ: Is there a path between node 6 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "361"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,21) (0,11) (0,15) (0,4) (0,22) (0,5) (0,3) (0,6) (0,20) (0,13) (0,18) (0,9) (0,1) (0,12) (0,24) (0,16) (0,8) (0,23) (0,2) (1,21) (1,11) (1,15) (1,4) (1,22) (1,5) (1,3) (1,6) (1,20) (1,13) (1,18) (1,9) (1,12) (1,24) (1,16) (1,8) (1,23) (1,2) (2,21) (2,11) (2,15) (2,4) (2,22) (2,5) (2,3) (2,6) (2,20) (2,13) (2,18) (2,9) (2,12) (2,24) (2,16) (2,8) (2,23) (3,21) (3,11) (3,15) (3,4) (3,22) (3,5) (3,6) (3,20) (3,13) (3,18) (3,9) (3,12) (3,24) (3,16) (3,8) (3,23) (4,21) (4,11) (4,15) (4,22) (4,5) (4,6) (4,20) (4,13) (4,18) (4,9) (4,12) (4,24) (4,16) (4,8) (4,23) (5,21) (5,11) (5,15) (5,22) (5,6) (5,20) (5,13) (5,18) (5,9) (5,12) (5,24) (5,16) (5,8) (5,23) (6,21) (6,11) (6,15) (6,22) (6,20) (6,13) (6,18) (6,9) (6,12) (6,24) (6,16) (6,8) (6,23) (7,10) (7,14) (7,17) (7,19) (8,21) (8,11) (8,15) (8,22) (8,20) (8,13) (8,18) (8,9) (8,12) (8,24) (8,16) (8,23) (9,21) (9,11) (9,15) (9,22) (9,20) (9,13) (9,18) (9,12) (9,24) (9,16) (9,23) (10,14) (10,17) (10,19) (11,21) (11,15) (11,22) (11,20) (11,13) (11,18) (11,12) (11,24) (11,16) (11,23) (12,21) (12,15) (12,22) (12,20) (12,13) (12,18) (12,24) (12,16) (12,23) (13,21) (13,15) (13,22) (13,20) (13,18) (13,24) (13,16) (13,23) (14,17) (14,19) (15,21) (15,22) (15,20) (15,18) (15,24) (15,16) (15,23) (16,21) (16,22) (16,20) (16,18) (16,24) (16,23) (17,19) (18,21) (18,22) (18,20) (18,24) (18,23) (20,21) (20,22) (20,24) (20,23) (21,22) (21,24) (21,23) (22,24) (22,23) (23,24)\nQ: Is there a path between node 14 and node 21?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "362"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,9) (0,2) (0,5) (0,10) (0,1) (1,4) (1,9) (1,2) (1,5) (1,10) (2,4) (2,9) (2,5) (2,10) (3,11) (3,8) (3,12) (3,7) (3,6) (4,9) (4,5) (4,10) (5,9) (5,10) (6,11) (6,8) (6,12) (6,7) (7,11) (7,8) (7,12) (8,11) (8,12) (9,10) (11,12)\nQ: Is there a path between node 12 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "363"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (1,27) (1,24) (1,21) (1,3) (2,10) (2,22) (2,6) (2,18) (2,25) (2,12) (3,19) (3,27) (3,24) (4,10) (4,6) (4,18) (4,25) (5,28) (5,16) (6,10) (6,13) (6,25) (6,12) (6,9) (7,28) (8,10) (8,14) (8,18) (8,29) (8,25) (8,23) (9,13) (9,14) (10,29) (10,25) (12,22) (12,18) (12,17) (13,29) (13,26) (14,20) (14,17) (15,19) (17,25) (18,20) (18,25) (20,29) (20,26) (20,23) (21,27) (21,24) (23,26) (23,25) (24,27) (26,29)\nQ: Is there a path between node 10 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "364"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,13) (0,30) (0,1) (0,4) (0,2) (0,22) (1,30) (1,17) (1,5) (1,4) (1,25) (1,29) (2,3) (2,5) (2,23) (3,28) (3,24) (3,4) (3,6) (3,8) (3,12) (4,15) (4,24) (4,25) (4,7) (4,6) (4,29) (5,21) (5,23) (5,7) (5,12) (6,20) (6,28) (6,23) (7,13) (7,15) (7,16) (7,8) (7,12) (8,20) (8,30) (8,24) (8,17) (8,23) (10,19) (11,19) (11,26) (12,20) (12,16) (12,25) (12,18) (13,28) (13,18) (14,20) (15,28) (15,24) (15,23) (16,20) (16,30) (16,24) (16,29) (17,21) (17,28) (17,25) (18,21) (18,23) (18,29) (20,24) (20,23) (20,22) (20,29) (21,25) (21,23) (21,22) (22,25) (23,24) (23,29) (24,28) (24,29) (25,28) (26,27) (29,30)\nQ: Is there a path between node 19 and node 27?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "365"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,11) (0,17) (0,3) (0,19) (0,9) (0,16) (0,15) (0,7) (0,12) (0,2) (1,11) (1,10) (1,3) (1,4) (1,8) (1,19) (1,13) (1,9) (1,16) (1,15) (1,7) (1,12) (1,2) (2,17) (2,5) (2,16) (2,15) (3,17) (3,10) (3,5) (3,6) (3,8) (3,13) (3,9) (3,16) (3,15) (3,7) (3,12) (4,11) (4,5) (4,8) (4,19) (4,13) (4,9) (4,7) (4,12) (5,11) (5,10) (5,6) (5,8) (5,19) (5,13) (5,7) (6,11) (6,17) (6,10) (6,8) (6,19) (6,13) (6,16) (6,15) (6,7) (6,12) (7,11) (7,17) (7,10) (7,19) (7,9) (7,16) (7,15) (8,11) (8,17) (8,10) (8,19) (8,13) (8,15) (8,12) (9,11) (9,17) (9,10) (9,13) (9,16) (9,15) (10,11) (10,17) (10,19) (10,13) (10,15) (10,12) (11,19) (11,15) (11,12) (12,17) (12,19) (12,13) (13,19) (13,16) (13,15) (14,18) (15,19) (15,16) (16,17) (17,19)\nQ: Is there a path between node 3 and node 19?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "366"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,17) (0,13) (0,12) (0,4) (0,1) (1,3) (1,17) (1,16) (1,14) (1,4) (2,5) (2,7) (2,9) (2,11) (2,8) (3,15) (3,13) (3,16) (3,12) (3,14) (3,6) (4,15) (4,13) (4,16) (4,12) (4,6) (5,9) (5,11) (5,10) (6,17) (6,13) (6,12) (7,11) (7,10) (7,8) (8,9) (8,11) (9,10) (10,11) (12,15) (12,17) (12,16) (12,14) (13,17) (13,16) (14,15) (14,17) (15,17) (15,16) (16,17)\nQ: Is there a path between node 1 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "367"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,10) (0,2) (2,15) (2,20) (2,23) (2,14) (2,17) (2,24) (2,18) (3,21) (4,27) (5,9) (5,22) (6,29) (6,8) (7,29) (7,25) (7,20) (7,17) (7,18) (7,8) (8,23) (8,24) (10,23) (10,18) (11,27) (12,13) (13,21) (14,25) (14,23) (14,17) (14,24) (15,29) (15,25) (15,23) (15,16) (16,29) (16,17) (17,25) (17,23) (17,24) (17,18) (18,29) (20,25) (22,26) (23,25) (24,29) (26,27)\nQ: Is there a path between node 8 and node 27?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "368"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (0,3) (0,4) (0,1) (1,2) (1,5) (1,6) (1,3) (1,4) (2,5) (2,6) (2,3) (2,4) (3,5) (3,6) (3,4) (4,5) (4,6) (5,6)\nQ: Is there a path between node 2 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "369"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,5) (0,20) (0,7) (0,19) (0,1) (0,14) (0,12) (0,15) (0,18) (0,4) (1,10) (1,5) (1,7) (1,2) (1,14) (1,12) (1,3) (1,15) (1,16) (1,4) (2,10) (2,5) (2,20) (2,7) (2,19) (2,14) (2,12) (2,15) (2,16) (2,17) (2,18) (2,4) (3,5) (3,20) (3,7) (3,19) (3,14) (3,16) (3,17) (3,18) (4,10) (4,5) (4,20) (4,7) (4,19) (4,14) (4,12) (4,15) (4,16) (4,17) (5,20) (5,7) (5,19) (5,14) (5,12) (5,16) (5,17) (5,18) (6,11) (6,8) (7,10) (7,19) (7,14) (7,12) (7,15) (7,16) (7,17) (7,18) (8,11) (9,21) (9,13) (10,19) (10,14) (10,12) (10,16) (10,18) (12,20) (12,19) (12,14) (12,15) (12,16) (12,17) (14,20) (14,19) (14,15) (14,16) (14,17) (15,20) (15,19) (15,16) (15,17) (15,18) (16,20) (16,19) (16,17) (16,18) (17,20) (17,19) (17,18) (18,19) (19,20)\nQ: Is there a path between node 21 and node 15?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "370"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,19) (0,17) (0,7) (0,16) (0,21) (1,22) (1,19) (1,20) (1,21) (2,23) (2,6) (3,13) (3,18) (3,4) (3,10) (3,21) (4,19) (4,10) (4,16) (5,14) (5,12) (5,9) (5,11) (6,14) (6,23) (7,15) (7,22) (7,18) (7,8) (7,17) (7,20) (8,13) (8,21) (9,12) (9,11) (10,17) (13,19) (13,17) (13,21) (15,20) (16,18) (16,20) (19,20) (19,21)\nQ: Is there a path between node 2 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "371"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,6) (1,4) (1,3) (1,2) (1,7) (2,10) (2,4) (2,8) (3,10) (3,6) (3,4) (3,8) (3,5) (4,6) (4,8) (4,5) (4,7) (5,10) (5,8) (6,10) (6,8) (7,10)\nQ: Is there a path between node 0 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "372"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,3) (1,20) (1,21) (1,8) (1,5) (1,16) (1,17) (1,19) (1,6) (1,12) (1,14) (1,9) (1,13) (1,18) (1,7) (1,11) (1,15) (1,2) (1,10) (2,20) (2,21) (2,8) (2,5) (2,16) (2,17) (2,19) (2,6) (2,12) (2,14) (2,9) (2,13) (2,18) (2,7) (2,11) (2,15) (2,10) (3,4) (5,20) (5,21) (5,8) (5,16) (5,17) (5,19) (5,6) (5,12) (5,14) (5,9) (5,13) (5,18) (5,7) (5,11) (5,15) (5,10) (6,20) (6,21) (6,8) (6,16) (6,17) (6,19) (6,12) (6,14) (6,9) (6,13) (6,18) (6,7) (6,11) (6,15) (6,10) (7,20) (7,21) (7,8) (7,16) (7,17) (7,19) (7,12) (7,14) (7,9) (7,13) (7,18) (7,11) (7,15) (7,10) (8,20) (8,21) (8,16) (8,17) (8,19) (8,12) (8,14) (8,9) (8,13) (8,18) (8,11) (8,15) (8,10) (9,20) (9,21) (9,16) (9,17) (9,19) (9,12) (9,14) (9,13) (9,18) (9,11) (9,15) (9,10) (10,20) (10,21) (10,16) (10,17) (10,19) (10,12) (10,14) (10,13) (10,18) (10,11) (10,15) (11,20) (11,21) (11,16) (11,17) (11,19) (11,12) (11,14) (11,13) (11,18) (11,15) (12,20) (12,21) (12,16) (12,17) (12,19) (12,14) (12,13) (12,18) (12,15) (13,20) (13,21) (13,16) (13,17) (13,19) (13,14) (13,18) (13,15) (14,20) (14,21) (14,16) (14,17) (14,19) (14,18) (14,15) (15,20) (15,21) (15,16) (15,17) (15,19) (15,18) (16,20) (16,21) (16,17) (16,19) (16,18) (17,20) (17,21) (17,19) (17,18) (18,20) (18,21) (18,19) (19,20) (19,21) (20,21)\nQ: Is there a path between node 19 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "373"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (1,4) (2,4)\nQ: Is there a path between node 0 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "374"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,3) (0,14) (1,8) (1,6) (1,14) (2,6) (2,12) (2,18) (3,8) (3,6) (3,12) (3,18) (4,12) (4,9) (4,14) (5,15) (5,16) (5,7) (6,8) (6,12) (6,14) (7,10) (9,11) (9,18) (15,17) (15,16)\nQ: Is there a path between node 0 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "375"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,11) (0,15) (0,25) (0,31) (0,23) (0,14) (1,28) (1,20) (1,12) (1,21) (1,19) (1,24) (1,27) (1,13) (1,6) (2,20) (2,22) (2,21) (2,19) (2,13) (2,6) (3,15) (3,4) (3,25) (3,23) (4,9) (4,15) (4,14) (5,8) (5,17) (5,10) (5,26) (5,7) (5,16) (6,20) (6,21) (6,19) (6,27) (6,13) (7,17) (7,16) (7,29) (8,17) (9,11) (9,15) (9,31) (9,23) (9,14) (10,17) (11,15) (11,30) (11,23) (11,14) (12,20) (12,22) (12,19) (12,27) (12,13) (12,18) (13,28) (13,22) (13,21) (13,24) (13,27) (13,18) (14,15) (14,25) (14,31) (14,23) (15,25) (15,30) (15,23) (16,26) (17,26) (17,29) (18,28) (18,20) (18,22) (18,21) (18,19) (18,24) (18,27) (19,22) (19,21) (19,24) (19,27) (20,28) (20,22) (20,21) (20,24) (20,27) (21,28) (21,22) (21,24) (22,24) (22,27) (23,30) (23,31) (24,28) (25,31) (27,28) (30,31)\nQ: Is there a path between node 30 and node 17?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "376"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,11) (0,17) (0,3) (0,19) (0,9) (0,16) (0,15) (0,7) (0,12) (0,2) (1,11) (1,10) (1,3) (1,4) (1,8) (1,19) (1,13) (1,9) (1,16) (1,15) (1,7) (1,12) (1,2) (2,17) (2,5) (2,16) (2,15) (3,17) (3,10) (3,5) (3,6) (3,8) (3,13) (3,9) (3,16) (3,15) (3,7) (3,12) (4,11) (4,5) (4,8) (4,19) (4,13) (4,9) (4,7) (4,12) (5,11) (5,10) (5,6) (5,8) (5,19) (5,13) (5,7) (6,11) (6,17) (6,10) (6,8) (6,19) (6,13) (6,16) (6,15) (6,7) (6,12) (7,11) (7,17) (7,10) (7,19) (7,9) (7,16) (7,15) (8,11) (8,17) (8,10) (8,19) (8,13) (8,15) (8,12) (9,11) (9,17) (9,10) (9,13) (9,16) (9,15) (10,11) (10,17) (10,19) (10,13) (10,15) (10,12) (11,19) (11,15) (11,12) (12,17) (12,19) (12,13) (13,19) (13,16) (13,15) (14,18) (15,19) (15,16) (16,17) (17,19)\nQ: Is there a path between node 3 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "377"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (2,8) (2,4) (2,3) (3,8) (5,7) (6,7)\nQ: Is there a path between node 0 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "378"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,3) (1,20) (1,21) (1,8) (1,5) (1,16) (1,17) (1,19) (1,6) (1,12) (1,14) (1,9) (1,13) (1,18) (1,7) (1,11) (1,15) (1,2) (1,10) (2,20) (2,21) (2,8) (2,5) (2,16) (2,17) (2,19) (2,6) (2,12) (2,14) (2,9) (2,13) (2,18) (2,7) (2,11) (2,15) (2,10) (3,4) (5,20) (5,21) (5,8) (5,16) (5,17) (5,19) (5,6) (5,12) (5,14) (5,9) (5,13) (5,18) (5,7) (5,11) (5,15) (5,10) (6,20) (6,21) (6,8) (6,16) (6,17) (6,19) (6,12) (6,14) (6,9) (6,13) (6,18) (6,7) (6,11) (6,15) (6,10) (7,20) (7,21) (7,8) (7,16) (7,17) (7,19) (7,12) (7,14) (7,9) (7,13) (7,18) (7,11) (7,15) (7,10) (8,20) (8,21) (8,16) (8,17) (8,19) (8,12) (8,14) (8,9) (8,13) (8,18) (8,11) (8,15) (8,10) (9,20) (9,21) (9,16) (9,17) (9,19) (9,12) (9,14) (9,13) (9,18) (9,11) (9,15) (9,10) (10,20) (10,21) (10,16) (10,17) (10,19) (10,12) (10,14) (10,13) (10,18) (10,11) (10,15) (11,20) (11,21) (11,16) (11,17) (11,19) (11,12) (11,14) (11,13) (11,18) (11,15) (12,20) (12,21) (12,16) (12,17) (12,19) (12,14) (12,13) (12,18) (12,15) (13,20) (13,21) (13,16) (13,17) (13,19) (13,14) (13,18) (13,15) (14,20) (14,21) (14,16) (14,17) (14,19) (14,18) (14,15) (15,20) (15,21) (15,16) (15,17) (15,19) (15,18) (16,20) (16,21) (16,17) (16,19) (16,18) (17,20) (17,21) (17,19) (17,18) (18,20) (18,21) (18,19) (19,20) (19,21) (20,21)\nQ: Is there a path between node 2 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "379"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,3) (0,2) (1,5) (1,3) (2,5) (2,3) (3,5)\nQ: Is there a path between node 4 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "380"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,1) (0,2) (0,7) (0,6) (1,2) (1,8) (1,7) (1,4) (1,6) (2,7) (2,4) (2,6) (3,5) (4,9) (4,8) (4,7) (6,9) (6,7) (7,8)\nQ: Is there a path between node 3 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "381"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,10) (0,25) (0,16) (0,24) (0,4) (0,8) (0,27) (0,19) (1,5) (1,28) (2,15) (3,12) (3,13) (3,21) (3,24) (3,4) (3,8) (4,26) (4,20) (4,21) (4,11) (4,9) (6,13) (6,14) (6,22) (6,21) (6,7) (6,23) (6,11) (7,12) (7,26) (7,20) (7,17) (7,14) (7,10) (7,25) (7,24) (7,8) (7,11) (7,19) (7,9) (8,25) (8,27) (8,11) (9,17) (9,14) (9,21) (9,23) (9,27) (9,11) (10,26) (10,20) (10,14) (10,25) (10,23) (10,24) (11,13) (11,17) (11,21) (11,25) (11,23) (11,19) (12,20) (12,17) (12,24) (13,26) (13,20) (13,17) (13,22) (13,25) (13,24) (13,19) (14,20) (14,16) (15,28) (15,18) (16,26) (16,21) (16,23) (17,26) (17,22) (17,23) (17,27) (18,28) (19,22) (20,23) (20,24) (20,27) (21,26) (21,27) (23,25) (24,25) (24,27) (25,27)\nQ: Is there a path between node 15 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "382"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,25) (0,13) (0,3) (0,1) (1,11) (1,25) (1,13) (1,2) (1,3) (1,8) (2,21) (2,22) (2,25) (2,13) (2,3) (3,18) (3,22) (3,11) (3,13) (4,23) (4,14) (4,6) (4,12) (4,27) (4,15) (4,5) (4,16) (4,26) (4,20) (4,7) (4,19) (5,14) (5,6) (5,12) (5,27) (5,15) (5,16) (5,9) (5,20) (5,7) (6,23) (6,14) (6,12) (6,24) (6,15) (6,16) (6,9) (6,17) (6,26) (6,20) (6,7) (6,19) (7,23) (7,14) (7,12) (7,24) (7,10) (7,16) (7,9) (7,17) (7,26) (7,20) (7,19) (8,21) (8,18) (8,22) (8,11) (8,25) (8,13) (9,23) (9,12) (9,10) (9,16) (9,17) (9,26) (9,20) (10,23) (10,14) (10,12) (10,24) (10,27) (10,16) (10,17) (10,26) (10,19) (11,21) (11,22) (11,25) (11,13) (12,23) (12,14) (12,24) (12,27) (12,16) (12,26) (12,20) (12,19) (13,22) (13,25) (14,23) (14,24) (14,16) (14,26) (14,19) (15,24) (15,27) (15,16) (15,26) (16,23) (16,27) (16,17) (16,26) (16,20) (17,27) (17,26) (17,20) (17,19) (18,22) (19,23) (19,24) (19,27) (19,26) (19,20) (20,23) (20,26) (21,22) (21,25) (22,25) (23,24) (23,27) (24,27) (24,26) (26,27)\nQ: Is there a path between node 19 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "383"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,7) (0,8) (0,9) (0,13) (0,14) (0,15) (0,5) (1,2) (1,12) (1,16) (1,11) (1,3) (1,6) (1,14) (1,4) (2,12) (2,7) (2,9) (2,13) (2,14) (3,16) (3,11) (3,7) (3,8) (3,14) (3,15) (3,5) (3,4) (4,12) (4,11) (4,8) (4,9) (4,13) (4,14) (4,5) (5,12) (5,16) (5,11) (5,7) (5,8) (5,13) (5,14) (5,15) (6,12) (6,16) (6,11) (6,7) (6,14) (6,15) (7,12) (7,16) (7,11) (7,8) (7,9) (7,13) (8,12) (8,16) (8,11) (8,9) (8,13) (8,14) (9,12) (9,16) (9,11) (9,14) (9,15) (11,12) (11,16) (11,14) (12,13) (12,15) (13,16) (13,15) (14,16)\nQ: Is there a path between node 8 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "384"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,10) (2,9) (2,5) (3,12) (3,14) (3,4) (3,8) (3,18) (4,19) (4,16) (4,11) (5,20) (5,12) (5,14) (5,11) (6,18) (6,16) (7,15) (8,20) (8,12) (8,18) (8,16) (9,20) (9,14) (9,19) (9,11) (11,13) (11,12) (11,18) (11,16) (12,18) (13,19) (13,18) (14,19) (16,20) (18,19)\nQ: Is there a path between node 10 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "385"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (0,1) (0,19) (0,15) (0,20) (0,9) (0,21) (0,3) (0,22) (0,32) (0,24) (0,14) (0,11) (0,17) (0,5) (0,34) (0,4) (0,26) (0,10) (0,8) (1,27) (1,23) (1,30) (1,6) (1,19) (1,20) (1,2) (1,9) (1,21) (1,3) (1,22) (1,24) (1,14) (1,11) (1,17) (1,5) (1,4) (1,26) (1,8) (2,27) (2,30) (2,6) (2,19) (2,20) (2,9) (2,21) (2,3) (2,22) (2,32) (2,7) (2,11) (2,17) (2,5) (2,34) (2,4) (2,26) (2,12) (2,10) (3,27) (3,23) (3,30) (3,6) (3,19) (3,15) (3,20) (3,9) (3,22) (3,24) (3,14) (3,34) (3,4) (3,12) (3,10) (3,8) (3,28) (4,27) (4,23) (4,30) (4,19) (4,15) (4,20) (4,9) (4,21) (4,32) (4,24) (4,14) (4,7) (4,11) (4,17) (4,5) (4,26) (4,12) (4,8) (4,28) (5,30) (5,19) (5,9) (5,21) (5,24) (5,7) (5,11) (5,17) (5,34) (5,12) (6,27) (6,23) (6,30) (6,19) (6,20) (6,9) (6,21) (6,22) (6,32) (6,24) (6,14) (6,7) (6,11) (6,17) (6,34) (6,26) (6,8) (6,28) (7,23) (7,30) (7,19) (7,15) (7,20) (7,21) (7,32) (7,24) (7,11) (7,17) (7,34) (7,12) (7,10) (7,8) (7,28) (8,23) (8,15) (8,20) (8,24) (8,14) (8,11) (8,17) (8,34) (8,26) (8,12) (8,10) (8,28) (9,30) (9,19) (9,15) (9,20) (9,22) (9,32) (9,24) (9,11) (9,34) (9,12) (9,10) (9,28) (10,27) (10,23) (10,30) (10,19) (10,21) (10,32) (10,24) (10,26) (10,12) (11,27) (11,30) (11,19) (11,20) (11,21) (11,22) (11,32) (11,24) (11,14) (11,17) (11,34) (11,12) (12,27) (12,30) (12,19) (12,20) (12,22) (12,32) (12,24) (12,14) (12,17) (12,34) (12,28) (14,27) (14,23) (14,30) (14,19) (14,15) (14,21) (14,22) (14,32) (14,17) (14,34) (14,28) (15,19) (15,20) (15,21) (15,22) (15,32) (15,24) (15,34) (15,26) (15,28) (16,33) (16,29) (16,18) (16,31) (17,27) (17,23) (17,30) (17,19) (17,20) (17,21) (17,22) (17,32) (17,24) (17,34) (17,28) (18,33) (18,31) (18,25) (19,27) (19,23) (19,30) (19,20) (19,22) (19,32) (19,34) (19,26) (19,28) (20,23) (20,30) (20,21) (20,22) (20,32) (20,24) (20,34) (20,26) (21,27) (21,23) (21,30) (21,22) (21,32) (21,24) (21,34) (21,26) (21,28) (22,27) (22,23) (22,24) (22,34) (22,26) (22,28) (23,32) (23,26) (23,28) (24,27) (24,32) (24,34) (24,26) (25,33) (26,30) (26,32) (26,34) (27,30) (27,32) (27,28) (28,30) (28,32) (28,34) (29,33) (29,31) (31,33) (32,34)\nQ: Is there a path between node 29 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "386"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,10) (0,26) (0,13) (0,23) (0,14) (0,27) (0,30) (0,31) (0,28) (0,2) (0,8) (0,12) (0,9) (0,24) (0,5) (1,19) (1,15) (1,6) (1,11) (1,29) (1,17) (1,21) (1,4) (1,25) (1,7) (2,3) (2,14) (2,31) (2,28) (2,18) (2,8) (2,12) (2,9) (2,24) (2,5) (3,10) (3,13) (3,23) (3,27) (3,30) (3,31) (3,28) (3,18) (3,8) (3,12) (3,9) (3,24) (3,5) (4,20) (4,19) (4,15) (4,11) (4,29) (4,16) (4,22) (4,7) (5,10) (5,13) (5,23) (5,14) (5,27) (5,31) (5,18) (5,8) (5,12) (5,9) (6,20) (6,15) (6,11) (6,29) (6,17) (6,21) (6,16) (6,25) (6,7) (7,20) (7,15) (7,11) (7,29) (7,17) (7,21) (7,25) (8,10) (8,26) (8,13) (8,23) (8,14) (8,27) (8,30) (8,12) (8,24) (9,10) (9,26) (9,13) (9,14) (9,27) (9,30) (9,31) (9,18) (9,24) (10,26) (10,13) (10,23) (10,14) (10,27) (10,30) (10,31) (10,18) (11,20) (11,19) (11,15) (11,29) (11,17) (11,21) (11,16) (11,25) (11,22) (12,13) (12,23) (12,14) (12,27) (12,28) (13,26) (13,23) (13,14) (13,27) (13,31) (13,28) (14,23) (14,30) (14,28) (14,18) (14,24) (15,19) (15,29) (15,21) (15,16) (15,22) (16,20) (16,19) (16,29) (16,17) (16,21) (16,25) (17,20) (17,19) (17,29) (17,21) (17,25) (17,22) (18,26) (18,27) (18,30) (18,31) (18,28) (19,29) (19,21) (19,25) (19,22) (20,29) (20,22) (21,29) (21,25) (21,22) (22,25) (23,26) (23,27) (23,30) (23,31) (23,24) (24,27) (24,30) (24,31) (25,29) (26,27) (26,30) (26,28) (27,30) (27,31) (28,30) (28,31) (30,31)\nQ: Is there a path between node 31 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "387"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,18) (1,12) (1,15) (1,7) (2,17) (2,3) (3,17) (4,12) (5,17) (5,19) (6,18) (6,10) (6,9) (6,12) (6,16) (7,18) (7,9) (7,13) (7,8) (8,14) (9,18) (9,14) (9,12) (9,13) (10,12) (10,15) (11,17) (12,16) (14,18)\nQ: Is there a path between node 18 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "388"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,21) (0,17) (0,7) (0,29) (1,20) (2,32) (2,6) (2,13) (3,22) (3,23) (3,8) (4,30) (4,31) (6,23) (6,16) (6,32) (7,19) (8,14) (8,23) (8,16) (8,32) (8,13) (9,24) (9,17) (9,29) (13,14) (13,32) (14,16) (14,32) (16,20) (16,28) (17,24) (20,28) (21,29) (24,29) (27,30) (30,31)\nQ: Is there a path between node 24 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "389"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,18) (0,19) (0,20) (0,23) (0,9) (0,10) (0,22) (0,13) (0,1) (0,12) (0,5) (0,7) (0,15) (0,4) (1,11) (1,18) (1,19) (1,20) (1,23) (1,9) (1,10) (1,22) (1,13) (1,12) (1,5) (1,7) (1,15) (1,4) (2,8) (2,6) (2,3) (2,24) (2,16) (2,21) (2,17) (2,14) (3,8) (3,6) (3,24) (3,16) (3,21) (3,17) (3,14) (4,11) (4,18) (4,19) (4,20) (4,23) (4,9) (4,10) (4,22) (4,13) (4,12) (4,5) (4,7) (4,15) (5,11) (5,18) (5,19) (5,20) (5,23) (5,9) (5,10) (5,22) (5,13) (5,12) (5,7) (5,15) (6,8) (6,24) (6,16) (6,21) (6,17) (6,14) (7,11) (7,18) (7,19) (7,20) (7,23) (7,9) (7,10) (7,22) (7,13) (7,12) (7,15) (8,24) (8,16) (8,21) (8,17) (8,14) (9,11) (9,18) (9,19) (9,20) (9,23) (9,10) (9,22) (9,13) (9,12) (9,15) (10,11) (10,18) (10,19) (10,20) (10,23) (10,22) (10,13) (10,12) (10,15) (11,18) (11,19) (11,20) (11,23) (11,22) (11,13) (11,12) (11,15) (12,18) (12,19) (12,20) (12,23) (12,22) (12,13) (12,15) (13,18) (13,19) (13,20) (13,23) (13,22) (13,15) (14,24) (14,16) (14,21) (14,17) (15,18) (15,19) (15,20) (15,23) (15,22) (16,24) (16,21) (16,17) (17,24) (17,21) (18,19) (18,20) (18,23) (18,22) (19,20) (19,23) (19,22) (20,23) (20,22) (21,24) (22,23)\nQ: Is there a path between node 2 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "390"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,2) (0,4) (0,5) (0,15) (0,7) (1,9) (1,13) (1,12) (1,3) (2,14) (2,10) (2,4) (2,8) (2,15) (2,7) (3,9) (3,13) (3,12) (3,11) (4,14) (4,6) (4,10) (4,8) (4,15) (5,6) (5,8) (5,7) (6,14) (6,8) (6,15) (7,14) (7,10) (7,8) (7,15) (8,14) (8,10) (8,15) (9,13) (9,12) (9,11) (10,14) (10,15) (11,13) (11,12) (12,13) (14,15)\nQ: Is there a path between node 2 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "391"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,27) (0,13) (0,10) (0,15) (0,2) (0,17) (1,5) (1,22) (1,8) (1,19) (1,26) (1,24) (1,18) (1,16) (1,14) (1,12) (1,4) (1,9) (2,7) (2,27) (2,13) (2,3) (2,6) (2,10) (2,11) (2,17) (3,7) (3,27) (3,20) (3,6) (3,10) (3,15) (3,21) (3,17) (4,5) (4,8) (4,19) (4,26) (4,25) (4,18) (4,14) (4,12) (5,8) (5,26) (5,18) (5,16) (5,14) (5,12) (6,7) (6,13) (6,10) (6,21) (7,20) (7,13) (7,10) (7,15) (7,11) (8,19) (8,26) (8,18) (8,16) (8,14) (8,9) (9,22) (9,19) (9,26) (9,25) (9,16) (9,14) (9,12) (10,13) (10,21) (10,17) (11,27) (11,13) (11,15) (11,21) (11,17) (12,22) (12,19) (12,26) (12,24) (12,25) (12,16) (12,14) (13,27) (13,15) (14,22) (14,19) (14,26) (15,27) (15,20) (15,21) (15,17) (16,22) (16,19) (16,24) (16,25) (16,18) (17,27) (17,20) (17,21) (18,22) (18,19) (18,26) (18,24) (19,26) (19,25) (20,27) (20,21) (21,27) (22,26) (22,24) (24,26)\nQ: Is there a path between node 13 and node 17?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "392"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,11) (0,6) (1,5) (1,8) (1,10) (1,15) (1,17) (1,13) (1,16) (2,5) (2,4) (2,8) (2,10) (2,14) (2,17) (2,13) (2,16) (3,9) (3,6) (3,12) (4,8) (4,15) (4,14) (4,17) (4,13) (5,8) (5,15) (5,17) (6,7) (6,9) (7,11) (7,9) (8,15) (8,17) (8,13) (8,16) (9,11) (10,15) (10,14) (10,17) (11,12) (13,15) (13,14) (13,16) (14,15) (14,17) (14,16) (15,17) (15,16) (16,17)\nQ: Is there a path between node 12 and node 17?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "393"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (1,15) (1,16) (2,18) (2,17) (2,7) (3,14) (3,7) (5,11) (6,13) (7,17) (8,15) (8,13) (9,17) (10,17) (13,15) (13,16) (16,19)\nQ: Is there a path between node 19 and node 18?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "394"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,14) (0,12) (1,20) (1,12) (2,13) (2,18) (3,17) (4,20) (7,21) (8,18) (9,20) (9,15) (10,13) (10,19) (13,18) (14,16) (14,15) (15,20)\nQ: Is there a path between node 14 and node 20?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "395"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,12) (1,25) (1,2) (1,10) (1,12) (1,3) (2,8) (2,22) (2,25) (2,26) (2,19) (2,11) (2,12) (2,7) (2,21) (3,25) (3,26) (3,10) (3,27) (3,21) (5,24) (5,6) (6,23) (6,9) (7,22) (7,25) (7,11) (8,20) (8,22) (8,25) (8,26) (8,27) (9,24) (10,14) (10,25) (10,13) (10,27) (10,21) (11,22) (11,12) (11,17) (11,21) (12,19) (12,18) (12,17) (12,27) (12,21) (13,17) (13,21) (14,17) (14,21) (15,23) (15,24) (16,22) (17,22) (17,25) (17,19) (18,20) (18,26) (18,21) (19,22) (19,26) (19,27) (20,27) (22,25) (25,26)\nQ: Is there a path between node 15 and node 19?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "396"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,6) (0,11) (0,19) (0,20) (0,1) (0,15) (0,12) (0,7) (0,22) (0,5) (0,21) (0,3) (0,4) (0,18) (0,17) (1,14) (1,6) (1,11) (1,19) (1,20) (1,15) (1,12) (1,7) (1,22) (1,5) (1,21) (1,3) (1,4) (1,18) (1,17) (2,13) (2,10) (2,8) (2,16) (2,9) (3,14) (3,6) (3,11) (3,19) (3,20) (3,15) (3,12) (3,7) (3,22) (3,5) (3,21) (3,4) (3,18) (3,17) (4,14) (4,6) (4,11) (4,19) (4,20) (4,15) (4,12) (4,7) (4,22) (4,5) (4,21) (4,18) (4,17) (5,14) (5,6) (5,11) (5,19) (5,20) (5,15) (5,12) (5,7) (5,22) (5,21) (5,18) (5,17) (6,14) (6,11) (6,19) (6,20) (6,15) (6,12) (6,7) (6,22) (6,21) (6,18) (6,17) (7,14) (7,11) (7,19) (7,20) (7,15) (7,12) (7,22) (7,21) (7,18) (7,17) (8,13) (8,10) (8,16) (8,9) (9,13) (9,10) (9,16) (10,13) (10,16) (11,14) (11,19) (11,20) (11,15) (11,12) (11,22) (11,21) (11,18) (11,17) (12,14) (12,19) (12,20) (12,15) (12,22) (12,21) (12,18) (12,17) (13,16) (14,19) (14,20) (14,15) (14,22) (14,21) (14,18) (14,17) (15,19) (15,20) (15,22) (15,21) (15,18) (15,17) (17,19) (17,20) (17,22) (17,21) (17,18) (18,19) (18,20) (18,22) (18,21) (19,20) (19,22) (19,21) (20,22) (20,21) (21,22)\nQ: Is there a path between node 0 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "397"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,6) (2,7) (2,6) (2,4) (5,7) (6,8)\nQ: Is there a path between node 5 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "398"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,6) (0,21) (0,18) (1,24) (1,3) (3,24) (3,14) (4,6) (4,5) (4,23) (6,14) (6,21) (6,23) (7,11) (8,19) (8,13) (9,15) (9,19) (10,11) (10,12) (10,16) (10,17) (11,12) (11,16) (12,17) (13,15) (13,22) (14,23) (15,22) (16,17) (18,24) (18,21)\nQ: Is there a path between node 17 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "399"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,7) (0,12) (0,32) (0,22) (0,9) (0,20) (0,2) (0,5) (0,14) (0,4) (0,26) (0,21) (1,11) (1,8) (1,24) (1,3) (1,31) (1,28) (1,6) (2,16) (2,7) (2,32) (2,22) (2,9) (2,20) (2,14) (2,4) (2,21) (3,11) (3,8) (3,24) (3,31) (3,28) (4,16) (4,32) (4,22) (4,9) (4,20) (4,5) (4,14) (4,26) (5,16) (5,7) (5,12) (5,32) (5,22) (5,9) (5,20) (5,14) (5,26) (5,21) (6,8) (6,24) (6,31) (6,28) (7,12) (7,32) (7,22) (7,9) (7,14) (7,26) (7,21) (8,24) (8,31) (8,28) (9,16) (9,12) (9,32) (9,20) (9,26) (9,21) (10,23) (10,13) (10,29) (10,19) (10,25) (10,18) (12,32) (12,22) (12,20) (12,26) (12,21) (13,30) (13,27) (13,29) (13,19) (13,25) (13,18) (14,16) (14,32) (14,22) (14,20) (14,26) (15,30) (15,29) (15,25) (15,18) (16,32) (16,22) (16,20) (16,26) (16,21) (17,30) (17,27) (18,30) (18,29) (19,30) (19,23) (19,27) (19,25) (20,32) (20,22) (20,26) (21,32) (21,26) (22,32) (22,26) (23,30) (23,29) (23,25) (24,28) (26,32) (27,30) (27,29) (28,31) (29,30)\nQ: Is there a path between node 21 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "400"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (1,5) (1,18) (1,7) (1,22) (1,11) (1,20) (1,4) (1,23) (2,14) (2,10) (2,21) (2,15) (2,16) (2,3) (3,14) (3,10) (3,15) (3,16) (3,6) (3,19) (4,18) (4,7) (4,22) (4,11) (4,20) (4,23) (5,13) (5,7) (5,22) (5,11) (5,20) (5,23) (6,10) (6,21) (6,15) (6,16) (6,9) (6,8) (6,19) (7,13) (7,22) (7,20) (7,23) (8,10) (8,9) (8,19) (9,21) (9,15) (9,19) (10,21) (10,16) (10,19) (11,18) (11,13) (11,22) (11,23) (12,17) (13,22) (13,20) (14,15) (14,16) (14,19) (15,16) (15,19) (16,21) (16,19) (18,20) (18,23) (19,21) (20,22) (20,23) (22,23)\nQ: Is there a path between node 18 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "401"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,12) (0,11) (0,4) (2,10) (2,8) (2,4) (4,6) (4,11) (5,9) (6,7) (6,10) (6,11) (7,8) (8,10) (8,9) (9,12) (10,11)\nQ: Is there a path between node 6 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "402"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,26) (2,26) (2,30) (2,6) (3,19) (4,29) (4,8) (4,11) (4,9) (5,25) (6,30) (6,19) (6,13) (6,25) (7,23) (7,29) (7,10) (7,28) (7,14) (8,23) (8,15) (8,27) (8,18) (8,11) (8,28) (8,9) (9,23) (9,29) (9,15) (9,18) (9,12) (10,15) (11,29) (11,27) (11,28) (11,14) (12,27) (13,16) (13,26) (14,17) (15,29) (15,21) (15,28) (16,25) (17,23) (17,29) (17,18) (19,20) (19,22) (20,22) (21,27) (21,28) (22,26) (23,29) (23,28) (24,26) (24,30) (25,26) (25,30) (27,28)\nQ: Is there a path between node 13 and node 20?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "403"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,9) (0,8) (0,19) (0,13) (0,11) (1,15) (1,6) (1,3) (1,12) (1,4) (1,2) (1,23) (1,5) (1,16) (1,22) (1,17) (1,18) (1,21) (1,24) (1,25) (2,15) (2,3) (2,4) (2,20) (2,23) (2,22) (2,27) (2,18) (2,21) (2,24) (3,15) (3,4) (3,26) (3,20) (3,23) (3,5) (3,16) (3,14) (3,22) (3,27) (3,18) (3,21) (3,24) (3,25) (4,15) (4,6) (4,12) (4,26) (4,20) (4,5) (4,22) (4,27) (4,17) (4,21) (4,25) (5,15) (5,6) (5,12) (5,20) (5,16) (5,14) (5,22) (5,27) (5,18) (5,21) (5,25) (6,15) (6,12) (6,27) (6,17) (6,21) (6,24) (6,25) (7,19) (7,13) (8,9) (8,19) (8,13) (9,19) (9,10) (10,19) (10,13) (10,11) (11,13) (12,15) (12,26) (12,20) (12,14) (12,22) (12,21) (12,24) (13,19) (14,15) (14,26) (14,20) (14,16) (14,22) (14,17) (14,21) (14,24) (14,25) (15,26) (15,20) (15,23) (15,16) (15,22) (15,17) (15,18) (15,24) (16,26) (16,27) (16,18) (16,25) (17,26) (17,23) (17,18) (17,21) (17,24) (17,25) (18,26) (18,20) (18,22) (18,27) (18,24) (18,25) (20,26) (20,23) (20,22) (20,27) (20,24) (20,25) (21,22) (21,27) (21,24) (21,25) (22,23) (22,27) (22,24) (22,25) (23,27) (23,25) (24,26) (24,27) (25,26) (25,27) (26,27)\nQ: Is there a path between node 20 and node 24?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "404"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,17) (1,4) (2,10) (3,19) (3,30) (3,13) (3,25) (3,8) (4,31) (5,16) (6,29) (6,11) (6,32) (7,14) (7,17) (8,21) (8,30) (8,13) (8,28) (9,20) (9,25) (11,29) (11,26) (11,22) (13,21) (13,15) (13,28) (13,23) (15,31) (15,16) (15,28) (15,23) (16,21) (16,25) (16,23) (18,29) (18,24) (20,31) (20,30) (20,25) (21,25) (22,24) (23,25) (23,28) (24,29) (24,32) (25,30) (26,32) (28,30)\nQ: Is there a path between node 30 and node 14?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "405"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,23) (0,8) (1,6) (1,26) (1,11) (2,6) (2,11) (3,12) (3,19) (3,20) (4,13) (4,21) (4,17) (4,10) (4,6) (4,23) (4,8) (5,13) (5,7) (5,21) (5,17) (5,28) (5,6) (5,23) (5,8) (5,26) (5,24) (5,11) (6,13) (6,17) (6,10) (6,23) (6,24) (7,17) (7,28) (7,23) (8,21) (8,10) (9,15) (10,13) (10,21) (10,23) (10,11) (11,13) (11,17) (12,19) (12,14) (12,27) (12,15) (12,22) (13,17) (13,16) (14,22) (15,19) (16,17) (16,28) (16,24) (17,24) (18,19) (18,27) (19,27) (21,26) (21,24) (22,25) (23,28) (24,28) (25,27)\nQ: Is there a path between node 1 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "406"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,19) (1,11) (2,4) (2,13) (3,17) (3,10) (3,11) (5,8) (5,13) (6,10) (6,12) (7,18) (7,9) (10,17) (10,12) (11,12) (12,17) (13,16) (13,15) (14,18)\nQ: Is there a path between node 17 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "407"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,11) (0,1) (0,25) (0,28) (0,16) (0,31) (0,2) (0,23) (1,20) (1,26) (1,24) (1,10) (1,31) (1,21) (2,26) (2,19) (2,11) (2,5) (2,15) (2,32) (2,33) (2,8) (2,16) (2,31) (2,21) (2,30) (3,12) (3,4) (4,18) (5,11) (5,24) (6,14) (6,12) (6,9) (6,13) (7,26) (7,25) (7,33) (7,8) (7,21) (8,26) (8,19) (8,32) (8,31) (9,12) (10,19) (10,11) (10,25) (11,33) (11,24) (12,14) (14,18) (15,19) (15,17) (15,32) (15,25) (15,31) (15,21) (16,26) (16,32) (17,20) (17,19) (17,23) (19,24) (19,31) (19,21) (19,30) (21,32) (21,25) (21,24) (21,31) (23,31) (24,28) (25,32) (25,33) (25,28) (26,32) (26,33) (26,28) (26,31) (26,30) (28,33) (28,30) (31,32)\nQ: Is there a path between node 19 and node 28?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "408"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (0,13) (0,3) (0,14) (0,15) (0,19) (0,7) (0,9) (0,10) (1,5) (1,18) (1,12) (1,13) (1,14) (1,6) (1,17) (1,16) (1,9) (1,10) (1,11) (2,18) (2,12) (2,13) (2,6) (2,15) (2,19) (2,7) (2,17) (2,16) (2,9) (2,10) (2,11) (3,18) (3,12) (3,13) (3,14) (3,6) (3,19) (3,17) (3,9) (3,10) (3,11) (5,18) (5,12) (5,13) (5,14) (5,6) (5,15) (5,19) (5,7) (5,16) (5,11) (6,18) (6,12) (6,7) (6,17) (6,16) (6,9) (6,10) (7,18) (7,12) (7,13) (7,15) (7,19) (7,17) (7,16) (7,10) (7,11) (9,18) (9,13) (9,15) (9,19) (9,16) (9,10) (10,18) (10,13) (10,14) (10,19) (10,17) (10,11) (11,12) (11,13) (11,14) (11,15) (11,19) (11,17) (11,16) (12,14) (12,19) (12,17) (12,16) (13,18) (13,15) (13,19) (13,17) (14,18) (14,15) (14,19) (14,17) (14,16) (15,18) (15,19) (15,16) (16,18) (17,18) (17,19) (18,19)\nQ: Is there a path between node 15 and node 16?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "409"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,12) (0,11) (0,8) (0,1) (0,13) (0,10) (0,3) (1,2) (1,5) (1,12) (1,11) (1,8) (1,13) (1,10) (1,3) (2,5) (2,12) (2,11) (2,8) (2,13) (2,10) (2,3) (3,5) (3,12) (3,11) (3,8) (3,13) (3,10) (4,9) (4,6) (4,7) (4,14) (5,12) (5,11) (5,8) (5,13) (5,10) (6,9) (6,7) (6,14) (7,9) (7,14) (8,12) (8,11) (8,13) (8,10) (9,14) (10,12) (10,11) (10,13) (11,12) (11,13) (12,13)\nQ: Is there a path between node 12 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "410"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,3) (0,13) (0,15) (0,7) (1,4) (1,6) (2,9) (2,18) (2,13) (3,12) (4,11) (6,8) (6,17) (7,16) (7,12) (7,13) (7,14) (8,11) (8,17) (8,20) (9,18) (9,21) (9,14) (9,15) (10,12) (12,16) (12,15) (13,18) (13,15) (14,16) (14,21) (15,16) (15,18) (16,18)\nQ: Is there a path between node 12 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "411"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,5) (0,1) (0,9) (0,3) (0,4) (1,6) (1,5) (1,9) (1,3) (1,4) (2,7) (2,8) (2,10) (3,6) (3,5) (3,9) (3,4) (4,6) (4,5) (4,9) (5,6) (5,9) (6,9) (7,8) (7,10) (8,10)\nQ: Is there a path between node 3 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "412"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,13) (0,5) (0,11) (0,15) (0,10) (0,16) (0,14) (0,8) (0,9) (1,18) (1,12) (1,7) (1,6) (2,13) (2,11) (2,15) (2,17) (2,16) (2,14) (2,3) (2,8) (2,9) (3,5) (3,11) (3,4) (3,15) (3,10) (3,14) (3,8) (3,9) (4,13) (4,5) (4,17) (4,16) (4,14) (4,8) (5,17) (5,16) (5,14) (6,12) (6,19) (6,20) (6,7) (7,18) (8,15) (8,17) (8,16) (8,14) (8,9) (9,13) (9,11) (9,17) (9,16) (9,14) (10,11) (10,15) (10,17) (10,16) (10,14) (11,13) (11,15) (11,16) (12,18) (12,19) (12,20) (13,17) (13,14) (14,15) (14,17) (14,16) (15,17) (16,17) (18,19) (18,20) (19,20)\nQ: Is there a path between node 0 and node 20?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "413"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,10) (0,19) (0,16) (0,7) (0,8) (0,4) (0,3) (0,11) (0,1) (0,18) (0,9) (0,5) (0,2) (0,13) (1,17) (1,10) (1,19) (1,16) (1,7) (1,8) (1,4) (1,3) (1,11) (1,18) (1,9) (1,5) (1,2) (1,13) (2,17) (2,10) (2,19) (2,16) (2,7) (2,8) (2,4) (2,3) (2,11) (2,18) (2,9) (2,5) (2,13) (3,17) (3,10) (3,19) (3,16) (3,7) (3,8) (3,4) (3,11) (3,18) (3,9) (3,5) (3,13) (4,17) (4,10) (4,19) (4,16) (4,7) (4,8) (4,11) (4,18) (4,9) (4,5) (4,13) (5,17) (5,10) (5,19) (5,16) (5,7) (5,8) (5,11) (5,18) (5,9) (5,13) (6,15) (7,17) (7,10) (7,19) (7,16) (7,8) (7,11) (7,18) (7,9) (7,13) (8,17) (8,10) (8,19) (8,16) (8,11) (8,18) (8,9) (8,13) (9,17) (9,10) (9,19) (9,16) (9,11) (9,18) (9,13) (10,17) (10,19) (10,16) (10,11) (10,18) (10,13) (11,17) (11,19) (11,16) (11,18) (11,13) (12,14) (13,17) (13,19) (13,16) (13,18) (16,17) (16,19) (16,18) (17,19) (17,18) (18,19)\nQ: Is there a path between node 6 and node 19?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "414"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,3) (0,5) (1,2) (1,10) (1,3) (1,5) (2,6) (2,10) (3,17) (3,14) (3,6) (3,9) (4,14) (4,7) (4,9) (5,17) (5,14) (5,6) (5,10) (5,7) (6,14) (6,16) (6,7) (9,17) (9,16) (9,10) (10,14) (11,15) (12,13) (14,17) (14,16) (14,15) (15,17)\nQ: Is there a path between node 9 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "415"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,10) (0,18) (0,21) (0,30) (0,28) (0,15) (1,27) (1,24) (1,22) (1,32) (1,14) (1,5) (2,29) (2,10) (2,18) (2,21) (2,19) (2,30) (2,16) (2,28) (2,15) (3,24) (3,13) (3,22) (3,20) (3,5) (4,17) (4,11) (4,6) (4,26) (4,23) (4,31) (4,25) (5,27) (5,13) (5,22) (5,20) (5,32) (5,14) (6,17) (6,9) (6,23) (6,31) (6,25) (7,29) (7,10) (7,18) (7,19) (7,30) (7,16) (7,15) (8,17) (8,11) (8,26) (8,23) (8,31) (9,17) (9,26) (9,23) (9,31) (9,25) (10,29) (10,18) (10,21) (10,30) (10,28) (10,15) (11,17) (11,26) (11,23) (12,27) (12,24) (12,13) (12,22) (12,32) (13,27) (13,24) (13,22) (13,20) (13,32) (13,14) (14,27) (14,22) (14,32) (15,29) (15,18) (15,21) (15,19) (15,28) (16,29) (16,21) (16,19) (16,28) (17,23) (18,29) (18,21) (18,30) (18,28) (19,29) (19,21) (19,30) (19,28) (20,24) (20,22) (20,32) (21,29) (21,30) (21,28) (22,27) (22,24) (22,32) (23,31) (24,27) (25,26) (26,31) (28,30)\nQ: Is there a path between node 1 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "416"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,21) (0,17) (0,7) (0,29) (1,20) (2,32) (2,6) (2,13) (3,22) (3,23) (3,8) (4,30) (4,31) (6,23) (6,16) (6,32) (7,19) (8,14) (8,23) (8,16) (8,32) (8,13) (9,24) (9,17) (9,29) (13,14) (13,32) (14,16) (14,32) (16,20) (16,28) (17,24) (20,28) (21,29) (24,29) (27,30) (30,31)\nQ: Is there a path between node 26 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "417"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,7) (0,8) (0,10) (0,3) (1,4) (1,11) (1,9) (1,6) (1,12) (1,2) (2,4) (2,11) (2,9) (2,6) (2,12) (3,5) (3,7) (3,8) (3,10) (4,11) (4,9) (4,6) (4,12) (5,7) (5,8) (5,10) (6,11) (6,9) (6,12) (7,8) (7,10) (8,10) (9,11) (9,12) (11,12)\nQ: Is there a path between node 5 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "418"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,4) (1,2) (3,4)\nQ: Is there a path between node 2 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "419"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (1,15) (1,16) (2,18) (2,17) (2,7) (3,14) (3,7) (5,11) (6,13) (7,17) (8,15) (8,13) (9,17) (10,17) (13,15) (13,16) (16,19)\nQ: Is there a path between node 10 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "420"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (1,24) (1,13) (1,7) (2,24) (2,15) (2,18) (2,8) (2,13) (2,7) (3,23) (3,6) (5,20) (5,14) (6,11) (6,23) (7,12) (7,10) (7,21) (7,8) (7,13) (8,10) (8,15) (8,18) (8,22) (8,13) (9,21) (9,13) (10,12) (10,15) (10,13) (12,24) (13,24) (13,22) (14,20) (15,24) (17,24) (19,20) (21,24)\nQ: Is there a path between node 13 and node 20?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "421"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,19) (1,11) (2,4) (2,13) (3,17) (3,10) (3,11) (5,8) (5,13) (6,10) (6,12) (7,18) (7,9) (10,17) (10,12) (11,12) (12,17) (13,16) (13,15) (14,18)\nQ: Is there a path between node 1 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "422"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,4) (0,15) (0,19) (0,8) (0,17) (0,13) (0,3) (0,14) (0,5) (0,2) (0,16) (0,1) (0,10) (1,20) (1,4) (1,15) (1,19) (1,8) (1,17) (1,13) (1,3) (1,14) (1,5) (1,2) (1,16) (1,10) (2,20) (2,4) (2,15) (2,19) (2,8) (2,17) (2,13) (2,3) (2,14) (2,5) (2,16) (2,10) (3,20) (3,4) (3,15) (3,19) (3,8) (3,17) (3,13) (3,14) (3,5) (3,16) (3,10) (4,20) (4,15) (4,19) (4,8) (4,17) (4,13) (4,14) (4,5) (4,16) (4,10) (5,20) (5,15) (5,19) (5,8) (5,17) (5,13) (5,14) (5,16) (5,10) (6,12) (6,22) (6,9) (6,18) (6,21) (6,7) (6,11) (7,12) (7,22) (7,9) (7,18) (7,21) (7,11) (8,20) (8,15) (8,19) (8,17) (8,13) (8,14) (8,16) (8,10) (9,12) (9,22) (9,18) (9,21) (9,11) (10,20) (10,15) (10,19) (10,17) (10,13) (10,14) (10,16) (11,12) (11,22) (11,18) (11,21) (12,22) (12,18) (12,21) (13,20) (13,15) (13,19) (13,17) (13,14) (13,16) (14,20) (14,15) (14,19) (14,17) (14,16) (15,20) (15,19) (15,17) (15,16) (16,20) (16,19) (16,17) (17,20) (17,19) (18,22) (18,21) (19,20) (21,22)\nQ: Is there a path between node 18 and node 19?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "423"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,12) (0,5) (0,6) (0,4) (0,8) (0,2) (0,9) (0,1) (0,7) (1,12) (1,5) (1,6) (1,4) (1,8) (1,2) (1,9) (1,10) (1,7) (2,8) (2,10) (2,7) (4,11) (4,12) (4,5) (4,6) (4,8) (4,9) (4,7) (5,11) (5,6) (5,8) (5,10) (5,7) (6,11) (6,12) (6,8) (6,9) (7,11) (7,12) (7,9) (7,10) (8,12) (8,9) (8,10) (9,11) (9,12) (9,10) (10,11) (10,12) (11,12)\nQ: Is there a path between node 3 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "424"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,27) (0,13) (0,10) (0,15) (0,2) (0,17) (1,5) (1,22) (1,8) (1,19) (1,26) (1,24) (1,18) (1,16) (1,14) (1,12) (1,4) (1,9) (2,7) (2,27) (2,13) (2,3) (2,6) (2,10) (2,11) (2,17) (3,7) (3,27) (3,20) (3,6) (3,10) (3,15) (3,21) (3,17) (4,5) (4,8) (4,19) (4,26) (4,25) (4,18) (4,14) (4,12) (5,8) (5,26) (5,18) (5,16) (5,14) (5,12) (6,7) (6,13) (6,10) (6,21) (7,20) (7,13) (7,10) (7,15) (7,11) (8,19) (8,26) (8,18) (8,16) (8,14) (8,9) (9,22) (9,19) (9,26) (9,25) (9,16) (9,14) (9,12) (10,13) (10,21) (10,17) (11,27) (11,13) (11,15) (11,21) (11,17) (12,22) (12,19) (12,26) (12,24) (12,25) (12,16) (12,14) (13,27) (13,15) (14,22) (14,19) (14,26) (15,27) (15,20) (15,21) (15,17) (16,22) (16,19) (16,24) (16,25) (16,18) (17,27) (17,20) (17,21) (18,22) (18,19) (18,26) (18,24) (19,26) (19,25) (20,27) (20,21) (21,27) (22,26) (22,24) (24,26)\nQ: Is there a path between node 24 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "425"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (1,17) (2,9) (3,16) (5,18) (5,11) (5,21) (6,21) (6,15) (7,19) (7,21) (8,10) (8,12) (8,16) (10,16) (14,23) (15,21) (16,19) (17,20) (18,19) (20,23)\nQ: Is there a path between node 19 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "426"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,16) (0,9) (0,3) (0,4) (0,8) (0,17) (1,6) (1,12) (1,13) (1,18) (1,2) (1,4) (1,8) (1,17) (2,6) (2,12) (2,15) (2,9) (2,13) (2,18) (2,4) (2,8) (2,17) (3,6) (3,16) (3,12) (3,9) (3,13) (3,18) (3,8) (3,17) (3,5) (4,6) (4,16) (4,12) (4,9) (4,18) (4,17) (4,5) (5,6) (5,12) (5,15) (5,9) (5,17) (6,12) (6,15) (6,9) (6,13) (6,18) (6,8) (7,10) (7,11) (7,19) (8,16) (8,15) (8,9) (8,18) (9,16) (9,12) (9,15) (9,13) (9,18) (9,17) (10,19) (11,14) (11,19) (12,16) (12,15) (12,13) (12,17) (13,18) (14,19) (15,17) (16,17) (17,18)\nQ: Is there a path between node 2 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "427"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,1) (0,3) (1,5) (1,3) (2,4) (3,5)\nQ: Is there a path between node 4 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "428"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (0,11) (0,8) (0,17) (0,13) (0,6) (0,3) (0,15) (0,7) (1,14) (1,19) (1,9) (1,21) (1,12) (1,22) (1,4) (1,18) (1,5) (1,10) (1,20) (2,16) (3,23) (3,11) (3,8) (3,17) (3,13) (3,6) (3,15) (3,7) (4,14) (4,19) (4,9) (4,21) (4,12) (4,22) (4,18) (4,5) (4,10) (4,20) (5,14) (5,19) (5,9) (5,21) (5,12) (5,22) (5,18) (5,10) (5,20) (6,23) (6,11) (6,8) (6,17) (6,13) (6,15) (6,7) (7,23) (7,11) (7,8) (7,17) (7,13) (7,15) (8,23) (8,11) (8,17) (8,13) (8,15) (9,14) (9,19) (9,21) (9,12) (9,22) (9,18) (9,10) (9,20) (10,14) (10,19) (10,21) (10,12) (10,22) (10,18) (10,20) (11,23) (11,17) (11,13) (11,15) (12,14) (12,19) (12,21) (12,22) (12,18) (12,20) (13,23) (13,17) (13,15) (14,19) (14,21) (14,22) (14,18) (14,20) (15,23) (15,17) (17,23) (18,19) (18,21) (18,22) (18,20) (19,21) (19,22) (19,20) (20,21) (20,22) (21,22)\nQ: Is there a path between node 0 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "429"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,11) (0,1) (0,3) (0,10) (0,4) (1,11) (1,3) (1,10) (1,4) (2,7) (3,11) (3,4) (4,5) (4,11) (5,11) (6,9) (6,8) (7,9) (7,8) (8,9) (10,11)\nQ: Is there a path between node 10 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "430"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,6) (1,4) (1,3) (1,2) (1,7) (2,10) (2,4) (2,8) (3,10) (3,6) (3,4) (3,8) (3,5) (4,6) (4,8) (4,5) (4,7) (5,10) (5,8) (6,10) (6,8) (7,10)\nQ: Is there a path between node 7 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "431"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,11) (0,6) (1,5) (1,8) (1,10) (1,15) (1,17) (1,13) (1,16) (2,5) (2,4) (2,8) (2,10) (2,14) (2,17) (2,13) (2,16) (3,9) (3,6) (3,12) (4,8) (4,15) (4,14) (4,17) (4,13) (5,8) (5,15) (5,17) (6,7) (6,9) (7,11) (7,9) (8,15) (8,17) (8,13) (8,16) (9,11) (10,15) (10,14) (10,17) (11,12) (13,15) (13,14) (13,16) (14,15) (14,17) (14,16) (15,17) (15,16) (16,17)\nQ: Is there a path between node 15 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "432"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,18) (0,12) (0,2) (0,11) (0,8) (0,13) (1,4) (1,10) (1,17) (1,5) (1,14) (1,7) (1,6) (1,15) (2,3) (2,18) (2,12) (2,11) (2,8) (2,13) (3,18) (3,12) (3,11) (3,8) (3,13) (4,10) (4,17) (4,5) (4,14) (4,7) (4,6) (4,15) (5,10) (5,17) (5,14) (5,7) (5,6) (5,15) (6,10) (6,17) (6,14) (6,7) (6,15) (7,10) (7,17) (7,14) (7,15) (8,18) (8,12) (8,11) (8,13) (9,16) (10,17) (10,14) (10,15) (11,18) (11,12) (11,13) (12,18) (12,13) (13,18) (14,17) (14,15) (15,17)\nQ: Is there a path between node 4 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "433"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,8) (0,5) (0,4) (0,25) (0,22) (0,16) (0,24) (0,21) (2,15) (2,23) (2,26) (2,10) (2,3) (2,11) (2,6) (2,27) (3,15) (3,23) (3,14) (3,26) (3,10) (3,11) (3,27) (4,8) (4,13) (4,5) (4,20) (4,18) (4,7) (4,22) (4,16) (4,24) (5,8) (5,13) (5,20) (5,7) (5,22) (5,24) (5,21) (6,15) (6,23) (6,14) (6,26) (6,10) (6,11) (6,27) (7,12) (7,20) (7,25) (7,16) (7,21) (8,12) (8,20) (8,25) (8,16) (8,24) (10,15) (10,23) (10,14) (10,26) (10,19) (10,11) (10,27) (11,15) (11,23) (11,26) (11,27) (12,16) (12,24) (12,21) (13,20) (13,18) (13,25) (13,22) (13,16) (13,24) (13,21) (14,15) (14,26) (15,26) (15,27) (16,22) (16,24) (16,21) (18,25) (18,22) (18,21) (19,23) (19,26) (19,27) (20,25) (20,24) (21,25) (21,24) (22,25) (22,24) (23,26) (23,27) (24,25) (26,27)\nQ: Is there a path between node 1 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "434"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,22) (0,15) (0,8) (0,12) (0,14) (0,2) (0,9) (0,1) (1,15) (1,20) (1,12) (2,20) (2,12) (2,7) (2,16) (3,15) (3,7) (3,16) (3,13) (3,14) (3,17) (3,21) (4,22) (4,8) (4,12) (4,17) (4,11) (6,23) (7,15) (7,17) (7,11) (7,21) (7,18) (8,22) (8,15) (8,20) (8,16) (8,9) (9,22) (9,13) (9,11) (9,21) (9,18) (10,22) (10,13) (10,21) (11,22) (11,15) (11,20) (11,12) (11,21) (11,18) (12,15) (12,13) (13,20) (13,18) (14,20) (17,22) (17,18) (18,20) (19,23) (20,22) (21,22)\nQ: Is there a path between node 8 and node 16?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "435"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,1) (0,2) (0,7) (0,6) (1,2) (1,8) (1,7) (1,4) (1,6) (2,7) (2,4) (2,6) (3,5) (4,9) (4,8) (4,7) (6,9) (6,7) (7,8)\nQ: Is there a path between node 5 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "436"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (1,20) (2,11) (2,23) (2,14) (2,8) (3,17) (3,14) (3,16) (4,7) (4,16) (4,8) (4,24) (5,6) (5,10) (5,20) (6,20) (7,12) (7,16) (7,8) (7,24) (8,12) (8,23) (8,21) (9,18) (10,18) (10,20) (11,17) (11,19) (11,24) (12,22) (12,17) (12,14) (13,24) (14,23) (14,24) (15,17) (15,19) (15,24) (16,22) (16,19) (17,19) (17,24) (19,24) (23,24)\nQ: Is there a path between node 17 and node 23?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "437"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,1) (1,12) (1,15) (2,9) (2,6) (3,10) (3,17) (3,15) (5,7) (6,10) (6,9) (6,11) (7,13) (8,17) (8,16) (10,15) (11,12) (15,17)\nQ: Is there a path between node 5 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "438"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,5) (0,11) (0,8) (0,6) (0,1) (1,10) (1,3) (1,5) (1,9) (1,6) (1,2) (2,10) (2,3) (2,5) (2,9) (2,8) (2,7) (2,6) (2,13) (3,9) (3,11) (3,8) (3,7) (4,12) (5,10) (5,9) (5,8) (5,7) (5,6) (6,10) (6,9) (6,11) (6,8) (7,10) (7,11) (7,8) (7,13) (8,10) (8,11) (8,13) (9,10) (9,11) (9,13) (10,11) (10,13)\nQ: Is there a path between node 10 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "439"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,19) (1,11) (2,4) (2,13) (3,17) (3,10) (3,11) (5,8) (5,13) (6,10) (6,12) (7,18) (7,9) (10,17) (10,12) (11,12) (12,17) (13,16) (13,15) (14,18)\nQ: Is there a path between node 12 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "440"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,3) (0,11) (0,8) (0,2) (0,12) (0,9) (0,1) (1,4) (1,3) (1,6) (1,11) (1,8) (1,7) (1,10) (1,2) (1,12) (2,3) (2,6) (2,11) (2,8) (2,9) (3,6) (3,11) (3,8) (3,7) (3,10) (3,9) (4,6) (4,11) (4,8) (4,7) (4,10) (4,12) (4,9) (6,8) (6,10) (7,10) (7,12) (7,9) (8,11) (8,10) (8,12) (9,10) (10,12)\nQ: Is there a path between node 5 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "441"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,2) (1,5) (1,2) (2,5) (2,10) (3,10) (3,4) (3,8) (4,5) (5,10) (5,8) (7,11) (8,10) (9,11)\nQ: Is there a path between node 5 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "442"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,14) (0,20) (0,13) (1,2) (1,8) (1,9) (2,9) (4,10) (4,20) (5,21) (5,17) (5,9) (6,10) (6,14) (6,13) (7,21) (7,22) (8,9) (10,19) (10,18) (10,12) (10,13) (11,16) (11,18) (12,16) (12,19) (12,18) (13,19) (14,19) (16,18) (17,22) (18,19)\nQ: Is there a path between node 12 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "443"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,5) (0,7) (0,6) (0,2) (0,4) (0,8) (0,9) (1,10) (2,3) (2,5) (2,7) (2,6) (2,4) (2,8) (2,9) (2,11) (3,5) (3,4) (3,8) (3,11) (4,5) (4,6) (4,9) (4,11) (5,6) (5,8) (5,9) (6,7) (6,8) (6,9) (6,11) (7,8) (7,11) (8,9) (9,11)\nQ: Is there a path between node 3 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "444"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,9) (0,2) (0,5) (0,10) (0,1) (1,4) (1,9) (1,2) (1,5) (1,10) (2,4) (2,9) (2,5) (2,10) (3,11) (3,8) (3,12) (3,7) (3,6) (4,9) (4,5) (4,10) (5,9) (5,10) (6,11) (6,8) (6,12) (6,7) (7,11) (7,8) (7,12) (8,11) (8,12) (9,10) (11,12)\nQ: Is there a path between node 5 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "445"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,27) (0,23) (0,4) (0,20) (0,17) (0,6) (1,5) (1,22) (1,11) (1,19) (1,24) (1,2) (1,15) (1,8) (1,30) (1,9) (1,28) (1,18) (2,5) (2,22) (2,24) (2,15) (2,8) (2,30) (2,9) (2,28) (2,18) (3,26) (3,13) (4,21) (4,29) (4,23) (4,20) (4,17) (4,6) (5,22) (5,19) (5,24) (5,14) (5,30) (5,28) (5,18) (6,21) (6,29) (6,27) (6,23) (6,20) (6,17) (7,26) (7,10) (7,13) (7,16) (7,12) (8,11) (8,24) (8,14) (8,30) (8,9) (8,28) (8,18) (9,22) (9,11) (9,19) (9,15) (9,28) (10,16) (10,12) (11,15) (11,30) (11,28) (11,18) (12,13) (12,16) (13,26) (13,16) (13,25) (14,22) (14,19) (14,15) (14,30) (15,19) (15,30) (15,28) (15,18) (16,26) (16,25) (17,29) (17,23) (18,19) (18,24) (18,28) (19,30) (19,28) (20,21) (20,27) (21,29) (21,27) (21,23) (22,24) (22,28) (23,27) (24,30) (24,28) (25,26) (28,30)\nQ: Is there a path between node 21 and node 17?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "446"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,3) (1,20) (1,21) (1,8) (1,5) (1,16) (1,17) (1,19) (1,6) (1,12) (1,14) (1,9) (1,13) (1,18) (1,7) (1,11) (1,15) (1,2) (1,10) (2,20) (2,21) (2,8) (2,5) (2,16) (2,17) (2,19) (2,6) (2,12) (2,14) (2,9) (2,13) (2,18) (2,7) (2,11) (2,15) (2,10) (3,4) (5,20) (5,21) (5,8) (5,16) (5,17) (5,19) (5,6) (5,12) (5,14) (5,9) (5,13) (5,18) (5,7) (5,11) (5,15) (5,10) (6,20) (6,21) (6,8) (6,16) (6,17) (6,19) (6,12) (6,14) (6,9) (6,13) (6,18) (6,7) (6,11) (6,15) (6,10) (7,20) (7,21) (7,8) (7,16) (7,17) (7,19) (7,12) (7,14) (7,9) (7,13) (7,18) (7,11) (7,15) (7,10) (8,20) (8,21) (8,16) (8,17) (8,19) (8,12) (8,14) (8,9) (8,13) (8,18) (8,11) (8,15) (8,10) (9,20) (9,21) (9,16) (9,17) (9,19) (9,12) (9,14) (9,13) (9,18) (9,11) (9,15) (9,10) (10,20) (10,21) (10,16) (10,17) (10,19) (10,12) (10,14) (10,13) (10,18) (10,11) (10,15) (11,20) (11,21) (11,16) (11,17) (11,19) (11,12) (11,14) (11,13) (11,18) (11,15) (12,20) (12,21) (12,16) (12,17) (12,19) (12,14) (12,13) (12,18) (12,15) (13,20) (13,21) (13,16) (13,17) (13,19) (13,14) (13,18) (13,15) (14,20) (14,21) (14,16) (14,17) (14,19) (14,18) (14,15) (15,20) (15,21) (15,16) (15,17) (15,19) (15,18) (16,20) (16,21) (16,17) (16,19) (16,18) (17,20) (17,21) (17,19) (17,18) (18,20) (18,21) (18,19) (19,20) (19,21) (20,21)\nQ: Is there a path between node 11 and node 13?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "447"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,3) (0,11) (0,18) (0,7) (0,8) (0,9) (0,1) (0,10) (0,15) (0,17) (0,13) (0,16) (0,19) (0,2) (0,6) (0,5) (0,14) (1,12) (1,3) (1,11) (1,18) (1,7) (1,8) (1,9) (1,10) (1,15) (1,17) (1,13) (1,16) (1,19) (1,2) (1,6) (1,5) (1,14) (2,12) (2,3) (2,11) (2,18) (2,7) (2,8) (2,9) (2,10) (2,15) (2,17) (2,13) (2,16) (2,19) (2,6) (2,5) (2,14) (3,12) (3,11) (3,18) (3,7) (3,8) (3,9) (3,10) (3,15) (3,17) (3,13) (3,16) (3,19) (3,6) (3,5) (3,14) (4,20) (4,21) (5,12) (5,11) (5,18) (5,7) (5,8) (5,9) (5,10) (5,15) (5,17) (5,13) (5,16) (5,19) (5,6) (5,14) (6,12) (6,11) (6,18) (6,7) (6,8) (6,9) (6,10) (6,15) (6,17) (6,13) (6,16) (6,19) (6,14) (7,12) (7,11) (7,18) (7,8) (7,9) (7,10) (7,15) (7,17) (7,13) (7,16) (7,19) (7,14) (8,12) (8,11) (8,18) (8,9) (8,10) (8,15) (8,17) (8,13) (8,16) (8,19) (8,14) (9,12) (9,11) (9,18) (9,10) (9,15) (9,17) (9,13) (9,16) (9,19) (9,14) (10,12) (10,11) (10,18) (10,15) (10,17) (10,13) (10,16) (10,19) (10,14) (11,12) (11,18) (11,15) (11,17) (11,13) (11,16) (11,19) (11,14) (12,18) (12,15) (12,17) (12,13) (12,16) (12,19) (12,14) (13,18) (13,15) (13,17) (13,16) (13,19) (13,14) (14,18) (14,15) (14,17) (14,16) (14,19) (15,18) (15,17) (15,16) (15,19) (16,18) (16,17) (16,19) (17,18) (17,19) (18,19) (20,21)\nQ: Is there a path between node 15 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "448"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,2) (3,5)\nQ: Is there a path between node 1 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "449"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (0,3) (0,4) (0,1) (1,2) (1,5) (1,6) (1,3) (1,4) (2,5) (2,6) (2,3) (2,4) (3,5) (3,6) (3,4) (4,5) (4,6) (5,6)\nQ: Is there a path between node 1 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "450"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,11) (0,1) (0,25) (0,28) (0,16) (0,31) (0,2) (0,23) (1,20) (1,26) (1,24) (1,10) (1,31) (1,21) (2,26) (2,19) (2,11) (2,5) (2,15) (2,32) (2,33) (2,8) (2,16) (2,31) (2,21) (2,30) (3,12) (3,4) (4,18) (5,11) (5,24) (6,14) (6,12) (6,9) (6,13) (7,26) (7,25) (7,33) (7,8) (7,21) (8,26) (8,19) (8,32) (8,31) (9,12) (10,19) (10,11) (10,25) (11,33) (11,24) (12,14) (14,18) (15,19) (15,17) (15,32) (15,25) (15,31) (15,21) (16,26) (16,32) (17,20) (17,19) (17,23) (19,24) (19,31) (19,21) (19,30) (21,32) (21,25) (21,24) (21,31) (23,31) (24,28) (25,32) (25,33) (25,28) (26,32) (26,33) (26,28) (26,31) (26,30) (28,33) (28,30) (31,32)\nQ: Is there a path between node 28 and node 25?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "451"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,1) (0,3) (1,5) (1,3) (2,4) (3,5)\nQ: Is there a path between node 4 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "452"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (1,12) (1,19) (2,13) (3,20) (3,11) (4,7) (4,16) (4,18) (5,17) (5,7) (6,15) (6,20) (6,11) (7,20) (7,11) (8,12) (8,13) (8,19) (11,17) (11,15) (12,19) (16,17) (16,20) (17,20) (18,20)\nQ: Is there a path between node 18 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "453"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,16) (0,22) (0,4) (0,15) (0,9) (1,8) (1,17) (1,12) (1,3) (1,5) (1,21) (1,6) (1,13) (1,19) (2,20) (2,16) (2,22) (2,4) (2,9) (3,8) (3,17) (3,14) (3,6) (3,10) (3,19) (4,20) (4,16) (4,22) (4,15) (4,9) (5,8) (5,17) (5,12) (5,14) (5,13) (5,10) (5,19) (6,17) (6,12) (6,14) (6,21) (6,13) (6,10) (6,19) (8,17) (8,12) (8,13) (8,19) (9,20) (9,22) (9,15) (10,17) (10,14) (10,21) (11,18) (11,23) (12,17) (12,21) (12,13) (12,19) (13,17) (13,14) (13,21) (15,20) (16,22) (17,21) (18,23)\nQ: Is there a path between node 11 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "454"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,9) (1,8) (1,4) (2,8) (2,4) (2,3) (3,7) (3,6) (3,10) (3,12) (3,11) (4,10) (4,12) (6,14) (6,8) (6,10) (7,14) (7,11) (8,14) (8,12) (10,14) (11,14) (12,14)\nQ: Is there a path between node 11 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "455"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,18) (0,24) (0,5) (0,12) (0,26) (0,14) (0,16) (0,21) (0,9) (0,1) (0,28) (0,25) (1,3) (1,18) (1,24) (1,5) (1,12) (1,26) (1,14) (1,16) (1,21) (1,2) (1,23) (1,20) (1,28) (1,25) (2,3) (2,18) (2,10) (2,24) (2,5) (2,12) (2,26) (2,14) (2,16) (2,9) (2,23) (2,20) (2,28) (2,7) (2,25) (2,22) (2,13) (3,18) (3,24) (3,12) (3,26) (3,16) (3,9) (3,19) (3,7) (3,25) (3,22) (4,11) (4,27) (4,17) (4,15) (4,8) (5,18) (5,24) (5,12) (5,26) (5,14) (5,16) (5,21) (5,9) (5,23) (5,19) (5,20) (5,7) (5,13) (6,11) (6,27) (6,29) (6,15) (6,8) (7,18) (7,10) (7,12) (7,26) (7,14) (7,16) (7,21) (7,9) (7,20) (7,25) (7,22) (7,13) (8,11) (8,27) (8,29) (8,17) (8,15) (9,18) (9,10) (9,24) (9,16) (9,21) (9,19) (9,20) (9,28) (9,25) (9,13) (10,18) (10,24) (10,12) (10,26) (10,14) (10,16) (10,23) (10,20) (10,28) (10,25) (10,22) (10,13) (11,27) (11,29) (12,18) (12,24) (12,16) (12,21) (12,23) (12,20) (12,28) (12,22) (12,13) (13,18) (13,24) (13,26) (13,14) (13,16) (13,21) (13,23) (13,20) (13,28) (13,25) (13,22) (14,26) (14,16) (14,21) (14,23) (14,19) (14,20) (14,28) (14,25) (15,27) (15,17) (16,18) (16,24) (16,26) (16,20) (16,25) (16,22) (17,29) (18,24) (18,26) (18,23) (18,19) (18,20) (18,25) (18,22) (19,21) (19,23) (19,28) (19,25) (20,26) (20,23) (20,28) (20,25) (20,22) (21,26) (21,23) (21,28) (21,22) (22,26) (22,23) (22,25) (23,24) (23,26) (24,26) (24,28) (25,26)\nQ: Is there a path between node 24 and node 18?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "456"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,4) (0,3) (0,6) (0,2) (0,8) (0,5) (0,11) (1,4) (1,3) (1,6) (1,2) (1,8) (1,5) (1,11) (2,4) (2,3) (2,6) (2,8) (2,5) (2,11) (3,4) (3,6) (3,8) (3,5) (3,11) (4,6) (4,8) (4,5) (4,11) (5,6) (5,8) (5,11) (6,8) (6,11) (7,9) (7,10) (8,11) (9,10)\nQ: Is there a path between node 0 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "457"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,17) (0,13) (0,12) (0,4) (0,1) (1,3) (1,17) (1,16) (1,14) (1,4) (2,5) (2,7) (2,9) (2,11) (2,8) (3,15) (3,13) (3,16) (3,12) (3,14) (3,6) (4,15) (4,13) (4,16) (4,12) (4,6) (5,9) (5,11) (5,10) (6,17) (6,13) (6,12) (7,11) (7,10) (7,8) (8,9) (8,11) (9,10) (10,11) (12,15) (12,17) (12,16) (12,14) (13,17) (13,16) (14,15) (14,17) (15,17) (15,16) (16,17)\nQ: Is there a path between node 1 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "458"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,2) (0,1) (0,4) (1,3) (1,2) (1,4) (1,6) (2,3) (2,4) (2,5) (3,4) (3,6) (4,6) (5,6)\nQ: Is there a path between node 5 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "459"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,6) (0,2) (0,5) (1,7) (1,16) (1,14) (1,17) (1,3) (1,9) (1,13) (1,10) (2,11) (2,6) (2,5) (3,7) (3,16) (3,14) (3,17) (3,9) (3,13) (3,10) (4,8) (4,15) (4,12) (5,11) (5,6) (6,11) (7,16) (7,14) (7,17) (7,9) (7,13) (7,10) (8,15) (8,12) (9,16) (9,14) (9,17) (9,13) (9,10) (10,16) (10,14) (10,17) (10,13) (12,15) (13,16) (13,14) (13,17) (14,16) (14,17) (16,17)\nQ: Is there a path between node 10 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "460"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,4) (0,1) (1,2) (1,5) (1,4) (2,5) (2,4) (4,5)\nQ: Is there a path between node 3 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "461"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,8) (0,5) (0,4) (0,25) (0,22) (0,16) (0,24) (0,21) (2,15) (2,23) (2,26) (2,10) (2,3) (2,11) (2,6) (2,27) (3,15) (3,23) (3,14) (3,26) (3,10) (3,11) (3,27) (4,8) (4,13) (4,5) (4,20) (4,18) (4,7) (4,22) (4,16) (4,24) (5,8) (5,13) (5,20) (5,7) (5,22) (5,24) (5,21) (6,15) (6,23) (6,14) (6,26) (6,10) (6,11) (6,27) (7,12) (7,20) (7,25) (7,16) (7,21) (8,12) (8,20) (8,25) (8,16) (8,24) (10,15) (10,23) (10,14) (10,26) (10,19) (10,11) (10,27) (11,15) (11,23) (11,26) (11,27) (12,16) (12,24) (12,21) (13,20) (13,18) (13,25) (13,22) (13,16) (13,24) (13,21) (14,15) (14,26) (15,26) (15,27) (16,22) (16,24) (16,21) (18,25) (18,22) (18,21) (19,23) (19,26) (19,27) (20,25) (20,24) (21,25) (21,24) (22,25) (22,24) (23,26) (23,27) (24,25) (26,27)\nQ: Is there a path between node 8 and node 20?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "462"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,7) (0,8) (0,9) (0,13) (0,14) (0,15) (0,5) (1,2) (1,12) (1,16) (1,11) (1,3) (1,6) (1,14) (1,4) (2,12) (2,7) (2,9) (2,13) (2,14) (3,16) (3,11) (3,7) (3,8) (3,14) (3,15) (3,5) (3,4) (4,12) (4,11) (4,8) (4,9) (4,13) (4,14) (4,5) (5,12) (5,16) (5,11) (5,7) (5,8) (5,13) (5,14) (5,15) (6,12) (6,16) (6,11) (6,7) (6,14) (6,15) (7,12) (7,16) (7,11) (7,8) (7,9) (7,13) (8,12) (8,16) (8,11) (8,9) (8,13) (8,14) (9,12) (9,16) (9,11) (9,14) (9,15) (11,12) (11,16) (11,14) (12,13) (12,15) (13,16) (13,15) (14,16)\nQ: Is there a path between node 14 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "463"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,2) (0,1) (1,5) (1,6) (2,6) (3,7) (4,7) (5,6)\nQ: Is there a path between node 4 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "464"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (0,10) (0,23) (0,3) (0,9) (0,26) (1,8) (1,20) (1,6) (1,4) (1,19) (1,16) (1,13) (1,24) (2,8) (2,20) (2,4) (2,19) (2,16) (2,13) (2,24) (2,12) (3,10) (3,9) (3,21) (3,22) (4,6) (4,19) (4,13) (4,24) (4,12) (5,15) (5,25) (5,11) (5,7) (6,8) (6,20) (6,19) (6,16) (6,13) (6,24) (7,15) (7,25) (7,14) (8,19) (8,13) (8,24) (8,12) (9,18) (9,23) (10,18) (10,23) (10,21) (10,26) (11,15) (11,17) (11,25) (12,20) (12,19) (12,16) (12,24) (13,20) (13,19) (13,16) (13,24) (14,17) (14,25) (15,17) (15,25) (16,20) (16,24) (17,25) (18,21) (18,22) (19,20) (19,24) (20,24) (21,23) (22,23) (22,26) (23,26)\nQ: Is there a path between node 15 and node 19?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "465"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,7) (0,12) (0,32) (0,22) (0,9) (0,20) (0,2) (0,5) (0,14) (0,4) (0,26) (0,21) (1,11) (1,8) (1,24) (1,3) (1,31) (1,28) (1,6) (2,16) (2,7) (2,32) (2,22) (2,9) (2,20) (2,14) (2,4) (2,21) (3,11) (3,8) (3,24) (3,31) (3,28) (4,16) (4,32) (4,22) (4,9) (4,20) (4,5) (4,14) (4,26) (5,16) (5,7) (5,12) (5,32) (5,22) (5,9) (5,20) (5,14) (5,26) (5,21) (6,8) (6,24) (6,31) (6,28) (7,12) (7,32) (7,22) (7,9) (7,14) (7,26) (7,21) (8,24) (8,31) (8,28) (9,16) (9,12) (9,32) (9,20) (9,26) (9,21) (10,23) (10,13) (10,29) (10,19) (10,25) (10,18) (12,32) (12,22) (12,20) (12,26) (12,21) (13,30) (13,27) (13,29) (13,19) (13,25) (13,18) (14,16) (14,32) (14,22) (14,20) (14,26) (15,30) (15,29) (15,25) (15,18) (16,32) (16,22) (16,20) (16,26) (16,21) (17,30) (17,27) (18,30) (18,29) (19,30) (19,23) (19,27) (19,25) (20,32) (20,22) (20,26) (21,32) (21,26) (22,32) (22,26) (23,30) (23,29) (23,25) (24,28) (26,32) (27,30) (27,29) (28,31) (29,30)\nQ: Is there a path between node 26 and node 25?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "466"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,13) (0,2) (0,14) (0,23) (0,8) (0,1) (0,25) (0,27) (0,10) (1,29) (1,13) (1,19) (1,28) (1,23) (1,30) (1,25) (1,24) (2,12) (2,5) (2,14) (2,17) (2,23) (3,7) (3,12) (3,19) (3,23) (3,8) (3,30) (3,25) (3,24) (4,33) (5,20) (5,23) (5,30) (6,15) (6,11) (7,32) (7,17) (7,23) (7,8) (7,10) (8,29) (8,12) (8,32) (8,20) (8,19) (8,17) (8,30) (9,29) (9,28) (9,30) (9,24) (10,13) (10,20) (10,14) (10,22) (11,31) (12,13) (12,23) (12,27) (12,26) (13,29) (13,32) (13,14) (13,28) (13,30) (13,24) (14,17) (14,30) (14,22) (14,27) (15,16) (15,31) (15,33) (17,32) (17,20) (17,19) (17,27) (17,24) (17,26) (18,21) (20,28) (20,30) (20,25) (21,31) (22,32) (22,28) (22,30) (23,28) (23,25) (23,27) (24,29) (24,28) (24,26) (25,32) (26,29) (26,27) (27,32) (27,30) (28,32) (28,30)\nQ: Is there a path between node 5 and node 12?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "467"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,18) (0,15) (0,12) (0,5) (1,24) (2,21) (2,23) (2,9) (2,15) (2,19) (3,23) (3,15) (3,8) (3,16) (5,21) (5,22) (5,6) (5,19) (5,8) (5,10) (5,16) (6,14) (6,22) (6,9) (6,12) (6,17) (9,23) (9,22) (9,20) (9,10) (10,22) (10,18) (10,19) (11,24) (12,14) (13,14) (13,21) (13,23) (13,18) (13,15) (14,21) (14,18) (14,15) (14,16) (15,20) (15,17) (17,23) (17,22) (17,18) (17,20) (17,19) (18,19) (19,20) (21,23)\nQ: Is there a path between node 12 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "468"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (1,3) (1,2) (1,6) (2,5) (2,6) (3,5) (5,6)\nQ: Is there a path between node 5 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "469"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,13) (0,2) (0,15) (0,6) (0,17) (0,8) (0,16) (0,18) (0,9) (0,12) (0,11) (1,10) (1,14) (1,7) (1,5) (1,4) (2,3) (2,13) (2,15) (2,6) (2,17) (2,8) (2,16) (2,18) (2,9) (2,12) (2,11) (3,13) (3,15) (3,6) (3,17) (3,8) (3,16) (3,18) (3,9) (3,12) (3,11) (4,10) (4,14) (4,7) (4,5) (5,10) (5,14) (5,7) (6,13) (6,15) (6,17) (6,8) (6,16) (6,18) (6,9) (6,12) (6,11) (7,10) (7,14) (8,13) (8,15) (8,17) (8,16) (8,18) (8,9) (8,12) (8,11) (9,13) (9,15) (9,17) (9,16) (9,18) (9,12) (9,11) (10,14) (11,13) (11,15) (11,17) (11,16) (11,18) (11,12) (12,13) (12,15) (12,17) (12,16) (12,18) (13,15) (13,17) (13,16) (13,18) (15,17) (15,16) (15,18) (16,17) (16,18) (17,18)\nQ: Is there a path between node 5 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "470"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,22) (0,12) (0,24) (0,18) (0,19) (0,30) (0,1) (0,21) (0,9) (0,5) (0,6) (0,7) (0,2) (1,22) (1,24) (1,18) (1,19) (1,30) (1,21) (1,9) (1,5) (1,6) (1,11) (1,7) (1,31) (1,2) (2,12) (2,24) (2,18) (2,19) (2,21) (2,5) (2,6) (2,11) (2,7) (2,31) (3,26) (3,16) (3,4) (3,28) (3,13) (3,20) (4,26) (4,16) (4,8) (4,28) (5,12) (5,24) (5,30) (5,21) (5,9) (5,11) (5,7) (5,31) (6,22) (6,12) (6,24) (6,30) (6,21) (6,9) (6,11) (6,7) (7,12) (7,18) (7,30) (7,9) (7,11) (7,31) (8,26) (8,16) (8,28) (9,22) (9,12) (9,24) (9,18) (9,19) (9,30) (9,11) (9,31) (10,25) (10,14) (10,29) (10,32) (10,15) (10,23) (11,22) (11,12) (11,24) (11,18) (11,30) (11,21) (12,24) (12,30) (12,21) (12,31) (13,26) (13,28) (14,27) (14,17) (14,29) (14,32) (14,15) (15,25) (15,27) (15,17) (15,29) (15,32) (15,23) (16,26) (17,29) (18,22) (18,24) (18,19) (18,21) (19,22) (19,30) (19,21) (20,26) (21,22) (21,24) (21,31) (22,24) (23,25) (23,27) (23,32) (24,30) (24,31) (25,27) (25,29) (25,32) (26,28) (27,29) (27,32) (30,31)\nQ: Is there a path between node 6 and node 30?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "471"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,23) (0,8) (1,6) (1,26) (1,11) (2,6) (2,11) (3,12) (3,19) (3,20) (4,13) (4,21) (4,17) (4,10) (4,6) (4,23) (4,8) (5,13) (5,7) (5,21) (5,17) (5,28) (5,6) (5,23) (5,8) (5,26) (5,24) (5,11) (6,13) (6,17) (6,10) (6,23) (6,24) (7,17) (7,28) (7,23) (8,21) (8,10) (9,15) (10,13) (10,21) (10,23) (10,11) (11,13) (11,17) (12,19) (12,14) (12,27) (12,15) (12,22) (13,17) (13,16) (14,22) (15,19) (16,17) (16,28) (16,24) (17,24) (18,19) (18,27) (19,27) (21,26) (21,24) (22,25) (23,28) (24,28) (25,27)\nQ: Is there a path between node 14 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "472"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,8) (1,5) (1,10) (1,8) (2,6) (2,7) (3,9) (3,10) (4,11) (4,8) (6,7) (8,9) (8,10) (11,12)\nQ: Is there a path between node 11 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "473"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (1,11) (1,9) (1,14) (2,5) (2,6) (3,11) (3,13) (4,11) (4,13) (4,15) (5,7) (5,6) (7,10) (8,11) (8,9) (9,14) (9,12) (11,13) (13,14) (13,15)\nQ: Is there a path between node 14 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "474"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,32) (0,29) (0,7) (0,15) (1,30) (1,10) (1,8) (2,27) (2,18) (2,20) (2,7) (2,26) (3,14) (3,9) (4,18) (4,11) (4,13) (4,15) (5,30) (5,21) (6,14) (6,21) (6,17) (7,18) (7,22) (7,31) (7,29) (7,26) (8,14) (8,10) (9,21) (10,12) (10,21) (10,17) (11,19) (11,22) (11,28) (11,32) (11,29) (11,15) (11,26) (12,30) (12,21) (13,27) (13,20) (13,28) (13,31) (14,17) (15,20) (15,31) (15,26) (16,27) (16,32) (17,30) (18,27) (18,28) (18,32) (18,26) (18,24) (18,23) (19,27) (19,20) (19,31) (19,29) (19,26) (19,24) (20,25) (20,28) (20,32) (20,26) (22,31) (22,23) (23,27) (23,28) (23,26) (25,26) (26,27) (26,28) (26,29) (28,32) (28,31) (29,31)\nQ: Is there a path between node 12 and node 18?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "475"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,29) (0,1) (0,9) (0,20) (0,34) (0,7) (0,19) (0,22) (0,31) (1,11) (1,30) (1,6) (1,21) (1,14) (1,28) (1,19) (1,31) (1,4) (2,3) (2,11) (2,18) (2,21) (2,20) (2,14) (2,7) (2,17) (3,11) (3,33) (3,15) (3,30) (3,18) (3,21) (3,14) (3,5) (4,10) (4,26) (4,27) (4,21) (4,34) (5,9) (5,27) (5,30) (5,6) (5,24) (5,14) (5,34) (5,28) (5,17) (6,11) (6,25) (6,10) (6,26) (6,29) (6,15) (6,16) (6,14) (6,7) (6,12) (6,22) (7,10) (7,26) (7,27) (7,18) (7,24) (7,8) (7,31) (8,11) (8,33) (8,9) (8,30) (8,24) (8,20) (8,16) (8,22) (8,17) (9,10) (9,20) (9,16) (9,14) (10,25) (10,33) (10,30) (10,18) (10,24) (10,20) (10,31) (11,15) (11,12) (11,19) (11,17) (12,25) (12,29) (12,27) (12,30) (12,34) (12,28) (12,17) (14,25) (14,33) (14,26) (14,29) (14,30) (14,21) (14,17) (15,20) (15,17) (16,21) (16,28) (16,19) (16,22) (17,27) (17,30) (17,24) (17,19) (18,26) (18,21) (18,28) (19,33) (19,27) (19,34) (19,22) (20,25) (20,26) (20,27) (20,21) (20,28) (20,31) (21,22) (22,24) (22,31) (24,34) (24,28) (25,26) (25,29) (25,27) (26,33) (26,27) (26,30) (27,30) (27,28) (28,31) (29,30) (29,34) (29,31) (30,33) (30,34) (31,33) (31,34)\nQ: Is there a path between node 19 and node 25?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "476"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,21) (0,14) (0,1) (0,22) (0,16) (0,19) (0,5) (0,10) (0,20) (0,11) (0,24) (0,13) (1,21) (1,9) (1,3) (1,14) (1,22) (1,10) (1,20) (1,12) (1,11) (1,24) (1,13) (1,23) (2,8) (2,4) (2,18) (2,15) (3,9) (3,14) (3,16) (3,19) (3,7) (3,6) (3,5) (3,10) (3,11) (4,8) (4,17) (4,18) (4,15) (5,9) (5,14) (5,22) (5,7) (5,6) (5,10) (5,20) (5,12) (5,11) (5,13) (5,23) (6,21) (6,9) (6,22) (6,19) (6,7) (6,20) (6,12) (6,11) (6,13) (6,23) (7,21) (7,9) (7,14) (7,16) (7,19) (7,10) (7,20) (7,12) (7,11) (7,24) (7,13) (7,23) (8,17) (8,18) (8,15) (9,21) (9,16) (9,10) (9,20) (9,12) (9,11) (9,24) (9,13) (9,23) (10,22) (10,19) (10,12) (10,11) (10,13) (10,23) (11,21) (11,22) (11,19) (11,20) (11,12) (11,24) (11,13) (11,23) (12,21) (12,14) (12,22) (12,20) (12,24) (12,13) (12,23) (13,21) (13,14) (13,22) (13,16) (13,20) (13,23) (14,21) (14,16) (14,20) (14,24) (14,23) (15,18) (16,21) (16,22) (16,19) (16,20) (16,24) (16,23) (17,18) (19,21) (19,20) (19,24) (19,23) (20,21) (20,24) (20,23) (21,24) (21,23) (22,23) (23,24)\nQ: Is there a path between node 21 and node 22?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "477"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,7) (0,8) (0,9) (0,13) (0,14) (0,15) (0,5) (1,2) (1,12) (1,16) (1,11) (1,3) (1,6) (1,14) (1,4) (2,12) (2,7) (2,9) (2,13) (2,14) (3,16) (3,11) (3,7) (3,8) (3,14) (3,15) (3,5) (3,4) (4,12) (4,11) (4,8) (4,9) (4,13) (4,14) (4,5) (5,12) (5,16) (5,11) (5,7) (5,8) (5,13) (5,14) (5,15) (6,12) (6,16) (6,11) (6,7) (6,14) (6,15) (7,12) (7,16) (7,11) (7,8) (7,9) (7,13) (8,12) (8,16) (8,11) (8,9) (8,13) (8,14) (9,12) (9,16) (9,11) (9,14) (9,15) (11,12) (11,16) (11,14) (12,13) (12,15) (13,16) (13,15) (14,16)\nQ: Is there a path between node 1 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "478"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,8) (0,5) (0,4) (0,25) (0,22) (0,16) (0,24) (0,21) (2,15) (2,23) (2,26) (2,10) (2,3) (2,11) (2,6) (2,27) (3,15) (3,23) (3,14) (3,26) (3,10) (3,11) (3,27) (4,8) (4,13) (4,5) (4,20) (4,18) (4,7) (4,22) (4,16) (4,24) (5,8) (5,13) (5,20) (5,7) (5,22) (5,24) (5,21) (6,15) (6,23) (6,14) (6,26) (6,10) (6,11) (6,27) (7,12) (7,20) (7,25) (7,16) (7,21) (8,12) (8,20) (8,25) (8,16) (8,24) (10,15) (10,23) (10,14) (10,26) (10,19) (10,11) (10,27) (11,15) (11,23) (11,26) (11,27) (12,16) (12,24) (12,21) (13,20) (13,18) (13,25) (13,22) (13,16) (13,24) (13,21) (14,15) (14,26) (15,26) (15,27) (16,22) (16,24) (16,21) (18,25) (18,22) (18,21) (19,23) (19,26) (19,27) (20,25) (20,24) (21,25) (21,24) (22,25) (22,24) (23,26) (23,27) (24,25) (26,27)\nQ: Is there a path between node 25 and node 24?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "479"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (1,2)\nQ: Is there a path between node 3 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "480"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,16) (0,9) (0,3) (0,4) (0,8) (0,17) (1,6) (1,12) (1,13) (1,18) (1,2) (1,4) (1,8) (1,17) (2,6) (2,12) (2,15) (2,9) (2,13) (2,18) (2,4) (2,8) (2,17) (3,6) (3,16) (3,12) (3,9) (3,13) (3,18) (3,8) (3,17) (3,5) (4,6) (4,16) (4,12) (4,9) (4,18) (4,17) (4,5) (5,6) (5,12) (5,15) (5,9) (5,17) (6,12) (6,15) (6,9) (6,13) (6,18) (6,8) (7,10) (7,11) (7,19) (8,16) (8,15) (8,9) (8,18) (9,16) (9,12) (9,15) (9,13) (9,18) (9,17) (10,19) (11,14) (11,19) (12,16) (12,15) (12,13) (12,17) (13,18) (14,19) (15,17) (16,17) (17,18)\nQ: Is there a path between node 13 and node 19?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "481"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,26) (2,26) (2,30) (2,6) (3,19) (4,29) (4,8) (4,11) (4,9) (5,25) (6,30) (6,19) (6,13) (6,25) (7,23) (7,29) (7,10) (7,28) (7,14) (8,23) (8,15) (8,27) (8,18) (8,11) (8,28) (8,9) (9,23) (9,29) (9,15) (9,18) (9,12) (10,15) (11,29) (11,27) (11,28) (11,14) (12,27) (13,16) (13,26) (14,17) (15,29) (15,21) (15,28) (16,25) (17,23) (17,29) (17,18) (19,20) (19,22) (20,22) (21,27) (21,28) (22,26) (23,29) (23,28) (24,26) (24,30) (25,26) (25,30) (27,28)\nQ: Is there a path between node 11 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "482"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,12) (0,1) (0,13) (0,14) (0,11) (0,20) (0,7) (0,21) (1,4) (1,13) (1,14) (1,16) (1,7) (1,21) (2,5) (2,22) (2,8) (2,15) (2,25) (2,9) (2,17) (2,26) (3,11) (3,20) (3,7) (4,13) (4,14) (4,11) (4,20) (4,21) (5,22) (5,18) (5,15) (5,23) (5,25) (5,17) (5,26) (5,24) (6,19) (7,12) (7,13) (7,14) (7,11) (7,20) (7,21) (8,22) (8,15) (8,23) (8,9) (8,17) (8,24) (9,18) (9,15) (9,23) (9,25) (9,17) (11,13) (11,14) (11,16) (11,20) (12,13) (12,14) (12,16) (12,20) (12,21) (13,16) (13,20) (14,16) (14,20) (14,21) (15,22) (15,18) (15,23) (15,25) (15,26) (15,24) (16,21) (17,22) (17,18) (17,23) (17,25) (18,25) (18,24) (20,21) (22,23) (22,25) (22,26) (22,24) (23,26) (23,24) (24,25) (25,26)\nQ: Is there a path between node 15 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "483"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,1) (0,2) (0,7) (0,6) (1,2) (1,8) (1,7) (1,4) (1,6) (2,7) (2,4) (2,6) (3,5) (4,9) (4,8) (4,7) (6,9) (6,7) (7,8)\nQ: Is there a path between node 6 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "484"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,15) (0,6) (0,17) (0,4) (0,12) (0,16) (0,9) (1,14) (1,23) (1,18) (1,19) (1,3) (1,21) (2,14) (2,5) (2,11) (2,23) (2,22) (2,8) (2,18) (2,19) (2,3) (2,20) (3,14) (3,5) (3,23) (3,22) (3,8) (3,18) (3,19) (3,20) (3,21) (4,7) (4,15) (4,6) (4,17) (4,13) (4,10) (4,16) (5,14) (5,8) (5,18) (5,19) (5,21) (6,13) (6,10) (6,16) (6,9) (7,15) (7,13) (7,9) (8,14) (8,11) (8,23) (8,22) (8,18) (8,19) (8,20) (8,21) (9,15) (9,13) (9,12) (9,16) (10,15) (10,17) (10,13) (10,12) (11,14) (11,23) (11,22) (11,18) (11,19) (12,17) (12,16) (13,17) (13,16) (14,23) (14,19) (15,17) (16,17) (18,23) (18,22) (18,19) (18,21) (19,23) (19,22) (19,20) (20,23) (20,21) (21,23) (22,23)\nQ: Is there a path between node 7 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "485"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,8) (0,4) (0,5) (0,13) (0,2) (0,17) (1,15) (1,8) (1,3) (1,4) (1,5) (1,13) (1,17) (2,15) (2,8) (2,3) (2,4) (2,5) (2,13) (3,8) (3,5) (3,17) (4,15) (4,13) (4,17) (5,15) (5,8) (5,17) (6,14) (6,7) (6,10) (6,16) (6,9) (6,12) (7,14) (7,16) (7,9) (8,13) (9,14) (9,10) (9,11) (9,16) (9,12) (10,14) (10,12) (11,14) (11,12) (12,14) (12,16) (13,17) (15,17)\nQ: Is there a path between node 16 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "486"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,12) (0,2) (0,3) (1,13) (1,22) (1,7) (1,11) (1,19) (1,6) (1,8) (2,14) (2,20) (2,3) (3,14) (3,20) (4,21) (4,18) (4,5) (4,17) (4,9) (4,15) (4,10) (5,21) (5,17) (5,9) (5,15) (5,10) (6,16) (6,13) (6,22) (6,7) (6,11) (6,19) (6,8) (7,16) (7,13) (7,22) (7,8) (8,16) (8,13) (8,11) (8,19) (9,18) (9,17) (9,15) (9,10) (10,21) (10,18) (11,16) (11,13) (11,22) (11,19) (12,14) (12,20) (13,16) (13,19) (14,20) (15,21) (15,18) (15,17) (16,22) (17,21) (17,18) (19,22)\nQ: Is there a path between node 0 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "487"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,22) (0,12) (0,24) (0,18) (0,19) (0,30) (0,1) (0,21) (0,9) (0,5) (0,6) (0,7) (0,2) (1,22) (1,24) (1,18) (1,19) (1,30) (1,21) (1,9) (1,5) (1,6) (1,11) (1,7) (1,31) (1,2) (2,12) (2,24) (2,18) (2,19) (2,21) (2,5) (2,6) (2,11) (2,7) (2,31) (3,26) (3,16) (3,4) (3,28) (3,13) (3,20) (4,26) (4,16) (4,8) (4,28) (5,12) (5,24) (5,30) (5,21) (5,9) (5,11) (5,7) (5,31) (6,22) (6,12) (6,24) (6,30) (6,21) (6,9) (6,11) (6,7) (7,12) (7,18) (7,30) (7,9) (7,11) (7,31) (8,26) (8,16) (8,28) (9,22) (9,12) (9,24) (9,18) (9,19) (9,30) (9,11) (9,31) (10,25) (10,14) (10,29) (10,32) (10,15) (10,23) (11,22) (11,12) (11,24) (11,18) (11,30) (11,21) (12,24) (12,30) (12,21) (12,31) (13,26) (13,28) (14,27) (14,17) (14,29) (14,32) (14,15) (15,25) (15,27) (15,17) (15,29) (15,32) (15,23) (16,26) (17,29) (18,22) (18,24) (18,19) (18,21) (19,22) (19,30) (19,21) (20,26) (21,22) (21,24) (21,31) (22,24) (23,25) (23,27) (23,32) (24,30) (24,31) (25,27) (25,29) (25,32) (26,28) (27,29) (27,32) (30,31)\nQ: Is there a path between node 26 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "488"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,4) (0,9) (0,1) (0,11) (0,2) (1,10) (1,6) (1,9) (1,15) (1,13) (2,12) (2,9) (2,17) (2,15) (3,4) (3,6) (3,11) (4,12) (4,9) (4,11) (6,10) (6,12) (6,9) (6,15) (6,13) (8,12) (8,9) (8,15) (8,13) (9,10) (9,11) (10,13) (10,11) (11,13) (12,13) (14,16)\nQ: Is there a path between node 16 and node 17?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "489"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,4) (0,1) (1,2) (1,5) (1,4) (2,5) (2,4) (4,5)\nQ: Is there a path between node 3 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "490"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,8) (0,10) (0,12) (0,13) (1,10) (2,5) (2,16) (3,13) (4,16) (5,7) (5,14) (6,7) (7,16) (7,14) (9,13) (10,15) (11,12) (12,15)\nQ: Is there a path between node 15 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "491"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,4) (1,23) (1,7) (1,18) (1,24) (1,32) (1,31) (1,21) (1,27) (1,11) (1,6) (1,29) (1,17) (1,20) (2,23) (2,7) (2,18) (2,33) (2,24) (2,31) (2,21) (2,8) (2,27) (2,11) (2,29) (2,17) (2,26) (3,9) (3,22) (3,13) (3,5) (3,30) (3,28) (3,16) (3,14) (3,15) (4,19) (4,10) (5,9) (5,22) (5,13) (5,28) (5,16) (5,14) (6,18) (6,32) (6,25) (6,21) (6,8) (6,11) (6,17) (6,20) (6,26) (7,18) (7,33) (7,24) (7,32) (7,25) (7,31) (7,21) (7,17) (7,20) (7,26) (8,18) (8,33) (8,32) (8,25) (8,31) (8,27) (8,11) (8,29) (8,20) (8,26) (9,22) (9,13) (9,30) (9,28) (9,14) (9,15) (10,19) (10,12) (11,18) (11,33) (11,24) (11,25) (11,31) (11,27) (11,29) (11,26) (12,19) (13,28) (13,15) (14,30) (14,28) (14,16) (14,15) (15,22) (15,30) (15,16) (16,22) (17,23) (17,18) (17,33) (17,25) (17,31) (17,21) (17,27) (17,29) (17,20) (17,26) (18,23) (18,32) (18,25) (18,21) (18,29) (18,20) (18,26) (20,23) (20,33) (20,32) (20,25) (20,31) (20,21) (20,27) (20,29) (20,26) (21,23) (21,33) (21,24) (21,25) (21,29) (23,33) (23,24) (23,25) (23,31) (23,27) (23,29) (23,26) (24,33) (24,32) (24,25) (24,27) (24,29) (24,26) (25,32) (25,31) (25,27) (25,29) (25,26) (26,33) (26,31) (26,27) (27,31) (27,29) (28,30) (31,32) (32,33)\nQ: Is there a path between node 29 and node 32?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "492"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,13) (0,30) (0,1) (0,4) (0,2) (0,22) (1,30) (1,17) (1,5) (1,4) (1,25) (1,29) (2,3) (2,5) (2,23) (3,28) (3,24) (3,4) (3,6) (3,8) (3,12) (4,15) (4,24) (4,25) (4,7) (4,6) (4,29) (5,21) (5,23) (5,7) (5,12) (6,20) (6,28) (6,23) (7,13) (7,15) (7,16) (7,8) (7,12) (8,20) (8,30) (8,24) (8,17) (8,23) (10,19) (11,19) (11,26) (12,20) (12,16) (12,25) (12,18) (13,28) (13,18) (14,20) (15,28) (15,24) (15,23) (16,20) (16,30) (16,24) (16,29) (17,21) (17,28) (17,25) (18,21) (18,23) (18,29) (20,24) (20,23) (20,22) (20,29) (21,25) (21,23) (21,22) (22,25) (23,24) (23,29) (24,28) (24,29) (25,28) (26,27) (29,30)\nQ: Is there a path between node 0 and node 21?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "493"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (1,4) (2,4)\nQ: Is there a path between node 1 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "494"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,4) (0,15) (0,19) (0,8) (0,17) (0,13) (0,3) (0,14) (0,5) (0,2) (0,16) (0,1) (0,10) (1,20) (1,4) (1,15) (1,19) (1,8) (1,17) (1,13) (1,3) (1,14) (1,5) (1,2) (1,16) (1,10) (2,20) (2,4) (2,15) (2,19) (2,8) (2,17) (2,13) (2,3) (2,14) (2,5) (2,16) (2,10) (3,20) (3,4) (3,15) (3,19) (3,8) (3,17) (3,13) (3,14) (3,5) (3,16) (3,10) (4,20) (4,15) (4,19) (4,8) (4,17) (4,13) (4,14) (4,5) (4,16) (4,10) (5,20) (5,15) (5,19) (5,8) (5,17) (5,13) (5,14) (5,16) (5,10) (6,12) (6,22) (6,9) (6,18) (6,21) (6,7) (6,11) (7,12) (7,22) (7,9) (7,18) (7,21) (7,11) (8,20) (8,15) (8,19) (8,17) (8,13) (8,14) (8,16) (8,10) (9,12) (9,22) (9,18) (9,21) (9,11) (10,20) (10,15) (10,19) (10,17) (10,13) (10,14) (10,16) (11,12) (11,22) (11,18) (11,21) (12,22) (12,18) (12,21) (13,20) (13,15) (13,19) (13,17) (13,14) (13,16) (14,20) (14,15) (14,19) (14,17) (14,16) (15,20) (15,19) (15,17) (15,16) (16,20) (16,19) (16,17) (17,20) (17,19) (18,22) (18,21) (19,20) (21,22)\nQ: Is there a path between node 9 and node 19?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "495"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,11) (0,5) (0,9) (0,6) (1,2) (1,7) (1,3) (1,10) (1,8) (2,7) (2,3) (2,10) (2,8) (3,7) (3,10) (3,8) (4,11) (4,5) (4,9) (4,6) (5,11) (5,9) (5,6) (6,11) (6,9) (7,10) (7,8) (8,10) (9,11)\nQ: Is there a path between node 11 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "496"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,1) (1,11) (1,5) (1,8) (2,14) (2,10) (2,6) (2,3) (2,13) (2,4) (3,7) (3,14) (3,6) (3,12) (3,13) (3,4) (4,9) (4,7) (4,10) (4,12) (4,13) (5,11) (5,8) (6,7) (6,10) (6,12) (6,13) (7,9) (7,14) (7,10) (7,13) (8,11) (10,14) (10,12) (10,13) (12,14) (12,13) (13,14)\nQ: Is there a path between node 13 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "497"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,12) (0,5) (0,6) (0,4) (0,8) (0,2) (0,9) (0,1) (0,7) (1,12) (1,5) (1,6) (1,4) (1,8) (1,2) (1,9) (1,10) (1,7) (2,8) (2,10) (2,7) (4,11) (4,12) (4,5) (4,6) (4,8) (4,9) (4,7) (5,11) (5,6) (5,8) (5,10) (5,7) (6,11) (6,12) (6,8) (6,9) (7,11) (7,12) (7,9) (7,10) (8,12) (8,9) (8,10) (9,11) (9,12) (9,10) (10,11) (10,12) (11,12)\nQ: Is there a path between node 1 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "498"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,18) (0,12) (0,2) (0,11) (0,8) (0,13) (1,4) (1,10) (1,17) (1,5) (1,14) (1,7) (1,6) (1,15) (2,3) (2,18) (2,12) (2,11) (2,8) (2,13) (3,18) (3,12) (3,11) (3,8) (3,13) (4,10) (4,17) (4,5) (4,14) (4,7) (4,6) (4,15) (5,10) (5,17) (5,14) (5,7) (5,6) (5,15) (6,10) (6,17) (6,14) (6,7) (6,15) (7,10) (7,17) (7,14) (7,15) (8,18) (8,12) (8,11) (8,13) (9,16) (10,17) (10,14) (10,15) (11,18) (11,12) (11,13) (12,18) (12,13) (13,18) (14,17) (14,15) (15,17)\nQ: Is there a path between node 18 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "499"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,5) (0,2) (0,3) (0,10) (0,6) (0,1) (0,4) (0,9) (0,7) (0,12) (1,8) (1,5) (1,2) (1,3) (1,10) (1,6) (1,4) (1,9) (1,7) (1,12) (2,8) (2,5) (2,3) (2,10) (2,6) (2,4) (2,9) (2,7) (2,12) (3,8) (3,5) (3,10) (3,6) (3,4) (3,9) (3,7) (3,12) (4,8) (4,5) (4,10) (4,6) (4,9) (4,7) (4,12) (5,8) (5,10) (5,6) (5,9) (5,7) (5,12) (6,8) (6,10) (6,9) (6,7) (6,12) (7,8) (7,10) (7,9) (7,12) (8,10) (8,9) (8,12) (9,10) (9,12) (10,12) (11,13)\nQ: Is there a path between node 11 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "500"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (1,27) (1,24) (1,21) (1,3) (2,10) (2,22) (2,6) (2,18) (2,25) (2,12) (3,19) (3,27) (3,24) (4,10) (4,6) (4,18) (4,25) (5,28) (5,16) (6,10) (6,13) (6,25) (6,12) (6,9) (7,28) (8,10) (8,14) (8,18) (8,29) (8,25) (8,23) (9,13) (9,14) (10,29) (10,25) (12,22) (12,18) (12,17) (13,29) (13,26) (14,20) (14,17) (15,19) (17,25) (18,20) (18,25) (20,29) (20,26) (20,23) (21,27) (21,24) (23,26) (23,25) (24,27) (26,29)\nQ: Is there a path between node 1 and node 17?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "501"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,8) (0,10) (0,4) (0,16) (0,5) (0,2) (0,7) (0,9) (0,15) (0,13) (0,1) (0,12) (0,14) (0,3) (1,11) (1,8) (1,10) (1,4) (1,16) (1,5) (1,2) (1,7) (1,9) (1,15) (1,13) (1,12) (1,14) (1,3) (2,11) (2,8) (2,10) (2,4) (2,16) (2,5) (2,7) (2,9) (2,15) (2,13) (2,12) (2,14) (2,3) (3,11) (3,8) (3,10) (3,4) (3,16) (3,5) (3,7) (3,9) (3,15) (3,13) (3,12) (3,14) (4,11) (4,8) (4,10) (4,16) (4,5) (4,7) (4,9) (4,15) (4,13) (4,12) (4,14) (5,11) (5,8) (5,10) (5,16) (5,7) (5,9) (5,15) (5,13) (5,12) (5,14) (7,11) (7,8) (7,10) (7,16) (7,9) (7,15) (7,13) (7,12) (7,14) (8,11) (8,10) (8,16) (8,9) (8,15) (8,13) (8,12) (8,14) (9,11) (9,10) (9,16) (9,15) (9,13) (9,12) (9,14) (10,11) (10,16) (10,15) (10,13) (10,12) (10,14) (11,16) (11,15) (11,13) (11,12) (11,14) (12,16) (12,15) (12,13) (12,14) (13,16) (13,15) (13,14) (14,16) (14,15) (15,16)\nQ: Is there a path between node 10 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "502"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,13) (0,30) (0,1) (0,4) (0,2) (0,22) (1,30) (1,17) (1,5) (1,4) (1,25) (1,29) (2,3) (2,5) (2,23) (3,28) (3,24) (3,4) (3,6) (3,8) (3,12) (4,15) (4,24) (4,25) (4,7) (4,6) (4,29) (5,21) (5,23) (5,7) (5,12) (6,20) (6,28) (6,23) (7,13) (7,15) (7,16) (7,8) (7,12) (8,20) (8,30) (8,24) (8,17) (8,23) (10,19) (11,19) (11,26) (12,20) (12,16) (12,25) (12,18) (13,28) (13,18) (14,20) (15,28) (15,24) (15,23) (16,20) (16,30) (16,24) (16,29) (17,21) (17,28) (17,25) (18,21) (18,23) (18,29) (20,24) (20,23) (20,22) (20,29) (21,25) (21,23) (21,22) (22,25) (23,24) (23,29) (24,28) (24,29) (25,28) (26,27) (29,30)\nQ: Is there a path between node 5 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "503"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,13) (0,1) (0,9) (0,5) (0,7) (0,3) (0,10) (0,23) (0,26) (0,27) (0,8) (0,14) (0,22) (0,20) (0,15) (0,4) (0,2) (1,25) (1,11) (1,21) (1,13) (1,9) (1,3) (1,10) (1,23) (1,26) (1,27) (1,14) (1,20) (1,15) (1,2) (1,28) (2,25) (2,11) (2,16) (2,21) (2,6) (2,13) (2,9) (2,7) (2,23) (2,26) (2,8) (2,20) (2,15) (3,25) (3,6) (3,13) (3,9) (3,10) (3,27) (3,20) (3,15) (3,4) (3,28) (4,11) (4,16) (4,6) (4,13) (4,10) (4,23) (4,26) (4,27) (4,8) (4,14) (4,22) (4,15) (4,28) (5,25) (5,16) (5,21) (5,6) (5,13) (5,9) (5,7) (5,26) (5,8) (5,22) (5,15) (5,28) (6,11) (6,16) (6,21) (6,13) (6,9) (6,7) (6,10) (6,27) (6,22) (6,20) (6,15) (7,25) (7,16) (7,21) (7,9) (7,10) (7,27) (7,8) (7,14) (7,22) (7,20) (7,15) (7,28) (8,25) (8,13) (8,23) (8,26) (8,27) (8,14) (8,20) (8,28) (9,25) (9,11) (9,16) (9,21) (9,10) (9,23) (9,26) (9,27) (9,22) (9,20) (9,28) (10,11) (10,16) (10,21) (10,13) (10,23) (10,26) (10,27) (10,14) (10,22) (10,20) (10,15) (10,28) (11,25) (11,16) (11,21) (11,13) (11,23) (11,26) (11,27) (11,14) (11,22) (11,20) (12,24) (12,19) (13,25) (13,16) (13,14) (13,22) (13,15) (13,28) (14,25) (14,21) (14,23) (14,26) (14,20) (14,15) (15,16) (15,21) (15,26) (15,27) (15,22) (15,28) (16,21) (16,23) (16,26) (16,27) (16,28) (17,18) (20,25) (20,23) (20,26) (20,27) (20,22) (20,28) (21,25) (21,23) (21,26) (21,22) (22,25) (22,23) (22,27) (23,25) (23,26) (23,27) (23,28) (25,26) (25,27) (26,27) (27,28)\nQ: Is there a path between node 17 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "504"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,15) (1,3) (1,20) (2,11) (3,12) (3,6) (3,16) (3,20) (5,14) (5,7) (6,20) (6,21) (7,13) (7,18) (8,14) (8,13) (9,12) (9,16) (9,21) (10,21) (11,17) (12,16) (14,18) (15,16) (15,21) (16,20) (20,21)\nQ: Is there a path between node 8 and node 13?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "505"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,10) (0,18) (0,21) (0,30) (0,28) (0,15) (1,27) (1,24) (1,22) (1,32) (1,14) (1,5) (2,29) (2,10) (2,18) (2,21) (2,19) (2,30) (2,16) (2,28) (2,15) (3,24) (3,13) (3,22) (3,20) (3,5) (4,17) (4,11) (4,6) (4,26) (4,23) (4,31) (4,25) (5,27) (5,13) (5,22) (5,20) (5,32) (5,14) (6,17) (6,9) (6,23) (6,31) (6,25) (7,29) (7,10) (7,18) (7,19) (7,30) (7,16) (7,15) (8,17) (8,11) (8,26) (8,23) (8,31) (9,17) (9,26) (9,23) (9,31) (9,25) (10,29) (10,18) (10,21) (10,30) (10,28) (10,15) (11,17) (11,26) (11,23) (12,27) (12,24) (12,13) (12,22) (12,32) (13,27) (13,24) (13,22) (13,20) (13,32) (13,14) (14,27) (14,22) (14,32) (15,29) (15,18) (15,21) (15,19) (15,28) (16,29) (16,21) (16,19) (16,28) (17,23) (18,29) (18,21) (18,30) (18,28) (19,29) (19,21) (19,30) (19,28) (20,24) (20,22) (20,32) (21,29) (21,30) (21,28) (22,27) (22,24) (22,32) (23,31) (24,27) (25,26) (26,31) (28,30)\nQ: Is there a path between node 8 and node 25?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "506"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,1) (3,4)\nQ: Is there a path between node 3 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "507"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,19) (0,17) (0,3) (0,10) (0,14) (1,7) (1,8) (1,15) (1,13) (2,9) (2,12) (2,18) (2,4) (3,6) (3,19) (3,17) (3,16) (3,10) (3,14) (4,12) (4,18) (5,9) (5,18) (6,19) (6,17) (6,16) (6,14) (6,20) (7,8) (7,15) (7,13) (9,12) (9,18) (10,16) (10,14) (10,20) (11,15) (12,18) (13,15) (14,19) (14,17) (14,20) (16,19) (16,17) (17,20) (19,20)\nQ: Is there a path between node 3 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "508"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,14) (0,10) (0,24) (0,2) (0,12) (0,19) (0,3) (0,17) (0,25) (0,23) (0,15) (1,18) (1,11) (1,8) (2,14) (2,10) (2,24) (2,7) (2,3) (2,21) (2,25) (2,23) (2,6) (3,14) (3,24) (3,12) (3,19) (3,17) (3,25) (3,23) (3,6) (3,15) (4,18) (4,8) (5,18) (5,11) (5,8) (6,16) (6,14) (6,10) (6,12) (6,7) (6,19) (6,21) (6,25) (6,23) (6,9) (6,15) (7,16) (7,10) (7,24) (7,12) (7,19) (7,17) (7,25) (7,9) (7,15) (8,18) (8,11) (9,16) (9,14) (9,10) (9,24) (9,12) (9,19) (9,17) (9,21) (9,23) (9,15) (10,16) (10,14) (10,19) (10,21) (10,25) (10,23) (10,15) (11,18) (12,16) (12,14) (12,24) (12,19) (12,17) (12,21) (12,25) (12,23) (12,15) (13,20) (14,16) (14,24) (14,17) (14,21) (14,25) (14,23) (14,15) (15,16) (15,24) (15,23) (16,21) (16,25) (16,23) (17,21) (17,23) (19,21) (19,25) (21,24) (21,25) (21,23) (23,25) (24,25)\nQ: Is there a path between node 14 and node 18?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "509"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,18) (1,12) (1,15) (1,7) (2,17) (2,3) (3,17) (4,12) (5,17) (5,19) (6,18) (6,10) (6,9) (6,12) (6,16) (7,18) (7,9) (7,13) (7,8) (8,14) (9,18) (9,14) (9,12) (9,13) (10,12) (10,15) (11,17) (12,16) (14,18)\nQ: Is there a path between node 9 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "510"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,3) (0,12) (0,6) (0,11) (1,16) (1,3) (1,12) (1,6) (1,11) (1,14) (1,10) (2,15) (2,7) (2,13) (2,5) (2,9) (2,4) (2,18) (3,17) (3,12) (3,11) (3,14) (4,15) (4,7) (4,5) (4,9) (4,8) (5,15) (5,13) (5,9) (5,8) (5,18) (6,16) (6,17) (6,12) (6,14) (6,10) (7,15) (7,13) (7,9) (7,18) (8,15) (8,9) (8,18) (9,13) (9,18) (10,16) (10,17) (10,12) (10,11) (11,16) (11,17) (11,12) (12,16) (12,17) (12,14) (13,15) (13,18) (14,16) (14,17) (15,18) (16,17)\nQ: Is there a path between node 13 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "511"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (1,8) (1,4) (1,5) (1,7) (1,2) (1,9) (1,6) (2,8) (2,4) (2,5) (2,7) (2,9) (2,6) (4,8) (4,5) (4,7) (4,9) (4,6) (5,8) (5,7) (5,9) (5,6) (6,8) (6,7) (6,9) (7,8) (7,9) (8,9)\nQ: Is there a path between node 2 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "512"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,5) (0,7) (0,6) (0,2) (0,4) (0,8) (0,9) (1,10) (2,3) (2,5) (2,7) (2,6) (2,4) (2,8) (2,9) (2,11) (3,5) (3,4) (3,8) (3,11) (4,5) (4,6) (4,9) (4,11) (5,6) (5,8) (5,9) (6,7) (6,8) (6,9) (6,11) (7,8) (7,11) (8,9) (9,11)\nQ: Is there a path between node 3 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "513"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,9) (0,4) (0,14) (0,6) (0,10) (0,12) (0,2) (1,13) (1,11) (1,3) (1,5) (1,7) (1,16) (1,8) (1,17) (2,15) (2,9) (2,4) (2,14) (2,6) (2,10) (2,12) (3,13) (3,11) (3,5) (3,7) (3,16) (3,8) (3,17) (4,15) (4,9) (4,14) (4,6) (4,10) (4,12) (5,13) (5,11) (5,7) (5,16) (5,8) (5,17) (6,15) (6,9) (6,14) (6,10) (6,12) (7,13) (7,11) (7,16) (7,8) (7,17) (8,13) (8,11) (8,16) (8,17) (9,15) (9,14) (9,10) (9,12) (10,15) (10,14) (10,12) (11,13) (11,16) (11,17) (12,15) (12,14) (13,16) (13,17) (14,15) (16,17)\nQ: Is there a path between node 10 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "514"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,4) (0,15) (0,19) (0,8) (0,17) (0,13) (0,3) (0,14) (0,5) (0,2) (0,16) (0,1) (0,10) (1,20) (1,4) (1,15) (1,19) (1,8) (1,17) (1,13) (1,3) (1,14) (1,5) (1,2) (1,16) (1,10) (2,20) (2,4) (2,15) (2,19) (2,8) (2,17) (2,13) (2,3) (2,14) (2,5) (2,16) (2,10) (3,20) (3,4) (3,15) (3,19) (3,8) (3,17) (3,13) (3,14) (3,5) (3,16) (3,10) (4,20) (4,15) (4,19) (4,8) (4,17) (4,13) (4,14) (4,5) (4,16) (4,10) (5,20) (5,15) (5,19) (5,8) (5,17) (5,13) (5,14) (5,16) (5,10) (6,12) (6,22) (6,9) (6,18) (6,21) (6,7) (6,11) (7,12) (7,22) (7,9) (7,18) (7,21) (7,11) (8,20) (8,15) (8,19) (8,17) (8,13) (8,14) (8,16) (8,10) (9,12) (9,22) (9,18) (9,21) (9,11) (10,20) (10,15) (10,19) (10,17) (10,13) (10,14) (10,16) (11,12) (11,22) (11,18) (11,21) (12,22) (12,18) (12,21) (13,20) (13,15) (13,19) (13,17) (13,14) (13,16) (14,20) (14,15) (14,19) (14,17) (14,16) (15,20) (15,19) (15,17) (15,16) (16,20) (16,19) (16,17) (17,20) (17,19) (18,22) (18,21) (19,20) (21,22)\nQ: Is there a path between node 17 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "515"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,18) (0,1) (0,8) (0,10) (0,11) (0,7) (0,4) (0,2) (0,6) (0,17) (0,14) (1,19) (1,18) (1,8) (1,10) (1,11) (1,7) (1,4) (1,2) (1,6) (1,17) (1,14) (2,19) (2,18) (2,8) (2,10) (2,11) (2,7) (2,4) (2,6) (2,17) (2,14) (3,13) (3,9) (3,15) (4,19) (4,18) (4,8) (4,10) (4,11) (4,7) (4,6) (4,17) (4,14) (5,12) (5,16) (6,19) (6,18) (6,8) (6,10) (6,11) (6,7) (6,17) (6,14) (7,19) (7,18) (7,8) (7,10) (7,11) (7,17) (7,14) (8,19) (8,18) (8,10) (8,11) (8,17) (8,14) (9,13) (9,15) (10,19) (10,18) (10,11) (10,17) (10,14) (11,19) (11,18) (11,17) (11,14) (12,16) (13,15) (14,19) (14,18) (14,17) (17,19) (17,18) (18,19)\nQ: Is there a path between node 1 and node 19?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "516"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,20) (0,13) (0,24) (0,4) (1,21) (1,3) (1,11) (1,10) (1,23) (1,8) (1,2) (1,22) (1,19) (1,18) (2,21) (2,3) (2,11) (2,10) (2,23) (2,8) (2,22) (2,19) (2,18) (3,21) (3,11) (3,10) (3,23) (3,8) (3,22) (3,19) (3,18) (4,14) (4,20) (4,13) (4,24) (5,7) (5,9) (5,12) (5,16) (5,15) (5,17) (5,6) (6,7) (6,9) (6,12) (6,16) (6,15) (6,17) (7,9) (7,12) (7,16) (7,15) (7,17) (8,21) (8,11) (8,10) (8,23) (8,22) (8,19) (8,18) (9,12) (9,16) (9,15) (9,17) (10,21) (10,11) (10,23) (10,22) (10,19) (10,18) (11,21) (11,23) (11,22) (11,19) (11,18) (12,16) (12,15) (12,17) (13,14) (13,20) (13,24) (14,20) (14,24) (15,16) (15,17) (16,17) (18,21) (18,23) (18,22) (18,19) (19,21) (19,23) (19,22) (20,24) (21,23) (21,22) (22,23)\nQ: Is there a path between node 9 and node 24?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "517"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,12) (0,2) (0,3) (1,13) (1,22) (1,7) (1,11) (1,19) (1,6) (1,8) (2,14) (2,20) (2,3) (3,14) (3,20) (4,21) (4,18) (4,5) (4,17) (4,9) (4,15) (4,10) (5,21) (5,17) (5,9) (5,15) (5,10) (6,16) (6,13) (6,22) (6,7) (6,11) (6,19) (6,8) (7,16) (7,13) (7,22) (7,8) (8,16) (8,13) (8,11) (8,19) (9,18) (9,17) (9,15) (9,10) (10,21) (10,18) (11,16) (11,13) (11,22) (11,19) (12,14) (12,20) (13,16) (13,19) (14,20) (15,21) (15,18) (15,17) (16,22) (17,21) (17,18) (19,22)\nQ: Is there a path between node 8 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "518"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,4) (1,2) (3,4)\nQ: Is there a path between node 1 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "519"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,4) (0,11) (0,13) (1,8) (1,21) (1,10) (1,7) (1,2) (2,24) (2,8) (2,9) (2,10) (2,22) (3,5) (3,11) (3,13) (4,15) (4,6) (4,16) (4,11) (5,12) (5,15) (5,19) (5,18) (5,27) (6,19) (6,11) (7,26) (7,23) (7,9) (8,23) (8,9) (8,10) (8,22) (9,25) (9,14) (10,25) (10,17) (10,23) (11,20) (11,27) (12,15) (12,16) (12,18) (14,22) (15,19) (15,27) (16,19) (17,26) (17,24) (17,28) (17,23) (17,22) (19,20) (19,27) (21,26) (21,25) (21,29) (21,22) (22,29) (23,24) (23,29) (26,28)\nQ: Is there a path between node 28 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "520"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,24) (0,1) (0,6) (0,14) (1,10) (2,25) (2,5) (2,20) (2,18) (3,22) (3,6) (3,19) (3,23) (4,9) (4,18) (5,15) (5,25) (5,17) (5,20) (6,11) (6,24) (6,14) (6,7) (6,21) (7,24) (8,25) (8,17) (8,20) (8,18) (9,25) (10,24) (10,22) (10,21) (11,22) (11,19) (11,23) (12,15) (12,16) (12,17) (13,19) (13,14) (14,22) (14,19) (15,16) (15,18) (16,17) (17,20) (18,25) (19,24) (19,22) (20,25) (21,23) (22,24) (22,23)\nQ: Is there a path between node 22 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "521"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (1,20) (2,11) (2,23) (2,14) (2,8) (3,17) (3,14) (3,16) (4,7) (4,16) (4,8) (4,24) (5,6) (5,10) (5,20) (6,20) (7,12) (7,16) (7,8) (7,24) (8,12) (8,23) (8,21) (9,18) (10,18) (10,20) (11,17) (11,19) (11,24) (12,22) (12,17) (12,14) (13,24) (14,23) (14,24) (15,17) (15,19) (15,24) (16,22) (16,19) (17,19) (17,24) (19,24) (23,24)\nQ: Is there a path between node 22 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "522"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,15) (0,25) (0,14) (0,7) (0,2) (0,9) (0,5) (1,26) (1,15) (1,25) (1,7) (1,6) (1,2) (1,20) (1,22) (2,25) (2,19) (2,14) (2,4) (3,12) (3,16) (4,15) (4,7) (4,6) (4,8) (5,26) (5,20) (5,8) (5,9) (5,22) (5,13) (6,19) (6,17) (6,7) (6,20) (6,22) (7,19) (7,17) (7,9) (8,19) (9,26) (9,14) (9,24) (11,12) (12,21) (12,18) (12,16) (13,17) (13,22) (14,26) (14,22) (15,19) (15,20) (16,21) (18,23) (19,20) (19,22) (25,26)\nQ: Is there a path between node 22 and node 13?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "523"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (1,18) (1,8) (1,4) (2,15) (2,18) (2,11) (2,23) (2,4) (3,12) (3,5) (4,23) (4,25) (5,12) (5,17) (6,22) (6,13) (7,18) (7,23) (7,8) (9,17) (10,19) (10,17) (11,15) (12,24) (14,20) (14,22) (15,18) (16,20) (16,22) (20,22) (21,22) (23,25)\nQ: Is there a path between node 8 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "524"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,6) (2,7) (2,6) (2,4) (5,7) (6,8)\nQ: Is there a path between node 0 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "525"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,23) (1,6) (1,19) (1,7) (2,17) (2,24) (2,10) (2,20) (3,22) (3,27) (4,17) (4,15) (5,19) (5,12) (5,25) (6,19) (6,7) (7,18) (7,23) (8,16) (8,13) (9,27) (9,13) (10,21) (10,15) (10,11) (11,17) (11,26) (11,24) (11,14) (12,25) (12,23) (14,17) (14,26) (15,21) (17,26) (17,21) (17,24) (20,21) (20,24) (21,26) (21,24) (23,25)\nQ: Is there a path between node 5 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "526"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,18) (1,12) (1,15) (1,7) (2,17) (2,3) (3,17) (4,12) (5,17) (5,19) (6,18) (6,10) (6,9) (6,12) (6,16) (7,18) (7,9) (7,13) (7,8) (8,14) (9,18) (9,14) (9,12) (9,13) (10,12) (10,15) (11,17) (12,16) (14,18)\nQ: Is there a path between node 9 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "527"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,18) (0,1) (0,8) (0,10) (0,11) (0,7) (0,4) (0,2) (0,6) (0,17) (0,14) (1,19) (1,18) (1,8) (1,10) (1,11) (1,7) (1,4) (1,2) (1,6) (1,17) (1,14) (2,19) (2,18) (2,8) (2,10) (2,11) (2,7) (2,4) (2,6) (2,17) (2,14) (3,13) (3,9) (3,15) (4,19) (4,18) (4,8) (4,10) (4,11) (4,7) (4,6) (4,17) (4,14) (5,12) (5,16) (6,19) (6,18) (6,8) (6,10) (6,11) (6,7) (6,17) (6,14) (7,19) (7,18) (7,8) (7,10) (7,11) (7,17) (7,14) (8,19) (8,18) (8,10) (8,11) (8,17) (8,14) (9,13) (9,15) (10,19) (10,18) (10,11) (10,17) (10,14) (11,19) (11,18) (11,17) (11,14) (12,16) (13,15) (14,19) (14,18) (14,17) (17,19) (17,18) (18,19)\nQ: Is there a path between node 2 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "528"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,10) (0,17) (0,5) (0,13) (0,15) (0,16) (0,3) (0,7) (0,11) (0,1) (0,4) (0,14) (1,12) (1,10) (1,17) (1,5) (1,13) (1,15) (1,16) (1,3) (1,7) (1,11) (1,4) (1,14) (2,8) (2,6) (3,12) (3,10) (3,17) (3,5) (3,13) (3,15) (3,16) (3,7) (3,11) (3,4) (3,14) (4,12) (4,10) (4,17) (4,5) (4,13) (4,15) (4,16) (4,7) (4,11) (4,14) (5,12) (5,10) (5,17) (5,13) (5,15) (5,16) (5,7) (5,11) (5,14) (6,8) (7,12) (7,10) (7,17) (7,13) (7,15) (7,16) (7,11) (7,14) (10,12) (10,17) (10,13) (10,15) (10,16) (10,11) (10,14) (11,12) (11,17) (11,13) (11,15) (11,16) (11,14) (12,17) (12,13) (12,15) (12,16) (12,14) (13,17) (13,15) (13,16) (13,14) (14,17) (14,15) (14,16) (15,17) (15,16) (16,17)\nQ: Is there a path between node 4 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "529"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,5) (0,1) (0,9) (0,3) (0,4) (1,6) (1,5) (1,9) (1,3) (1,4) (2,7) (2,8) (2,10) (3,6) (3,5) (3,9) (3,4) (4,6) (4,5) (4,9) (5,6) (5,9) (6,9) (7,8) (7,10) (8,10)\nQ: Is there a path between node 3 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "530"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (1,20) (2,11) (2,23) (2,14) (2,8) (3,17) (3,14) (3,16) (4,7) (4,16) (4,8) (4,24) (5,6) (5,10) (5,20) (6,20) (7,12) (7,16) (7,8) (7,24) (8,12) (8,23) (8,21) (9,18) (10,18) (10,20) (11,17) (11,19) (11,24) (12,22) (12,17) (12,14) (13,24) (14,23) (14,24) (15,17) (15,19) (15,24) (16,22) (16,19) (17,19) (17,24) (19,24) (23,24)\nQ: Is there a path between node 20 and node 23?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "531"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,14) (0,5) (0,9) (0,8) (0,6) (0,21) (1,4) (1,15) (1,18) (1,11) (1,10) (1,12) (2,20) (2,14) (2,5) (2,9) (2,22) (2,6) (2,16) (3,9) (3,23) (3,22) (3,6) (3,21) (4,15) (4,11) (4,19) (4,13) (5,20) (5,14) (5,9) (5,8) (5,6) (5,21) (6,20) (6,14) (6,9) (6,23) (6,8) (6,16) (7,18) (7,11) (7,10) (7,12) (7,19) (7,13) (8,20) (8,14) (8,23) (8,21) (9,20) (9,23) (9,22) (9,21) (10,15) (10,18) (10,11) (10,12) (10,19) (10,13) (11,15) (11,13) (12,18) (12,19) (13,18) (13,19) (14,23) (14,22) (14,21) (15,19) (16,23) (16,22) (20,21) (22,23)\nQ: Is there a path between node 7 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "532"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,17) (0,1) (0,4) (0,15) (0,2) (0,13) (0,10) (0,6) (0,18) (0,11) (0,12) (0,5) (1,19) (1,17) (1,4) (1,15) (1,2) (1,13) (1,10) (1,6) (1,18) (1,11) (1,12) (1,5) (2,19) (2,17) (2,4) (2,15) (2,13) (2,10) (2,6) (2,18) (2,11) (2,12) (2,5) (3,20) (3,16) (3,14) (3,8) (4,19) (4,17) (4,15) (4,13) (4,10) (4,6) (4,18) (4,11) (4,12) (4,5) (5,19) (5,17) (5,15) (5,13) (5,10) (5,6) (5,18) (5,11) (5,12) (6,19) (6,17) (6,15) (6,13) (6,10) (6,18) (6,11) (6,12) (7,9) (8,20) (8,16) (8,14) (10,19) (10,17) (10,15) (10,13) (10,18) (10,11) (10,12) (11,19) (11,17) (11,15) (11,13) (11,18) (11,12) (12,19) (12,17) (12,15) (12,13) (12,18) (13,19) (13,17) (13,15) (13,18) (14,20) (14,16) (15,19) (15,17) (15,18) (16,20) (17,19) (17,18) (18,19)\nQ: Is there a path between node 8 and node 16?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "533"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,3) (0,11) (0,8) (0,2) (0,12) (0,9) (0,1) (1,4) (1,3) (1,6) (1,11) (1,8) (1,7) (1,10) (1,2) (1,12) (2,3) (2,6) (2,11) (2,8) (2,9) (3,6) (3,11) (3,8) (3,7) (3,10) (3,9) (4,6) (4,11) (4,8) (4,7) (4,10) (4,12) (4,9) (6,8) (6,10) (7,10) (7,12) (7,9) (8,11) (8,10) (8,12) (9,10) (10,12)\nQ: Is there a path between node 1 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "534"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,29) (0,1) (0,9) (0,20) (0,34) (0,7) (0,19) (0,22) (0,31) (1,11) (1,30) (1,6) (1,21) (1,14) (1,28) (1,19) (1,31) (1,4) (2,3) (2,11) (2,18) (2,21) (2,20) (2,14) (2,7) (2,17) (3,11) (3,33) (3,15) (3,30) (3,18) (3,21) (3,14) (3,5) (4,10) (4,26) (4,27) (4,21) (4,34) (5,9) (5,27) (5,30) (5,6) (5,24) (5,14) (5,34) (5,28) (5,17) (6,11) (6,25) (6,10) (6,26) (6,29) (6,15) (6,16) (6,14) (6,7) (6,12) (6,22) (7,10) (7,26) (7,27) (7,18) (7,24) (7,8) (7,31) (8,11) (8,33) (8,9) (8,30) (8,24) (8,20) (8,16) (8,22) (8,17) (9,10) (9,20) (9,16) (9,14) (10,25) (10,33) (10,30) (10,18) (10,24) (10,20) (10,31) (11,15) (11,12) (11,19) (11,17) (12,25) (12,29) (12,27) (12,30) (12,34) (12,28) (12,17) (14,25) (14,33) (14,26) (14,29) (14,30) (14,21) (14,17) (15,20) (15,17) (16,21) (16,28) (16,19) (16,22) (17,27) (17,30) (17,24) (17,19) (18,26) (18,21) (18,28) (19,33) (19,27) (19,34) (19,22) (20,25) (20,26) (20,27) (20,21) (20,28) (20,31) (21,22) (22,24) (22,31) (24,34) (24,28) (25,26) (25,29) (25,27) (26,33) (26,27) (26,30) (27,30) (27,28) (28,31) (29,30) (29,34) (29,31) (30,33) (30,34) (31,33) (31,34)\nQ: Is there a path between node 34 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "535"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,14) (0,10) (0,24) (0,2) (0,12) (0,19) (0,3) (0,17) (0,25) (0,23) (0,15) (1,18) (1,11) (1,8) (2,14) (2,10) (2,24) (2,7) (2,3) (2,21) (2,25) (2,23) (2,6) (3,14) (3,24) (3,12) (3,19) (3,17) (3,25) (3,23) (3,6) (3,15) (4,18) (4,8) (5,18) (5,11) (5,8) (6,16) (6,14) (6,10) (6,12) (6,7) (6,19) (6,21) (6,25) (6,23) (6,9) (6,15) (7,16) (7,10) (7,24) (7,12) (7,19) (7,17) (7,25) (7,9) (7,15) (8,18) (8,11) (9,16) (9,14) (9,10) (9,24) (9,12) (9,19) (9,17) (9,21) (9,23) (9,15) (10,16) (10,14) (10,19) (10,21) (10,25) (10,23) (10,15) (11,18) (12,16) (12,14) (12,24) (12,19) (12,17) (12,21) (12,25) (12,23) (12,15) (13,20) (14,16) (14,24) (14,17) (14,21) (14,25) (14,23) (14,15) (15,16) (15,24) (15,23) (16,21) (16,25) (16,23) (17,21) (17,23) (19,21) (19,25) (21,24) (21,25) (21,23) (23,25) (24,25)\nQ: Is there a path between node 11 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "536"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,15) (0,22) (0,18) (1,5) (1,14) (1,21) (1,16) (1,19) (1,3) (1,17) (1,13) (1,11) (1,2) (1,20) (1,8) (1,6) (1,12) (1,9) (1,7) (2,5) (2,14) (2,21) (2,16) (2,19) (2,3) (2,17) (2,13) (2,11) (2,20) (2,8) (2,6) (2,12) (2,9) (2,7) (3,5) (3,14) (3,21) (3,16) (3,19) (3,17) (3,13) (3,11) (3,20) (3,8) (3,6) (3,12) (3,9) (3,7) (5,14) (5,21) (5,16) (5,19) (5,17) (5,13) (5,11) (5,20) (5,8) (5,6) (5,12) (5,9) (5,7) (6,14) (6,21) (6,16) (6,19) (6,17) (6,13) (6,11) (6,20) (6,8) (6,12) (6,9) (6,7) (7,14) (7,21) (7,16) (7,19) (7,17) (7,13) (7,11) (7,20) (7,8) (7,12) (7,9) (8,14) (8,21) (8,16) (8,19) (8,17) (8,13) (8,11) (8,20) (8,12) (8,9) (9,14) (9,21) (9,16) (9,19) (9,17) (9,13) (9,11) (9,20) (9,12) (10,15) (10,22) (10,18) (11,14) (11,21) (11,16) (11,19) (11,17) (11,13) (11,20) (11,12) (12,14) (12,21) (12,16) (12,19) (12,17) (12,13) (12,20) (13,14) (13,21) (13,16) (13,19) (13,17) (13,20) (14,21) (14,16) (14,19) (14,17) (14,20) (15,22) (15,18) (16,21) (16,19) (16,17) (16,20) (17,21) (17,19) (17,20) (18,22) (19,21) (19,20) (20,21)\nQ: Is there a path between node 13 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "537"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,21) (0,11) (0,15) (0,4) (0,22) (0,5) (0,3) (0,6) (0,20) (0,13) (0,18) (0,9) (0,1) (0,12) (0,24) (0,16) (0,8) (0,23) (0,2) (1,21) (1,11) (1,15) (1,4) (1,22) (1,5) (1,3) (1,6) (1,20) (1,13) (1,18) (1,9) (1,12) (1,24) (1,16) (1,8) (1,23) (1,2) (2,21) (2,11) (2,15) (2,4) (2,22) (2,5) (2,3) (2,6) (2,20) (2,13) (2,18) (2,9) (2,12) (2,24) (2,16) (2,8) (2,23) (3,21) (3,11) (3,15) (3,4) (3,22) (3,5) (3,6) (3,20) (3,13) (3,18) (3,9) (3,12) (3,24) (3,16) (3,8) (3,23) (4,21) (4,11) (4,15) (4,22) (4,5) (4,6) (4,20) (4,13) (4,18) (4,9) (4,12) (4,24) (4,16) (4,8) (4,23) (5,21) (5,11) (5,15) (5,22) (5,6) (5,20) (5,13) (5,18) (5,9) (5,12) (5,24) (5,16) (5,8) (5,23) (6,21) (6,11) (6,15) (6,22) (6,20) (6,13) (6,18) (6,9) (6,12) (6,24) (6,16) (6,8) (6,23) (7,10) (7,14) (7,17) (7,19) (8,21) (8,11) (8,15) (8,22) (8,20) (8,13) (8,18) (8,9) (8,12) (8,24) (8,16) (8,23) (9,21) (9,11) (9,15) (9,22) (9,20) (9,13) (9,18) (9,12) (9,24) (9,16) (9,23) (10,14) (10,17) (10,19) (11,21) (11,15) (11,22) (11,20) (11,13) (11,18) (11,12) (11,24) (11,16) (11,23) (12,21) (12,15) (12,22) (12,20) (12,13) (12,18) (12,24) (12,16) (12,23) (13,21) (13,15) (13,22) (13,20) (13,18) (13,24) (13,16) (13,23) (14,17) (14,19) (15,21) (15,22) (15,20) (15,18) (15,24) (15,16) (15,23) (16,21) (16,22) (16,20) (16,18) (16,24) (16,23) (17,19) (18,21) (18,22) (18,20) (18,24) (18,23) (20,21) (20,22) (20,24) (20,23) (21,22) (21,24) (21,23) (22,24) (22,23) (23,24)\nQ: Is there a path between node 8 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "538"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,8) (0,2) (0,20) (0,16) (0,14) (0,15) (0,7) (1,18) (1,24) (1,22) (1,5) (1,19) (1,11) (1,17) (2,6) (2,4) (2,23) (2,8) (2,20) (2,16) (2,21) (2,14) (2,15) (2,10) (3,6) (3,4) (3,23) (3,8) (3,16) (3,14) (3,25) (3,15) (3,7) (4,6) (4,23) (4,8) (4,20) (4,16) (4,21) (4,14) (4,15) (4,10) (4,7) (5,18) (5,24) (5,22) (5,13) (5,9) (5,11) (5,12) (6,23) (6,8) (6,20) (6,16) (6,14) (6,25) (6,15) (7,23) (7,20) (7,16) (7,21) (7,14) (7,25) (7,15) (7,10) (8,20) (8,16) (8,14) (8,25) (8,15) (9,18) (9,24) (9,22) (9,19) (9,11) (9,17) (9,12) (10,23) (10,20) (10,16) (10,21) (10,14) (10,25) (11,22) (11,19) (11,17) (11,12) (12,18) (12,13) (12,19) (13,18) (13,24) (13,22) (13,17) (14,23) (14,20) (14,16) (14,25) (15,20) (15,16) (15,21) (15,25) (16,23) (16,20) (16,25) (17,18) (17,22) (17,19) (18,24) (18,22) (18,19) (19,24) (19,22) (20,21) (20,25) (21,23) (21,25) (22,24) (23,25)\nQ: Is there a path between node 13 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "539"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,17) (1,4) (2,10) (3,19) (3,30) (3,13) (3,25) (3,8) (4,31) (5,16) (6,29) (6,11) (6,32) (7,14) (7,17) (8,21) (8,30) (8,13) (8,28) (9,20) (9,25) (11,29) (11,26) (11,22) (13,21) (13,15) (13,28) (13,23) (15,31) (15,16) (15,28) (15,23) (16,21) (16,25) (16,23) (18,29) (18,24) (20,31) (20,30) (20,25) (21,25) (22,24) (23,25) (23,28) (24,29) (24,32) (25,30) (26,32) (28,30)\nQ: Is there a path between node 4 and node 27?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "540"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,5) (0,11) (0,8) (0,6) (0,1) (1,10) (1,3) (1,5) (1,9) (1,6) (1,2) (2,10) (2,3) (2,5) (2,9) (2,8) (2,7) (2,6) (2,13) (3,9) (3,11) (3,8) (3,7) (4,12) (5,10) (5,9) (5,8) (5,7) (5,6) (6,10) (6,9) (6,11) (6,8) (7,10) (7,11) (7,8) (7,13) (8,10) (8,11) (8,13) (9,10) (9,11) (9,13) (10,11) (10,13)\nQ: Is there a path between node 6 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "541"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (3,7) (4,6) (5,6)\nQ: Is there a path between node 2 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "542"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,21) (0,7) (0,6) (0,3) (0,17) (0,20) (0,22) (0,16) (0,23) (0,25) (0,27) (1,5) (1,21) (1,4) (1,7) (1,15) (1,18) (1,2) (1,24) (1,20) (1,11) (1,16) (1,25) (1,27) (2,14) (2,5) (2,21) (2,4) (2,15) (2,24) (2,22) (2,11) (2,23) (2,25) (2,27) (3,14) (3,13) (3,21) (3,7) (3,15) (3,6) (3,17) (3,24) (3,22) (3,11) (3,16) (3,23) (4,14) (4,13) (4,5) (4,19) (4,7) (4,18) (4,17) (4,22) (4,11) (4,23) (4,25) (4,27) (5,13) (5,19) (5,15) (5,18) (5,24) (5,20) (5,22) (5,11) (5,23) (5,27) (6,14) (6,21) (6,19) (6,7) (6,15) (6,18) (6,17) (6,24) (6,20) (6,11) (6,16) (6,25) (6,27) (7,14) (7,13) (7,21) (7,19) (7,15) (7,18) (7,17) (7,20) (7,22) (7,11) (7,23) (7,27) (8,30) (8,28) (9,31) (9,10) (9,26) (9,29) (10,31) (10,26) (10,29) (11,13) (11,21) (11,19) (11,15) (11,24) (11,22) (11,25) (11,27) (12,28) (13,14) (13,21) (13,15) (13,18) (13,17) (13,24) (13,20) (13,16) (13,23) (13,25) (13,27) (14,21) (14,19) (14,24) (14,20) (14,22) (14,16) (14,23) (14,25) (15,21) (15,18) (15,17) (15,24) (15,20) (15,22) (15,16) (15,25) (15,27) (16,21) (16,18) (16,17) (16,24) (16,20) (16,22) (16,25) (17,21) (17,19) (17,18) (17,24) (17,20) (17,22) (17,23) (17,25) (17,27) (18,21) (18,24) (18,20) (18,25) (18,27) (19,21) (19,20) (19,22) (19,27) (20,21) (20,24) (20,22) (20,23) (20,27) (21,24) (21,22) (21,25) (21,27) (22,25) (23,25) (23,27) (25,27) (26,31) (26,29) (29,31)\nQ: Is there a path between node 15 and node 31?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "543"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,13) (0,12) (0,14) (0,8) (0,3) (0,6) (0,2) (0,9) (0,5) (1,10) (1,7) (1,11) (2,4) (2,13) (2,12) (2,14) (2,8) (2,3) (2,6) (2,9) (2,5) (3,4) (3,13) (3,12) (3,14) (3,8) (3,6) (3,9) (3,5) (4,13) (4,12) (4,14) (4,8) (4,6) (4,9) (4,5) (5,13) (5,12) (5,14) (5,8) (5,6) (5,9) (6,13) (6,12) (6,14) (6,8) (6,9) (7,10) (7,11) (8,13) (8,12) (8,14) (8,9) (9,13) (9,12) (9,14) (10,11) (12,13) (12,14) (13,14)\nQ: Is there a path between node 14 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "544"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,5) (0,1) (0,9) (0,3) (0,4) (1,6) (1,5) (1,9) (1,3) (1,4) (2,7) (2,8) (2,10) (3,6) (3,5) (3,9) (3,4) (4,6) (4,5) (4,9) (5,6) (5,9) (6,9) (7,8) (7,10) (8,10)\nQ: Is there a path between node 8 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "545"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,27) (0,23) (0,4) (0,20) (0,17) (0,6) (1,5) (1,22) (1,11) (1,19) (1,24) (1,2) (1,15) (1,8) (1,30) (1,9) (1,28) (1,18) (2,5) (2,22) (2,24) (2,15) (2,8) (2,30) (2,9) (2,28) (2,18) (3,26) (3,13) (4,21) (4,29) (4,23) (4,20) (4,17) (4,6) (5,22) (5,19) (5,24) (5,14) (5,30) (5,28) (5,18) (6,21) (6,29) (6,27) (6,23) (6,20) (6,17) (7,26) (7,10) (7,13) (7,16) (7,12) (8,11) (8,24) (8,14) (8,30) (8,9) (8,28) (8,18) (9,22) (9,11) (9,19) (9,15) (9,28) (10,16) (10,12) (11,15) (11,30) (11,28) (11,18) (12,13) (12,16) (13,26) (13,16) (13,25) (14,22) (14,19) (14,15) (14,30) (15,19) (15,30) (15,28) (15,18) (16,26) (16,25) (17,29) (17,23) (18,19) (18,24) (18,28) (19,30) (19,28) (20,21) (20,27) (21,29) (21,27) (21,23) (22,24) (22,28) (23,27) (24,30) (24,28) (25,26) (28,30)\nQ: Is there a path between node 19 and node 26?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "546"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,11) (0,1) (0,3) (0,10) (0,4) (1,11) (1,3) (1,10) (1,4) (2,7) (3,11) (3,4) (4,5) (4,11) (5,11) (6,9) (6,8) (7,9) (7,8) (8,9) (10,11)\nQ: Is there a path between node 10 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "547"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,4) (0,1) (0,11) (0,9) (0,12) (1,2) (1,4) (1,11) (1,9) (1,13) (1,8) (1,12) (2,6) (2,3) (2,4) (2,11) (2,9) (2,13) (2,8) (3,6) (3,9) (3,13) (3,8) (3,12) (4,6) (4,11) (4,9) (4,13) (4,8) (4,12) (5,7) (5,10) (6,11) (6,9) (6,8) (6,12) (8,9) (8,12) (9,11) (9,12) (11,13) (12,13)\nQ: Is there a path between node 4 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "548"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,24) (0,2) (0,7) (0,15) (0,14) (0,22) (0,10) (0,18) (0,5) (0,9) (0,4) (0,11) (0,8) (0,20) (0,13) (1,2) (1,7) (1,15) (1,14) (1,18) (1,5) (1,16) (1,9) (1,4) (1,11) (1,8) (1,13) (2,24) (2,7) (2,15) (2,14) (2,22) (2,18) (2,16) (2,9) (2,4) (2,11) (2,8) (2,20) (2,23) (3,21) (4,7) (4,14) (4,22) (4,18) (4,16) (4,13) (4,23) (5,24) (5,7) (5,15) (5,14) (5,22) (5,10) (5,18) (5,20) (5,23) (6,12) (7,24) (7,15) (7,14) (7,10) (7,18) (7,16) (7,9) (7,11) (7,8) (7,20) (7,13) (7,23) (8,24) (8,14) (8,10) (8,18) (8,9) (8,13) (8,23) (9,24) (9,15) (9,14) (9,22) (9,10) (9,16) (9,20) (9,23) (10,24) (10,15) (10,14) (10,22) (10,18) (10,16) (10,20) (11,15) (11,14) (11,18) (11,16) (11,20) (11,13) (11,23) (13,24) (13,15) (13,18) (13,16) (13,23) (14,24) (14,15) (14,22) (14,18) (14,16) (14,23) (15,24) (15,22) (15,18) (15,16) (15,20) (15,23) (16,24) (16,20) (16,23) (18,22) (18,20) (18,23) (19,21) (20,22) (22,24) (22,23) (23,24)\nQ: Is there a path between node 19 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "549"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,18) (0,1) (0,8) (0,10) (0,11) (0,7) (0,4) (0,2) (0,6) (0,17) (0,14) (1,19) (1,18) (1,8) (1,10) (1,11) (1,7) (1,4) (1,2) (1,6) (1,17) (1,14) (2,19) (2,18) (2,8) (2,10) (2,11) (2,7) (2,4) (2,6) (2,17) (2,14) (3,13) (3,9) (3,15) (4,19) (4,18) (4,8) (4,10) (4,11) (4,7) (4,6) (4,17) (4,14) (5,12) (5,16) (6,19) (6,18) (6,8) (6,10) (6,11) (6,7) (6,17) (6,14) (7,19) (7,18) (7,8) (7,10) (7,11) (7,17) (7,14) (8,19) (8,18) (8,10) (8,11) (8,17) (8,14) (9,13) (9,15) (10,19) (10,18) (10,11) (10,17) (10,14) (11,19) (11,18) (11,17) (11,14) (12,16) (13,15) (14,19) (14,18) (14,17) (17,19) (17,18) (18,19)\nQ: Is there a path between node 11 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "550"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,7) (0,4) (0,10) (0,5) (0,13) (0,12) (0,1) (0,2) (0,3) (0,15) (0,6) (0,8) (0,14) (1,11) (1,7) (1,4) (1,10) (1,5) (1,13) (1,12) (1,2) (1,3) (1,15) (1,6) (1,8) (1,14) (2,11) (2,7) (2,4) (2,10) (2,5) (2,13) (2,12) (2,3) (2,15) (2,6) (2,8) (2,14) (3,11) (3,7) (3,4) (3,10) (3,5) (3,13) (3,12) (3,15) (3,6) (3,8) (3,14) (4,11) (4,7) (4,10) (4,5) (4,13) (4,12) (4,15) (4,6) (4,8) (4,14) (5,11) (5,7) (5,10) (5,13) (5,12) (5,15) (5,6) (5,8) (5,14) (6,11) (6,7) (6,10) (6,13) (6,12) (6,15) (6,8) (6,14) (7,11) (7,10) (7,13) (7,12) (7,15) (7,8) (7,14) (8,11) (8,10) (8,13) (8,12) (8,15) (8,14) (10,11) (10,13) (10,12) (10,15) (10,14) (11,13) (11,12) (11,15) (11,14) (12,13) (12,15) (12,14) (13,15) (13,14) (14,15)\nQ: Is there a path between node 5 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "551"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,11) (0,2) (0,7) (0,8) (0,16) (0,15) (1,11) (1,2) (1,7) (1,8) (1,16) (1,15) (1,14) (2,4) (2,11) (2,5) (2,7) (2,12) (2,16) (2,15) (3,13) (3,10) (4,6) (4,5) (4,7) (4,8) (4,12) (4,16) (4,15) (4,14) (5,6) (5,7) (5,8) (5,12) (5,16) (5,14) (6,11) (6,7) (6,8) (6,12) (6,16) (6,15) (6,14) (7,11) (7,8) (7,16) (7,14) (8,11) (8,12) (8,16) (11,12) (11,16) (11,15) (11,14) (12,14) (14,16) (14,15)\nQ: Is there a path between node 16 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "552"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,17) (0,1) (0,4) (0,15) (0,2) (0,13) (0,10) (0,6) (0,18) (0,11) (0,12) (0,5) (1,19) (1,17) (1,4) (1,15) (1,2) (1,13) (1,10) (1,6) (1,18) (1,11) (1,12) (1,5) (2,19) (2,17) (2,4) (2,15) (2,13) (2,10) (2,6) (2,18) (2,11) (2,12) (2,5) (3,20) (3,16) (3,14) (3,8) (4,19) (4,17) (4,15) (4,13) (4,10) (4,6) (4,18) (4,11) (4,12) (4,5) (5,19) (5,17) (5,15) (5,13) (5,10) (5,6) (5,18) (5,11) (5,12) (6,19) (6,17) (6,15) (6,13) (6,10) (6,18) (6,11) (6,12) (7,9) (8,20) (8,16) (8,14) (10,19) (10,17) (10,15) (10,13) (10,18) (10,11) (10,12) (11,19) (11,17) (11,15) (11,13) (11,18) (11,12) (12,19) (12,17) (12,15) (12,13) (12,18) (13,19) (13,17) (13,15) (13,18) (14,20) (14,16) (15,19) (15,17) (15,18) (16,20) (17,19) (17,18) (18,19)\nQ: Is there a path between node 3 and node 16?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "553"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,6) (0,1) (0,7) (0,4) (1,5) (1,6) (1,7) (1,4) (2,3) (4,5) (4,6) (4,7) (5,6) (5,7) (6,7)\nQ: Is there a path between node 1 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "554"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,4) (0,1) (1,2) (1,5) (1,4) (2,5) (2,4) (4,5)\nQ: Is there a path between node 4 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "555"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,2) (0,4) (0,5) (0,15) (0,7) (1,9) (1,13) (1,12) (1,3) (2,14) (2,10) (2,4) (2,8) (2,15) (2,7) (3,9) (3,13) (3,12) (3,11) (4,14) (4,6) (4,10) (4,8) (4,15) (5,6) (5,8) (5,7) (6,14) (6,8) (6,15) (7,14) (7,10) (7,8) (7,15) (8,14) (8,10) (8,15) (9,13) (9,12) (9,11) (10,14) (10,15) (11,13) (11,12) (12,13) (14,15)\nQ: Is there a path between node 9 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "556"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,18) (0,24) (0,5) (0,12) (0,26) (0,14) (0,16) (0,21) (0,9) (0,1) (0,28) (0,25) (1,3) (1,18) (1,24) (1,5) (1,12) (1,26) (1,14) (1,16) (1,21) (1,2) (1,23) (1,20) (1,28) (1,25) (2,3) (2,18) (2,10) (2,24) (2,5) (2,12) (2,26) (2,14) (2,16) (2,9) (2,23) (2,20) (2,28) (2,7) (2,25) (2,22) (2,13) (3,18) (3,24) (3,12) (3,26) (3,16) (3,9) (3,19) (3,7) (3,25) (3,22) (4,11) (4,27) (4,17) (4,15) (4,8) (5,18) (5,24) (5,12) (5,26) (5,14) (5,16) (5,21) (5,9) (5,23) (5,19) (5,20) (5,7) (5,13) (6,11) (6,27) (6,29) (6,15) (6,8) (7,18) (7,10) (7,12) (7,26) (7,14) (7,16) (7,21) (7,9) (7,20) (7,25) (7,22) (7,13) (8,11) (8,27) (8,29) (8,17) (8,15) (9,18) (9,10) (9,24) (9,16) (9,21) (9,19) (9,20) (9,28) (9,25) (9,13) (10,18) (10,24) (10,12) (10,26) (10,14) (10,16) (10,23) (10,20) (10,28) (10,25) (10,22) (10,13) (11,27) (11,29) (12,18) (12,24) (12,16) (12,21) (12,23) (12,20) (12,28) (12,22) (12,13) (13,18) (13,24) (13,26) (13,14) (13,16) (13,21) (13,23) (13,20) (13,28) (13,25) (13,22) (14,26) (14,16) (14,21) (14,23) (14,19) (14,20) (14,28) (14,25) (15,27) (15,17) (16,18) (16,24) (16,26) (16,20) (16,25) (16,22) (17,29) (18,24) (18,26) (18,23) (18,19) (18,20) (18,25) (18,22) (19,21) (19,23) (19,28) (19,25) (20,26) (20,23) (20,28) (20,25) (20,22) (21,26) (21,23) (21,28) (21,22) (22,26) (22,23) (22,25) (23,24) (23,26) (24,26) (24,28) (25,26)\nQ: Is there a path between node 3 and node 28?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "557"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,2) (0,1) (0,4) (1,3) (1,2) (1,4) (1,6) (2,3) (2,4) (2,5) (3,4) (3,6) (4,6) (5,6)\nQ: Is there a path between node 7 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "558"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,13) (0,2) (0,14) (0,23) (0,8) (0,1) (0,25) (0,27) (0,10) (1,29) (1,13) (1,19) (1,28) (1,23) (1,30) (1,25) (1,24) (2,12) (2,5) (2,14) (2,17) (2,23) (3,7) (3,12) (3,19) (3,23) (3,8) (3,30) (3,25) (3,24) (4,33) (5,20) (5,23) (5,30) (6,15) (6,11) (7,32) (7,17) (7,23) (7,8) (7,10) (8,29) (8,12) (8,32) (8,20) (8,19) (8,17) (8,30) (9,29) (9,28) (9,30) (9,24) (10,13) (10,20) (10,14) (10,22) (11,31) (12,13) (12,23) (12,27) (12,26) (13,29) (13,32) (13,14) (13,28) (13,30) (13,24) (14,17) (14,30) (14,22) (14,27) (15,16) (15,31) (15,33) (17,32) (17,20) (17,19) (17,27) (17,24) (17,26) (18,21) (20,28) (20,30) (20,25) (21,31) (22,32) (22,28) (22,30) (23,28) (23,25) (23,27) (24,29) (24,28) (24,26) (25,32) (26,29) (26,27) (27,32) (27,30) (28,32) (28,30)\nQ: Is there a path between node 11 and node 18?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "559"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,27) (0,13) (0,10) (0,15) (0,2) (0,17) (1,5) (1,22) (1,8) (1,19) (1,26) (1,24) (1,18) (1,16) (1,14) (1,12) (1,4) (1,9) (2,7) (2,27) (2,13) (2,3) (2,6) (2,10) (2,11) (2,17) (3,7) (3,27) (3,20) (3,6) (3,10) (3,15) (3,21) (3,17) (4,5) (4,8) (4,19) (4,26) (4,25) (4,18) (4,14) (4,12) (5,8) (5,26) (5,18) (5,16) (5,14) (5,12) (6,7) (6,13) (6,10) (6,21) (7,20) (7,13) (7,10) (7,15) (7,11) (8,19) (8,26) (8,18) (8,16) (8,14) (8,9) (9,22) (9,19) (9,26) (9,25) (9,16) (9,14) (9,12) (10,13) (10,21) (10,17) (11,27) (11,13) (11,15) (11,21) (11,17) (12,22) (12,19) (12,26) (12,24) (12,25) (12,16) (12,14) (13,27) (13,15) (14,22) (14,19) (14,26) (15,27) (15,20) (15,21) (15,17) (16,22) (16,19) (16,24) (16,25) (16,18) (17,27) (17,20) (17,21) (18,22) (18,19) (18,26) (18,24) (19,26) (19,25) (20,27) (20,21) (21,27) (22,26) (22,24) (24,26)\nQ: Is there a path between node 15 and node 28?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "560"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,15) (1,3) (1,20) (2,11) (3,12) (3,6) (3,16) (3,20) (5,14) (5,7) (6,20) (6,21) (7,13) (7,18) (8,14) (8,13) (9,12) (9,16) (9,21) (10,21) (11,17) (12,16) (14,18) (15,16) (15,21) (16,20) (20,21)\nQ: Is there a path between node 11 and node 19?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "561"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,18) (0,1) (0,8) (0,10) (0,11) (0,7) (0,4) (0,2) (0,6) (0,17) (0,14) (1,19) (1,18) (1,8) (1,10) (1,11) (1,7) (1,4) (1,2) (1,6) (1,17) (1,14) (2,19) (2,18) (2,8) (2,10) (2,11) (2,7) (2,4) (2,6) (2,17) (2,14) (3,13) (3,9) (3,15) (4,19) (4,18) (4,8) (4,10) (4,11) (4,7) (4,6) (4,17) (4,14) (5,12) (5,16) (6,19) (6,18) (6,8) (6,10) (6,11) (6,7) (6,17) (6,14) (7,19) (7,18) (7,8) (7,10) (7,11) (7,17) (7,14) (8,19) (8,18) (8,10) (8,11) (8,17) (8,14) (9,13) (9,15) (10,19) (10,18) (10,11) (10,17) (10,14) (11,19) (11,18) (11,17) (11,14) (12,16) (13,15) (14,19) (14,18) (14,17) (17,19) (17,18) (18,19)\nQ: Is there a path between node 12 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "562"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,13) (0,11) (0,21) (0,8) (0,18) (0,3) (0,7) (0,15) (0,20) (0,17) (0,10) (0,22) (0,1) (0,9) (0,6) (0,19) (1,23) (1,14) (1,5) (1,13) (1,11) (1,12) (1,21) (1,8) (1,18) (1,3) (1,25) (1,7) (1,28) (1,15) (1,20) (1,17) (1,10) (1,22) (1,9) (1,6) (1,16) (1,19) (3,27) (3,14) (3,5) (3,13) (3,4) (3,21) (3,18) (3,25) (3,28) (3,15) (3,20) (3,17) (3,22) (3,6) (3,16) (3,19) (4,27) (4,23) (4,5) (4,13) (4,11) (4,12) (4,8) (4,28) (4,15) (4,20) (4,17) (4,10) (4,24) (4,6) (5,27) (5,23) (5,14) (5,13) (5,11) (5,12) (5,21) (5,8) (5,18) (5,25) (5,7) (5,15) (5,10) (5,22) (5,24) (5,9) (5,6) (5,16) (5,19) (6,27) (6,14) (6,11) (6,12) (6,18) (6,25) (6,7) (6,20) (6,17) (6,10) (6,22) (6,24) (6,9) (6,16) (6,19) (7,23) (7,14) (7,13) (7,12) (7,21) (7,8) (7,25) (7,28) (7,20) (7,10) (7,22) (7,16) (7,19) (8,27) (8,13) (8,18) (8,25) (8,15) (8,17) (8,10) (8,22) (8,24) (8,9) (8,16) (8,19) (9,27) (9,23) (9,11) (9,21) (9,25) (9,28) (9,15) (9,20) (9,17) (9,10) (9,22) (9,24) (9,16) (9,19) (10,27) (10,14) (10,11) (10,12) (10,25) (10,28) (10,15) (10,20) (10,17) (10,24) (10,16) (10,19) (11,23) (11,21) (11,18) (11,25) (11,28) (11,15) (11,17) (11,22) (11,24) (11,19) (12,27) (12,23) (12,13) (12,21) (12,18) (12,25) (12,28) (12,15) (12,17) (12,22) (12,24) (12,16) (13,27) (13,14) (13,21) (13,18) (13,28) (13,15) (13,17) (13,24) (13,16) (13,19) (14,27) (14,25) (14,28) (14,15) (14,17) (14,22) (14,24) (14,16) (15,23) (15,21) (15,18) (15,25) (15,20) (15,24) (16,27) (16,23) (16,17) (16,24) (16,19) (17,27) (17,23) (17,18) (17,25) (17,28) (17,20) (17,22) (17,24) (17,19) (18,23) (18,21) (18,25) (18,28) (18,20) (18,22) (18,24) (18,19) (19,27) (19,23) (19,21) (19,25) (19,24) (20,27) (20,23) (20,21) (20,25) (20,24) (21,23) (21,22) (23,27) (23,24) (25,27) (25,28) (27,28)\nQ: Is there a path between node 23 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "563"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,2) (0,4) (0,5) (0,15) (0,7) (1,9) (1,13) (1,12) (1,3) (2,14) (2,10) (2,4) (2,8) (2,15) (2,7) (3,9) (3,13) (3,12) (3,11) (4,14) (4,6) (4,10) (4,8) (4,15) (5,6) (5,8) (5,7) (6,14) (6,8) (6,15) (7,14) (7,10) (7,8) (7,15) (8,14) (8,10) (8,15) (9,13) (9,12) (9,11) (10,14) (10,15) (11,13) (11,12) (12,13) (14,15)\nQ: Is there a path between node 6 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "564"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,5) (0,20) (0,7) (0,19) (0,1) (0,14) (0,12) (0,15) (0,18) (0,4) (1,10) (1,5) (1,7) (1,2) (1,14) (1,12) (1,3) (1,15) (1,16) (1,4) (2,10) (2,5) (2,20) (2,7) (2,19) (2,14) (2,12) (2,15) (2,16) (2,17) (2,18) (2,4) (3,5) (3,20) (3,7) (3,19) (3,14) (3,16) (3,17) (3,18) (4,10) (4,5) (4,20) (4,7) (4,19) (4,14) (4,12) (4,15) (4,16) (4,17) (5,20) (5,7) (5,19) (5,14) (5,12) (5,16) (5,17) (5,18) (6,11) (6,8) (7,10) (7,19) (7,14) (7,12) (7,15) (7,16) (7,17) (7,18) (8,11) (9,21) (9,13) (10,19) (10,14) (10,12) (10,16) (10,18) (12,20) (12,19) (12,14) (12,15) (12,16) (12,17) (14,20) (14,19) (14,15) (14,16) (14,17) (15,20) (15,19) (15,16) (15,17) (15,18) (16,20) (16,19) (16,17) (16,18) (17,20) (17,19) (17,18) (18,19) (19,20)\nQ: Is there a path between node 18 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "565"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,1) (0,14) (0,18) (1,17) (1,14) (1,18) (2,19) (2,7) (2,10) (2,3) (2,12) (2,16) (2,11) (2,5) (2,9) (2,15) (2,6) (2,20) (2,8) (2,4) (2,13) (3,19) (3,7) (3,10) (3,12) (3,16) (3,11) (3,5) (3,9) (3,15) (3,6) (3,20) (3,8) (3,4) (3,13) (4,19) (4,7) (4,10) (4,12) (4,16) (4,11) (4,5) (4,9) (4,15) (4,6) (4,20) (4,8) (4,13) (5,19) (5,7) (5,10) (5,12) (5,16) (5,11) (5,9) (5,15) (5,6) (5,20) (5,8) (5,13) (6,19) (6,7) (6,10) (6,12) (6,16) (6,11) (6,9) (6,15) (6,20) (6,8) (6,13) (7,19) (7,10) (7,12) (7,16) (7,11) (7,9) (7,15) (7,20) (7,8) (7,13) (8,19) (8,10) (8,12) (8,16) (8,11) (8,9) (8,15) (8,20) (8,13) (9,19) (9,10) (9,12) (9,16) (9,11) (9,15) (9,20) (9,13) (10,19) (10,12) (10,16) (10,11) (10,15) (10,20) (10,13) (11,19) (11,12) (11,16) (11,15) (11,20) (11,13) (12,19) (12,16) (12,15) (12,20) (12,13) (13,19) (13,16) (13,15) (13,20) (14,17) (14,18) (15,19) (15,16) (15,20) (16,19) (16,20) (17,18) (19,20)\nQ: Is there a path between node 8 and node 16?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "566"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,19) (0,17) (0,3) (0,10) (0,14) (1,7) (1,8) (1,15) (1,13) (2,9) (2,12) (2,18) (2,4) (3,6) (3,19) (3,17) (3,16) (3,10) (3,14) (4,12) (4,18) (5,9) (5,18) (6,19) (6,17) (6,16) (6,14) (6,20) (7,8) (7,15) (7,13) (9,12) (9,18) (10,16) (10,14) (10,20) (11,15) (12,18) (13,15) (14,19) (14,17) (14,20) (16,19) (16,17) (17,20) (19,20)\nQ: Is there a path between node 10 and node 20?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "567"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,25) (0,13) (0,3) (0,1) (1,11) (1,25) (1,13) (1,2) (1,3) (1,8) (2,21) (2,22) (2,25) (2,13) (2,3) (3,18) (3,22) (3,11) (3,13) (4,23) (4,14) (4,6) (4,12) (4,27) (4,15) (4,5) (4,16) (4,26) (4,20) (4,7) (4,19) (5,14) (5,6) (5,12) (5,27) (5,15) (5,16) (5,9) (5,20) (5,7) (6,23) (6,14) (6,12) (6,24) (6,15) (6,16) (6,9) (6,17) (6,26) (6,20) (6,7) (6,19) (7,23) (7,14) (7,12) (7,24) (7,10) (7,16) (7,9) (7,17) (7,26) (7,20) (7,19) (8,21) (8,18) (8,22) (8,11) (8,25) (8,13) (9,23) (9,12) (9,10) (9,16) (9,17) (9,26) (9,20) (10,23) (10,14) (10,12) (10,24) (10,27) (10,16) (10,17) (10,26) (10,19) (11,21) (11,22) (11,25) (11,13) (12,23) (12,14) (12,24) (12,27) (12,16) (12,26) (12,20) (12,19) (13,22) (13,25) (14,23) (14,24) (14,16) (14,26) (14,19) (15,24) (15,27) (15,16) (15,26) (16,23) (16,27) (16,17) (16,26) (16,20) (17,27) (17,26) (17,20) (17,19) (18,22) (19,23) (19,24) (19,27) (19,26) (19,20) (20,23) (20,26) (21,22) (21,25) (22,25) (23,24) (23,27) (24,27) (24,26) (26,27)\nQ: Is there a path between node 21 and node 15?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "568"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,9) (0,14) (0,18) (0,3) (0,1) (0,17) (0,4) (0,8) (0,7) (0,15) (0,11) (0,10) (0,13) (1,5) (1,9) (1,14) (1,18) (1,3) (1,17) (1,4) (1,8) (1,7) (1,15) (1,11) (1,10) (1,13) (3,5) (3,9) (3,14) (3,18) (3,17) (3,4) (3,8) (3,7) (3,15) (3,11) (3,10) (3,13) (4,5) (4,9) (4,14) (4,18) (4,17) (4,8) (4,7) (4,15) (4,11) (4,10) (4,13) (5,9) (5,14) (5,18) (5,17) (5,8) (5,7) (5,15) (5,11) (5,10) (5,13) (6,12) (6,16) (7,9) (7,14) (7,18) (7,17) (7,8) (7,15) (7,11) (7,10) (7,13) (8,9) (8,14) (8,18) (8,17) (8,15) (8,11) (8,10) (8,13) (9,14) (9,18) (9,17) (9,15) (9,11) (9,10) (9,13) (10,14) (10,18) (10,17) (10,15) (10,11) (10,13) (11,14) (11,18) (11,17) (11,15) (11,13) (12,16) (13,14) (13,18) (13,17) (13,15) (14,18) (14,17) (14,15) (15,18) (15,17) (17,18)\nQ: Is there a path between node 10 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "569"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,14) (0,10) (0,24) (0,2) (0,12) (0,19) (0,3) (0,17) (0,25) (0,23) (0,15) (1,18) (1,11) (1,8) (2,14) (2,10) (2,24) (2,7) (2,3) (2,21) (2,25) (2,23) (2,6) (3,14) (3,24) (3,12) (3,19) (3,17) (3,25) (3,23) (3,6) (3,15) (4,18) (4,8) (5,18) (5,11) (5,8) (6,16) (6,14) (6,10) (6,12) (6,7) (6,19) (6,21) (6,25) (6,23) (6,9) (6,15) (7,16) (7,10) (7,24) (7,12) (7,19) (7,17) (7,25) (7,9) (7,15) (8,18) (8,11) (9,16) (9,14) (9,10) (9,24) (9,12) (9,19) (9,17) (9,21) (9,23) (9,15) (10,16) (10,14) (10,19) (10,21) (10,25) (10,23) (10,15) (11,18) (12,16) (12,14) (12,24) (12,19) (12,17) (12,21) (12,25) (12,23) (12,15) (13,20) (14,16) (14,24) (14,17) (14,21) (14,25) (14,23) (14,15) (15,16) (15,24) (15,23) (16,21) (16,25) (16,23) (17,21) (17,23) (19,21) (19,25) (21,24) (21,25) (21,23) (23,25) (24,25)\nQ: Is there a path between node 2 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "570"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,18) (0,19) (0,20) (0,23) (0,9) (0,10) (0,22) (0,13) (0,1) (0,12) (0,5) (0,7) (0,15) (0,4) (1,11) (1,18) (1,19) (1,20) (1,23) (1,9) (1,10) (1,22) (1,13) (1,12) (1,5) (1,7) (1,15) (1,4) (2,8) (2,6) (2,3) (2,24) (2,16) (2,21) (2,17) (2,14) (3,8) (3,6) (3,24) (3,16) (3,21) (3,17) (3,14) (4,11) (4,18) (4,19) (4,20) (4,23) (4,9) (4,10) (4,22) (4,13) (4,12) (4,5) (4,7) (4,15) (5,11) (5,18) (5,19) (5,20) (5,23) (5,9) (5,10) (5,22) (5,13) (5,12) (5,7) (5,15) (6,8) (6,24) (6,16) (6,21) (6,17) (6,14) (7,11) (7,18) (7,19) (7,20) (7,23) (7,9) (7,10) (7,22) (7,13) (7,12) (7,15) (8,24) (8,16) (8,21) (8,17) (8,14) (9,11) (9,18) (9,19) (9,20) (9,23) (9,10) (9,22) (9,13) (9,12) (9,15) (10,11) (10,18) (10,19) (10,20) (10,23) (10,22) (10,13) (10,12) (10,15) (11,18) (11,19) (11,20) (11,23) (11,22) (11,13) (11,12) (11,15) (12,18) (12,19) (12,20) (12,23) (12,22) (12,13) (12,15) (13,18) (13,19) (13,20) (13,23) (13,22) (13,15) (14,24) (14,16) (14,21) (14,17) (15,18) (15,19) (15,20) (15,23) (15,22) (16,24) (16,21) (16,17) (17,24) (17,21) (18,19) (18,20) (18,23) (18,22) (19,20) (19,23) (19,22) (20,23) (20,22) (21,24) (22,23)\nQ: Is there a path between node 1 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "571"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,19) (0,25) (0,2) (0,13) (0,1) (1,17) (1,24) (1,25) (1,11) (2,17) (2,25) (2,16) (2,13) (3,17) (4,23) (4,7) (4,14) (4,8) (5,18) (5,16) (6,18) (6,16) (6,21) (7,14) (7,15) (7,10) (8,23) (8,10) (9,14) (9,10) (10,23) (10,20) (11,17) (11,18) (11,25) (11,16) (11,13) (12,16) (13,17) (13,24) (13,25) (13,21) (14,15) (16,21) (17,19) (17,18) (17,25) (19,25) (19,21) (21,25)\nQ: Is there a path between node 21 and node 16?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "572"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,25) (0,13) (0,3) (0,1) (1,11) (1,25) (1,13) (1,2) (1,3) (1,8) (2,21) (2,22) (2,25) (2,13) (2,3) (3,18) (3,22) (3,11) (3,13) (4,23) (4,14) (4,6) (4,12) (4,27) (4,15) (4,5) (4,16) (4,26) (4,20) (4,7) (4,19) (5,14) (5,6) (5,12) (5,27) (5,15) (5,16) (5,9) (5,20) (5,7) (6,23) (6,14) (6,12) (6,24) (6,15) (6,16) (6,9) (6,17) (6,26) (6,20) (6,7) (6,19) (7,23) (7,14) (7,12) (7,24) (7,10) (7,16) (7,9) (7,17) (7,26) (7,20) (7,19) (8,21) (8,18) (8,22) (8,11) (8,25) (8,13) (9,23) (9,12) (9,10) (9,16) (9,17) (9,26) (9,20) (10,23) (10,14) (10,12) (10,24) (10,27) (10,16) (10,17) (10,26) (10,19) (11,21) (11,22) (11,25) (11,13) (12,23) (12,14) (12,24) (12,27) (12,16) (12,26) (12,20) (12,19) (13,22) (13,25) (14,23) (14,24) (14,16) (14,26) (14,19) (15,24) (15,27) (15,16) (15,26) (16,23) (16,27) (16,17) (16,26) (16,20) (17,27) (17,26) (17,20) (17,19) (18,22) (19,23) (19,24) (19,27) (19,26) (19,20) (20,23) (20,26) (21,22) (21,25) (22,25) (23,24) (23,27) (24,27) (24,26) (26,27)\nQ: Is there a path between node 2 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "573"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,19) (0,17) (0,7) (0,16) (0,21) (1,22) (1,19) (1,20) (1,21) (2,23) (2,6) (3,13) (3,18) (3,4) (3,10) (3,21) (4,19) (4,10) (4,16) (5,14) (5,12) (5,9) (5,11) (6,14) (6,23) (7,15) (7,22) (7,18) (7,8) (7,17) (7,20) (8,13) (8,21) (9,12) (9,11) (10,17) (13,19) (13,17) (13,21) (15,20) (16,18) (16,20) (19,20) (19,21)\nQ: Is there a path between node 16 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "574"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,24) (0,1) (0,6) (0,14) (1,10) (2,25) (2,5) (2,20) (2,18) (3,22) (3,6) (3,19) (3,23) (4,9) (4,18) (5,15) (5,25) (5,17) (5,20) (6,11) (6,24) (6,14) (6,7) (6,21) (7,24) (8,25) (8,17) (8,20) (8,18) (9,25) (10,24) (10,22) (10,21) (11,22) (11,19) (11,23) (12,15) (12,16) (12,17) (13,19) (13,14) (14,22) (14,19) (15,16) (15,18) (16,17) (17,20) (18,25) (19,24) (19,22) (20,25) (21,23) (22,24) (22,23)\nQ: Is there a path between node 4 and node 18?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "575"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,4) (0,9) (0,1) (0,11) (0,2) (1,10) (1,6) (1,9) (1,15) (1,13) (2,12) (2,9) (2,17) (2,15) (3,4) (3,6) (3,11) (4,12) (4,9) (4,11) (6,10) (6,12) (6,9) (6,15) (6,13) (8,12) (8,9) (8,15) (8,13) (9,10) (9,11) (10,13) (10,11) (11,13) (12,13) (14,16)\nQ: Is there a path between node 2 and node 17?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "576"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,10) (0,17) (0,5) (0,13) (0,15) (0,16) (0,3) (0,7) (0,11) (0,1) (0,4) (0,14) (1,12) (1,10) (1,17) (1,5) (1,13) (1,15) (1,16) (1,3) (1,7) (1,11) (1,4) (1,14) (2,8) (2,6) (3,12) (3,10) (3,17) (3,5) (3,13) (3,15) (3,16) (3,7) (3,11) (3,4) (3,14) (4,12) (4,10) (4,17) (4,5) (4,13) (4,15) (4,16) (4,7) (4,11) (4,14) (5,12) (5,10) (5,17) (5,13) (5,15) (5,16) (5,7) (5,11) (5,14) (6,8) (7,12) (7,10) (7,17) (7,13) (7,15) (7,16) (7,11) (7,14) (10,12) (10,17) (10,13) (10,15) (10,16) (10,11) (10,14) (11,12) (11,17) (11,13) (11,15) (11,16) (11,14) (12,17) (12,13) (12,15) (12,16) (12,14) (13,17) (13,15) (13,16) (13,14) (14,17) (14,15) (14,16) (15,17) (15,16) (16,17)\nQ: Is there a path between node 7 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "577"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,6) (1,2) (3,7) (3,5)\nQ: Is there a path between node 2 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "578"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,9) (1,8) (1,4) (2,8) (2,4) (2,3) (3,7) (3,6) (3,10) (3,12) (3,11) (4,10) (4,12) (6,14) (6,8) (6,10) (7,14) (7,11) (8,14) (8,12) (10,14) (11,14) (12,14)\nQ: Is there a path between node 9 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "579"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,19) (0,17) (0,7) (0,16) (0,21) (1,22) (1,19) (1,20) (1,21) (2,23) (2,6) (3,13) (3,18) (3,4) (3,10) (3,21) (4,19) (4,10) (4,16) (5,14) (5,12) (5,9) (5,11) (6,14) (6,23) (7,15) (7,22) (7,18) (7,8) (7,17) (7,20) (8,13) (8,21) (9,12) (9,11) (10,17) (13,19) (13,17) (13,21) (15,20) (16,18) (16,20) (19,20) (19,21)\nQ: Is there a path between node 0 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "580"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,31) (1,4) (1,27) (1,25) (2,31) (2,24) (2,13) (2,10) (3,30) (3,32) (3,27) (3,15) (4,30) (4,6) (4,28) (4,8) (5,22) (6,27) (7,20) (7,11) (7,12) (8,15) (9,14) (10,17) (10,23) (10,13) (11,14) (12,18) (13,23) (14,22) (15,30) (15,27) (15,25) (15,16) (15,28) (17,23) (17,21) (18,22) (18,33) (20,22) (21,31) (23,24) (25,30) (25,27) (25,28) (26,31) (27,30) (27,32) (28,32)\nQ: Is there a path between node 16 and node 20?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "581"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,9) (0,4) (0,14) (0,6) (0,10) (0,12) (0,2) (1,13) (1,11) (1,3) (1,5) (1,7) (1,16) (1,8) (1,17) (2,15) (2,9) (2,4) (2,14) (2,6) (2,10) (2,12) (3,13) (3,11) (3,5) (3,7) (3,16) (3,8) (3,17) (4,15) (4,9) (4,14) (4,6) (4,10) (4,12) (5,13) (5,11) (5,7) (5,16) (5,8) (5,17) (6,15) (6,9) (6,14) (6,10) (6,12) (7,13) (7,11) (7,16) (7,8) (7,17) (8,13) (8,11) (8,16) (8,17) (9,15) (9,14) (9,10) (9,12) (10,15) (10,14) (10,12) (11,13) (11,16) (11,17) (12,15) (12,14) (13,16) (13,17) (14,15) (16,17)\nQ: Is there a path between node 11 and node 14?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "582"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,21) (0,14) (0,1) (0,22) (0,16) (0,19) (0,5) (0,10) (0,20) (0,11) (0,24) (0,13) (1,21) (1,9) (1,3) (1,14) (1,22) (1,10) (1,20) (1,12) (1,11) (1,24) (1,13) (1,23) (2,8) (2,4) (2,18) (2,15) (3,9) (3,14) (3,16) (3,19) (3,7) (3,6) (3,5) (3,10) (3,11) (4,8) (4,17) (4,18) (4,15) (5,9) (5,14) (5,22) (5,7) (5,6) (5,10) (5,20) (5,12) (5,11) (5,13) (5,23) (6,21) (6,9) (6,22) (6,19) (6,7) (6,20) (6,12) (6,11) (6,13) (6,23) (7,21) (7,9) (7,14) (7,16) (7,19) (7,10) (7,20) (7,12) (7,11) (7,24) (7,13) (7,23) (8,17) (8,18) (8,15) (9,21) (9,16) (9,10) (9,20) (9,12) (9,11) (9,24) (9,13) (9,23) (10,22) (10,19) (10,12) (10,11) (10,13) (10,23) (11,21) (11,22) (11,19) (11,20) (11,12) (11,24) (11,13) (11,23) (12,21) (12,14) (12,22) (12,20) (12,24) (12,13) (12,23) (13,21) (13,14) (13,22) (13,16) (13,20) (13,23) (14,21) (14,16) (14,20) (14,24) (14,23) (15,18) (16,21) (16,22) (16,19) (16,20) (16,24) (16,23) (17,18) (19,21) (19,20) (19,24) (19,23) (20,21) (20,24) (20,23) (21,24) (21,23) (22,23) (23,24)\nQ: Is there a path between node 3 and node 18?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "583"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,10) (0,25) (0,16) (0,24) (0,4) (0,8) (0,27) (0,19) (1,5) (1,28) (2,15) (3,12) (3,13) (3,21) (3,24) (3,4) (3,8) (4,26) (4,20) (4,21) (4,11) (4,9) (6,13) (6,14) (6,22) (6,21) (6,7) (6,23) (6,11) (7,12) (7,26) (7,20) (7,17) (7,14) (7,10) (7,25) (7,24) (7,8) (7,11) (7,19) (7,9) (8,25) (8,27) (8,11) (9,17) (9,14) (9,21) (9,23) (9,27) (9,11) (10,26) (10,20) (10,14) (10,25) (10,23) (10,24) (11,13) (11,17) (11,21) (11,25) (11,23) (11,19) (12,20) (12,17) (12,24) (13,26) (13,20) (13,17) (13,22) (13,25) (13,24) (13,19) (14,20) (14,16) (15,28) (15,18) (16,26) (16,21) (16,23) (17,26) (17,22) (17,23) (17,27) (18,28) (19,22) (20,23) (20,24) (20,27) (21,26) (21,27) (23,25) (24,25) (24,27) (25,27)\nQ: Is there a path between node 22 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "584"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,4) (0,3) (0,6) (0,2) (0,8) (0,5) (0,11) (1,4) (1,3) (1,6) (1,2) (1,8) (1,5) (1,11) (2,4) (2,3) (2,6) (2,8) (2,5) (2,11) (3,4) (3,6) (3,8) (3,5) (3,11) (4,6) (4,8) (4,5) (4,11) (5,6) (5,8) (5,11) (6,8) (6,11) (7,9) (7,10) (8,11) (9,10)\nQ: Is there a path between node 10 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "585"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,17) (1,4) (2,10) (3,19) (3,30) (3,13) (3,25) (3,8) (4,31) (5,16) (6,29) (6,11) (6,32) (7,14) (7,17) (8,21) (8,30) (8,13) (8,28) (9,20) (9,25) (11,29) (11,26) (11,22) (13,21) (13,15) (13,28) (13,23) (15,31) (15,16) (15,28) (15,23) (16,21) (16,25) (16,23) (18,29) (18,24) (20,31) (20,30) (20,25) (21,25) (22,24) (23,25) (23,28) (24,29) (24,32) (25,30) (26,32) (28,30)\nQ: Is there a path between node 31 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "586"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,2) (0,14) (0,7) (0,13) (1,17) (1,3) (1,10) (1,6) (2,11) (2,12) (2,14) (2,13) (3,17) (3,10) (3,6) (4,9) (4,5) (5,9) (5,16) (6,17) (6,8) (6,10) (7,11) (7,12) (7,14) (7,13) (8,17) (8,15) (9,18) (9,16) (10,17) (12,14) (12,13) (13,14) (15,17)\nQ: Is there a path between node 17 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "587"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,3) (0,2) (1,5) (1,3) (2,5) (2,3) (3,5)\nQ: Is there a path between node 3 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "588"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,2) (1,5) (1,2) (2,5) (2,10) (3,10) (3,4) (3,8) (4,5) (5,10) (5,8) (7,11) (8,10) (9,11)\nQ: Is there a path between node 0 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "589"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,10) (0,17) (0,15) (0,4) (0,12) (0,24) (0,9) (0,3) (0,13) (0,23) (0,7) (0,19) (0,16) (0,6) (0,25) (0,8) (1,10) (1,17) (1,4) (1,12) (1,24) (1,3) (1,13) (1,23) (1,26) (1,22) (1,19) (1,6) (1,14) (1,25) (1,8) (1,20) (2,10) (2,17) (2,11) (2,4) (2,24) (2,9) (2,3) (2,13) (2,23) (2,26) (2,7) (2,22) (2,19) (2,6) (2,14) (2,25) (2,8) (3,10) (3,17) (3,11) (3,15) (3,4) (3,12) (3,24) (3,9) (3,13) (3,26) (3,7) (3,19) (3,16) (3,14) (3,25) (3,8) (3,20) (4,10) (4,17) (4,11) (4,15) (4,12) (4,24) (4,9) (4,7) (4,19) (4,16) (4,6) (4,25) (4,20) (5,18) (6,10) (6,17) (6,15) (6,12) (6,24) (6,9) (6,23) (6,7) (6,16) (6,25) (6,8) (7,10) (7,11) (7,15) (7,12) (7,13) (7,22) (7,19) (7,16) (7,25) (7,8) (7,20) (8,10) (8,17) (8,11) (8,15) (8,12) (8,24) (8,9) (8,23) (8,22) (8,19) (8,16) (8,14) (8,25) (8,20) (9,10) (9,17) (9,11) (9,12) (9,24) (9,13) (9,23) (9,26) (9,22) (9,19) (9,16) (9,20) (10,17) (10,11) (10,15) (10,12) (10,24) (10,13) (10,23) (10,26) (10,19) (10,14) (10,20) (11,15) (11,12) (11,24) (11,13) (11,23) (11,26) (11,19) (11,16) (11,14) (11,20) (12,15) (12,24) (12,23) (12,22) (12,19) (12,16) (12,14) (12,25) (12,20) (13,15) (13,24) (13,23) (13,19) (13,16) (13,14) (13,25) (13,20) (14,17) (14,15) (14,24) (14,23) (14,26) (14,22) (14,19) (14,16) (14,25) (14,20) (15,17) (15,24) (15,23) (15,26) (15,16) (15,20) (16,24) (16,23) (16,26) (16,19) (16,25) (16,20) (17,23) (17,20) (18,21) (19,23) (19,22) (19,25) (19,20) (20,24) (20,23) (20,22) (20,25) (22,26) (22,25) (23,24) (23,26) (23,25) (24,26) (24,25) (25,26)\nQ: Is there a path between node 17 and node 20?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "590"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,5) (0,11) (0,8) (0,6) (0,1) (1,10) (1,3) (1,5) (1,9) (1,6) (1,2) (2,10) (2,3) (2,5) (2,9) (2,8) (2,7) (2,6) (2,13) (3,9) (3,11) (3,8) (3,7) (4,12) (5,10) (5,9) (5,8) (5,7) (5,6) (6,10) (6,9) (6,11) (6,8) (7,10) (7,11) (7,8) (7,13) (8,10) (8,11) (8,13) (9,10) (9,11) (9,13) (10,11) (10,13)\nQ: Is there a path between node 4 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "591"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,21) (0,11) (0,15) (0,4) (0,22) (0,5) (0,3) (0,6) (0,20) (0,13) (0,18) (0,9) (0,1) (0,12) (0,24) (0,16) (0,8) (0,23) (0,2) (1,21) (1,11) (1,15) (1,4) (1,22) (1,5) (1,3) (1,6) (1,20) (1,13) (1,18) (1,9) (1,12) (1,24) (1,16) (1,8) (1,23) (1,2) (2,21) (2,11) (2,15) (2,4) (2,22) (2,5) (2,3) (2,6) (2,20) (2,13) (2,18) (2,9) (2,12) (2,24) (2,16) (2,8) (2,23) (3,21) (3,11) (3,15) (3,4) (3,22) (3,5) (3,6) (3,20) (3,13) (3,18) (3,9) (3,12) (3,24) (3,16) (3,8) (3,23) (4,21) (4,11) (4,15) (4,22) (4,5) (4,6) (4,20) (4,13) (4,18) (4,9) (4,12) (4,24) (4,16) (4,8) (4,23) (5,21) (5,11) (5,15) (5,22) (5,6) (5,20) (5,13) (5,18) (5,9) (5,12) (5,24) (5,16) (5,8) (5,23) (6,21) (6,11) (6,15) (6,22) (6,20) (6,13) (6,18) (6,9) (6,12) (6,24) (6,16) (6,8) (6,23) (7,10) (7,14) (7,17) (7,19) (8,21) (8,11) (8,15) (8,22) (8,20) (8,13) (8,18) (8,9) (8,12) (8,24) (8,16) (8,23) (9,21) (9,11) (9,15) (9,22) (9,20) (9,13) (9,18) (9,12) (9,24) (9,16) (9,23) (10,14) (10,17) (10,19) (11,21) (11,15) (11,22) (11,20) (11,13) (11,18) (11,12) (11,24) (11,16) (11,23) (12,21) (12,15) (12,22) (12,20) (12,13) (12,18) (12,24) (12,16) (12,23) (13,21) (13,15) (13,22) (13,20) (13,18) (13,24) (13,16) (13,23) (14,17) (14,19) (15,21) (15,22) (15,20) (15,18) (15,24) (15,16) (15,23) (16,21) (16,22) (16,20) (16,18) (16,24) (16,23) (17,19) (18,21) (18,22) (18,20) (18,24) (18,23) (20,21) (20,22) (20,24) (20,23) (21,22) (21,24) (21,23) (22,24) (22,23) (23,24)\nQ: Is there a path between node 14 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "592"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,14) (0,10) (0,24) (0,2) (0,12) (0,19) (0,3) (0,17) (0,25) (0,23) (0,15) (1,18) (1,11) (1,8) (2,14) (2,10) (2,24) (2,7) (2,3) (2,21) (2,25) (2,23) (2,6) (3,14) (3,24) (3,12) (3,19) (3,17) (3,25) (3,23) (3,6) (3,15) (4,18) (4,8) (5,18) (5,11) (5,8) (6,16) (6,14) (6,10) (6,12) (6,7) (6,19) (6,21) (6,25) (6,23) (6,9) (6,15) (7,16) (7,10) (7,24) (7,12) (7,19) (7,17) (7,25) (7,9) (7,15) (8,18) (8,11) (9,16) (9,14) (9,10) (9,24) (9,12) (9,19) (9,17) (9,21) (9,23) (9,15) (10,16) (10,14) (10,19) (10,21) (10,25) (10,23) (10,15) (11,18) (12,16) (12,14) (12,24) (12,19) (12,17) (12,21) (12,25) (12,23) (12,15) (13,20) (14,16) (14,24) (14,17) (14,21) (14,25) (14,23) (14,15) (15,16) (15,24) (15,23) (16,21) (16,25) (16,23) (17,21) (17,23) (19,21) (19,25) (21,24) (21,25) (21,23) (23,25) (24,25)\nQ: Is there a path between node 11 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "593"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,3) (0,2) (0,1) (1,6) (1,3) (1,2) (2,6) (2,3) (3,6) (4,5)\nQ: Is there a path between node 0 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "594"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,18) (0,17) (0,10) (1,7) (1,24) (1,27) (2,4) (2,8) (2,13) (2,19) (2,27) (3,16) (3,28) (3,9) (4,18) (4,6) (4,10) (4,11) (4,27) (6,20) (6,8) (6,7) (6,27) (7,8) (7,18) (7,17) (7,23) (7,24) (7,10) (7,13) (7,19) (7,11) (7,14) (8,17) (8,22) (8,24) (8,10) (8,11) (10,18) (10,17) (10,12) (10,11) (10,27) (11,17) (11,12) (12,20) (12,18) (12,17) (12,14) (13,20) (13,18) (13,24) (13,27) (13,26) (14,18) (15,28) (15,25) (16,25) (17,20) (17,18) (17,26) (18,22) (18,23) (18,19) (18,27) (19,23) (19,27) (19,26) (20,24) (22,23) (22,24) (22,26) (26,27)\nQ: Is there a path between node 25 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "595"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,5) (0,1) (0,9) (0,3) (0,4) (1,6) (1,5) (1,9) (1,3) (1,4) (2,7) (2,8) (2,10) (3,6) (3,5) (3,9) (3,4) (4,6) (4,5) (4,9) (5,6) (5,9) (6,9) (7,8) (7,10) (8,10)\nQ: Is there a path between node 7 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "596"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (1,18) (1,8) (1,4) (2,15) (2,18) (2,11) (2,23) (2,4) (3,12) (3,5) (4,23) (4,25) (5,12) (5,17) (6,22) (6,13) (7,18) (7,23) (7,8) (9,17) (10,19) (10,17) (11,15) (12,24) (14,20) (14,22) (15,18) (16,20) (16,22) (20,22) (21,22) (23,25)\nQ: Is there a path between node 12 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "597"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,17) (0,13) (0,12) (0,4) (0,1) (1,3) (1,17) (1,16) (1,14) (1,4) (2,5) (2,7) (2,9) (2,11) (2,8) (3,15) (3,13) (3,16) (3,12) (3,14) (3,6) (4,15) (4,13) (4,16) (4,12) (4,6) (5,9) (5,11) (5,10) (6,17) (6,13) (6,12) (7,11) (7,10) (7,8) (8,9) (8,11) (9,10) (10,11) (12,15) (12,17) (12,16) (12,14) (13,17) (13,16) (14,15) (14,17) (15,17) (15,16) (16,17)\nQ: Is there a path between node 1 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "598"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,6) (0,3) (0,18) (0,1) (0,15) (0,12) (0,14) (0,9) (0,16) (0,8) (0,2) (0,11) (0,19) (1,7) (1,6) (1,3) (1,18) (1,15) (1,9) (1,8) (1,2) (1,20) (2,7) (2,3) (2,18) (2,15) (2,12) (2,14) (2,9) (2,16) (2,8) (2,11) (2,19) (2,20) (3,18) (3,15) (3,12) (3,9) (3,16) (3,8) (3,19) (3,20) (4,13) (4,17) (5,17) (6,7) (6,18) (6,15) (6,14) (6,9) (6,16) (6,11) (6,19) (6,20) (7,15) (7,12) (7,14) (7,9) (7,16) (8,18) (8,12) (8,14) (8,9) (8,16) (8,11) (8,19) (8,20) (9,18) (9,15) (9,12) (9,11) (9,19) (9,20) (10,13) (11,18) (11,12) (11,14) (11,16) (11,19) (11,20) (12,18) (12,15) (12,14) (12,19) (12,20) (13,17) (14,19) (16,18) (16,19) (18,20)\nQ: Is there a path between node 0 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "599"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,14) (0,10) (0,24) (0,2) (0,12) (0,19) (0,3) (0,17) (0,25) (0,23) (0,15) (1,18) (1,11) (1,8) (2,14) (2,10) (2,24) (2,7) (2,3) (2,21) (2,25) (2,23) (2,6) (3,14) (3,24) (3,12) (3,19) (3,17) (3,25) (3,23) (3,6) (3,15) (4,18) (4,8) (5,18) (5,11) (5,8) (6,16) (6,14) (6,10) (6,12) (6,7) (6,19) (6,21) (6,25) (6,23) (6,9) (6,15) (7,16) (7,10) (7,24) (7,12) (7,19) (7,17) (7,25) (7,9) (7,15) (8,18) (8,11) (9,16) (9,14) (9,10) (9,24) (9,12) (9,19) (9,17) (9,21) (9,23) (9,15) (10,16) (10,14) (10,19) (10,21) (10,25) (10,23) (10,15) (11,18) (12,16) (12,14) (12,24) (12,19) (12,17) (12,21) (12,25) (12,23) (12,15) (13,20) (14,16) (14,24) (14,17) (14,21) (14,25) (14,23) (14,15) (15,16) (15,24) (15,23) (16,21) (16,25) (16,23) (17,21) (17,23) (19,21) (19,25) (21,24) (21,25) (21,23) (23,25) (24,25)\nQ: Is there a path between node 8 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "600"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,4) (1,13) (2,11) (3,4) (3,6) (3,19) (4,20) (4,12) (4,16) (5,14) (5,9) (6,18) (6,8) (7,13) (7,8) (7,19) (7,15) (8,18) (8,20) (8,15) (11,14) (12,20) (12,13) (12,19) (12,16) (13,18) (13,15) (15,18) (15,19) (18,20) (18,19)\nQ: Is there a path between node 16 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "601"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,13) (1,6) (1,8) (1,3) (1,4) (2,5) (2,9) (3,12) (3,9) (3,13) (4,6) (4,10) (5,6) (5,9) (6,12) (6,8) (8,9) (9,10) (12,13)\nQ: Is there a path between node 11 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "602"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,18) (0,25) (0,19) (0,16) (0,22) (0,8) (0,10) (0,31) (0,13) (0,5) (0,14) (0,24) (0,27) (0,1) (0,15) (0,23) (1,9) (1,30) (1,25) (1,19) (1,16) (1,17) (1,22) (1,8) (1,21) (1,4) (1,31) (1,13) (1,14) (1,24) (1,12) (1,27) (1,15) (2,11) (2,28) (2,29) (2,7) (3,9) (3,18) (3,25) (3,19) (3,16) (3,22) (3,10) (3,4) (3,31) (3,13) (3,5) (3,14) (3,24) (3,12) (3,20) (3,27) (3,15) (3,23) (4,18) (4,30) (4,19) (4,22) (4,8) (4,21) (4,31) (4,5) (4,24) (4,12) (4,27) (4,23) (5,18) (5,30) (5,25) (5,19) (5,17) (5,10) (5,21) (5,31) (5,12) (5,20) (5,15) (5,23) (6,28) (6,29) (6,7) (6,26) (7,28) (8,9) (8,25) (8,19) (8,16) (8,22) (8,10) (8,13) (8,14) (8,24) (8,12) (8,27) (8,15) (8,23) (9,18) (9,30) (9,19) (9,16) (9,17) (9,22) (9,10) (9,31) (9,13) (9,27) (9,15) (9,23) (10,18) (10,30) (10,25) (10,16) (10,22) (10,21) (10,31) (10,14) (10,24) (10,12) (10,20) (10,15) (11,28) (11,26) (12,19) (12,22) (12,21) (12,13) (12,24) (12,15) (12,23) (13,25) (13,19) (13,16) (13,17) (13,22) (13,31) (13,14) (13,27) (14,30) (14,25) (14,16) (14,17) (14,22) (14,31) (14,24) (14,20) (14,15) (14,23) (15,18) (15,30) (15,25) (15,19) (15,16) (15,22) (15,31) (15,24) (16,18) (16,30) (16,22) (16,21) (16,31) (16,20) (16,27) (17,18) (17,30) (17,25) (17,19) (17,22) (17,21) (17,31) (17,24) (17,27) (17,23) (18,30) (18,25) (18,19) (18,22) (18,21) (18,31) (18,24) (18,27) (18,23) (19,30) (19,25) (19,21) (19,24) (19,20) (19,27) (19,23) (20,21) (20,31) (20,24) (20,27) (20,23) (21,25) (21,22) (21,31) (21,24) (21,27) (21,23) (22,30) (22,31) (22,24) (22,23) (23,30) (23,25) (23,24) (23,27) (24,30) (24,25) (24,31) (24,27) (25,30) (25,27) (26,28) (27,30) (27,31) (28,29) (30,31)\nQ: Is there a path between node 27 and node 20?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "603"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,4) (0,9) (0,1) (0,11) (0,2) (1,10) (1,6) (1,9) (1,15) (1,13) (2,12) (2,9) (2,17) (2,15) (3,4) (3,6) (3,11) (4,12) (4,9) (4,11) (6,10) (6,12) (6,9) (6,15) (6,13) (8,12) (8,9) (8,15) (8,13) (9,10) (9,11) (10,13) (10,11) (11,13) (12,13) (14,16)\nQ: Is there a path between node 4 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "604"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,7) (0,10) (0,6) (0,2) (0,8) (0,4) (0,1) (1,3) (1,7) (1,10) (1,6) (1,2) (1,8) (1,4) (2,3) (2,7) (2,10) (2,6) (2,8) (2,4) (3,7) (3,10) (3,6) (3,8) (3,4) (4,7) (4,10) (4,6) (4,8) (5,9) (6,7) (6,10) (6,8) (7,10) (7,8) (8,10)\nQ: Is there a path between node 9 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "605"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,14) (1,21) (1,3) (1,15) (1,7) (3,12) (4,10) (5,10) (6,22) (7,21) (7,15) (9,12) (11,13) (11,21) (14,20) (15,17) (15,21) (16,18) (18,22)\nQ: Is there a path between node 4 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "606"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,4) (1,23) (1,7) (1,18) (1,24) (1,32) (1,31) (1,21) (1,27) (1,11) (1,6) (1,29) (1,17) (1,20) (2,23) (2,7) (2,18) (2,33) (2,24) (2,31) (2,21) (2,8) (2,27) (2,11) (2,29) (2,17) (2,26) (3,9) (3,22) (3,13) (3,5) (3,30) (3,28) (3,16) (3,14) (3,15) (4,19) (4,10) (5,9) (5,22) (5,13) (5,28) (5,16) (5,14) (6,18) (6,32) (6,25) (6,21) (6,8) (6,11) (6,17) (6,20) (6,26) (7,18) (7,33) (7,24) (7,32) (7,25) (7,31) (7,21) (7,17) (7,20) (7,26) (8,18) (8,33) (8,32) (8,25) (8,31) (8,27) (8,11) (8,29) (8,20) (8,26) (9,22) (9,13) (9,30) (9,28) (9,14) (9,15) (10,19) (10,12) (11,18) (11,33) (11,24) (11,25) (11,31) (11,27) (11,29) (11,26) (12,19) (13,28) (13,15) (14,30) (14,28) (14,16) (14,15) (15,22) (15,30) (15,16) (16,22) (17,23) (17,18) (17,33) (17,25) (17,31) (17,21) (17,27) (17,29) (17,20) (17,26) (18,23) (18,32) (18,25) (18,21) (18,29) (18,20) (18,26) (20,23) (20,33) (20,32) (20,25) (20,31) (20,21) (20,27) (20,29) (20,26) (21,23) (21,33) (21,24) (21,25) (21,29) (23,33) (23,24) (23,25) (23,31) (23,27) (23,29) (23,26) (24,33) (24,32) (24,25) (24,27) (24,29) (24,26) (25,32) (25,31) (25,27) (25,29) (25,26) (26,33) (26,31) (26,27) (27,31) (27,29) (28,30) (31,32) (32,33)\nQ: Is there a path between node 14 and node 17?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "607"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,30) (0,6) (0,12) (1,15) (2,17) (2,4) (3,25) (3,30) (3,12) (4,18) (4,16) (4,20) (4,22) (4,28) (4,8) (4,17) (5,12) (5,11) (6,19) (7,9) (7,10) (8,22) (8,28) (8,21) (9,23) (10,12) (10,11) (11,30) (11,19) (11,12) (12,25) (12,19) (13,27) (13,26) (15,26) (16,18) (16,29) (16,20) (16,24) (16,22) (16,28) (16,17) (17,22) (17,28) (17,21) (18,29) (18,20) (18,24) (18,22) (19,30) (20,22) (20,28) (21,24) (24,28) (25,30)\nQ: Is there a path between node 22 and node 30?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "608"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,7) (0,6) (0,8) (0,4) (0,1) (1,2) (1,7) (1,6) (1,8) (1,4) (2,7) (2,6) (2,8) (2,4) (3,5) (4,7) (4,6) (4,8) (6,7) (6,8) (7,8)\nQ: Is there a path between node 1 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "609"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,2) (0,1) (1,5) (1,6) (2,6) (3,7) (4,7) (5,6)\nQ: Is there a path between node 1 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "610"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,14) (0,5) (0,9) (0,8) (0,6) (0,21) (1,4) (1,15) (1,18) (1,11) (1,10) (1,12) (2,20) (2,14) (2,5) (2,9) (2,22) (2,6) (2,16) (3,9) (3,23) (3,22) (3,6) (3,21) (4,15) (4,11) (4,19) (4,13) (5,20) (5,14) (5,9) (5,8) (5,6) (5,21) (6,20) (6,14) (6,9) (6,23) (6,8) (6,16) (7,18) (7,11) (7,10) (7,12) (7,19) (7,13) (8,20) (8,14) (8,23) (8,21) (9,20) (9,23) (9,22) (9,21) (10,15) (10,18) (10,11) (10,12) (10,19) (10,13) (11,15) (11,13) (12,18) (12,19) (13,18) (13,19) (14,23) (14,22) (14,21) (15,19) (16,23) (16,22) (20,21) (22,23)\nQ: Is there a path between node 22 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "611"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,2) (0,1) (1,5) (1,6) (2,6) (3,7) (4,7) (5,6)\nQ: Is there a path between node 3 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "612"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (1,4) (1,11) (2,21) (2,20) (2,24) (3,24) (4,13) (4,15) (4,8) (5,19) (5,24) (6,20) (6,24) (7,25) (7,21) (8,17) (8,15) (8,12) (9,13) (9,12) (10,16) (11,13) (11,18) (11,23) (11,14) (11,12) (13,17) (14,23) (15,18) (15,23) (18,23) (19,25) (19,24) (20,21) (21,25) (24,25)\nQ: Is there a path between node 21 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "613"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,9) (0,13) (0,3) (0,1) (0,2) (0,7) (0,8) (0,11) (1,14) (1,13) (1,8) (1,10) (1,11) (1,5) (2,9) (2,13) (2,3) (2,7) (2,8) (2,10) (3,14) (3,9) (3,13) (3,8) (3,11) (3,5) (4,6) (4,12) (5,14) (5,9) (5,7) (5,8) (5,10) (5,11) (6,12) (7,14) (7,13) (7,8) (7,10) (8,14) (8,9) (8,10) (9,14) (9,13) (10,14) (10,13) (11,14) (13,14)\nQ: Is there a path between node 9 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "614"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,1) (1,11) (1,5) (1,8) (2,14) (2,10) (2,6) (2,3) (2,13) (2,4) (3,7) (3,14) (3,6) (3,12) (3,13) (3,4) (4,9) (4,7) (4,10) (4,12) (4,13) (5,11) (5,8) (6,7) (6,10) (6,12) (6,13) (7,9) (7,14) (7,10) (7,13) (8,11) (10,14) (10,12) (10,13) (12,14) (12,13) (13,14)\nQ: Is there a path between node 10 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "615"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,8) (0,18) (0,6) (0,1) (0,12) (0,3) (0,7) (0,14) (0,10) (0,19) (0,16) (0,13) (1,17) (1,8) (1,18) (1,2) (1,19) (2,8) (2,6) (2,20) (2,14) (3,17) (3,18) (3,6) (3,14) (3,10) (3,19) (4,17) (4,18) (4,6) (4,19) (4,13) (5,15) (6,17) (6,8) (6,18) (6,13) (7,17) (7,14) (7,10) (8,20) (9,15) (9,11) (10,17) (10,18) (11,15) (12,17) (12,18) (12,14) (12,19) (13,17) (13,18) (13,20) (14,17) (14,18) (14,20) (18,20) (19,20)\nQ: Is there a path between node 3 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "616"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,1) (0,14) (0,18) (1,17) (1,14) (1,18) (2,19) (2,7) (2,10) (2,3) (2,12) (2,16) (2,11) (2,5) (2,9) (2,15) (2,6) (2,20) (2,8) (2,4) (2,13) (3,19) (3,7) (3,10) (3,12) (3,16) (3,11) (3,5) (3,9) (3,15) (3,6) (3,20) (3,8) (3,4) (3,13) (4,19) (4,7) (4,10) (4,12) (4,16) (4,11) (4,5) (4,9) (4,15) (4,6) (4,20) (4,8) (4,13) (5,19) (5,7) (5,10) (5,12) (5,16) (5,11) (5,9) (5,15) (5,6) (5,20) (5,8) (5,13) (6,19) (6,7) (6,10) (6,12) (6,16) (6,11) (6,9) (6,15) (6,20) (6,8) (6,13) (7,19) (7,10) (7,12) (7,16) (7,11) (7,9) (7,15) (7,20) (7,8) (7,13) (8,19) (8,10) (8,12) (8,16) (8,11) (8,9) (8,15) (8,20) (8,13) (9,19) (9,10) (9,12) (9,16) (9,11) (9,15) (9,20) (9,13) (10,19) (10,12) (10,16) (10,11) (10,15) (10,20) (10,13) (11,19) (11,12) (11,16) (11,15) (11,20) (11,13) (12,19) (12,16) (12,15) (12,20) (12,13) (13,19) (13,16) (13,15) (13,20) (14,17) (14,18) (15,19) (15,16) (15,20) (16,19) (16,20) (17,18) (19,20)\nQ: Is there a path between node 8 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "617"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,6) (1,2) (3,7) (3,5)\nQ: Is there a path between node 6 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "618"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,25) (0,13) (0,3) (0,1) (1,11) (1,25) (1,13) (1,2) (1,3) (1,8) (2,21) (2,22) (2,25) (2,13) (2,3) (3,18) (3,22) (3,11) (3,13) (4,23) (4,14) (4,6) (4,12) (4,27) (4,15) (4,5) (4,16) (4,26) (4,20) (4,7) (4,19) (5,14) (5,6) (5,12) (5,27) (5,15) (5,16) (5,9) (5,20) (5,7) (6,23) (6,14) (6,12) (6,24) (6,15) (6,16) (6,9) (6,17) (6,26) (6,20) (6,7) (6,19) (7,23) (7,14) (7,12) (7,24) (7,10) (7,16) (7,9) (7,17) (7,26) (7,20) (7,19) (8,21) (8,18) (8,22) (8,11) (8,25) (8,13) (9,23) (9,12) (9,10) (9,16) (9,17) (9,26) (9,20) (10,23) (10,14) (10,12) (10,24) (10,27) (10,16) (10,17) (10,26) (10,19) (11,21) (11,22) (11,25) (11,13) (12,23) (12,14) (12,24) (12,27) (12,16) (12,26) (12,20) (12,19) (13,22) (13,25) (14,23) (14,24) (14,16) (14,26) (14,19) (15,24) (15,27) (15,16) (15,26) (16,23) (16,27) (16,17) (16,26) (16,20) (17,27) (17,26) (17,20) (17,19) (18,22) (19,23) (19,24) (19,27) (19,26) (19,20) (20,23) (20,26) (21,22) (21,25) (22,25) (23,24) (23,27) (24,27) (24,26) (26,27)\nQ: Is there a path between node 26 and node 18?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "619"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,3) (0,5) (1,2) (1,8) (1,7) (2,8) (2,7) (3,11) (3,9) (3,13) (5,11) (5,12) (10,11) (11,12) (12,13)\nQ: Is there a path between node 0 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "620"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,19) (0,17) (0,7) (0,16) (0,21) (1,22) (1,19) (1,20) (1,21) (2,23) (2,6) (3,13) (3,18) (3,4) (3,10) (3,21) (4,19) (4,10) (4,16) (5,14) (5,12) (5,9) (5,11) (6,14) (6,23) (7,15) (7,22) (7,18) (7,8) (7,17) (7,20) (8,13) (8,21) (9,12) (9,11) (10,17) (13,19) (13,17) (13,21) (15,20) (16,18) (16,20) (19,20) (19,21)\nQ: Is there a path between node 2 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "621"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,10) (0,12) (0,20) (0,14) (0,8) (0,3) (0,6) (0,5) (0,15) (0,19) (0,7) (0,9) (0,22) (0,2) (0,21) (0,18) (1,4) (1,10) (1,12) (1,20) (1,8) (1,5) (1,15) (1,16) (1,19) (1,7) (1,9) (1,22) (1,2) (1,18) (2,4) (2,10) (2,12) (2,14) (2,3) (2,5) (2,15) (2,19) (2,7) (2,22) (2,21) (2,18) (3,4) (3,12) (3,20) (3,14) (3,6) (3,5) (3,15) (3,16) (3,19) (3,7) (3,9) (3,22) (3,21) (3,18) (4,10) (4,12) (4,8) (4,6) (4,5) (4,15) (4,16) (4,19) (4,7) (4,9) (4,21) (4,18) (5,12) (5,14) (5,8) (5,6) (5,15) (5,16) (5,19) (5,7) (5,9) (5,22) (5,18) (6,10) (6,12) (6,20) (6,14) (6,16) (6,19) (6,7) (6,9) (6,22) (6,21) (6,18) (7,10) (7,12) (7,14) (7,8) (7,16) (7,9) (7,22) (7,21) (7,18) (8,10) (8,12) (8,14) (8,15) (8,16) (8,19) (8,9) (8,21) (9,12) (9,20) (9,15) (9,16) (9,22) (9,21) (9,18) (10,12) (10,20) (10,14) (10,15) (10,16) (10,18) (12,16) (12,19) (13,17) (14,20) (14,16) (15,16) (15,22) (15,21) (16,20) (16,21) (16,18) (18,22) (18,21) (19,20) (19,22) (19,21) (21,22)\nQ: Is there a path between node 15 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "622"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,1) (1,11) (1,5) (1,8) (2,14) (2,10) (2,6) (2,3) (2,13) (2,4) (3,7) (3,14) (3,6) (3,12) (3,13) (3,4) (4,9) (4,7) (4,10) (4,12) (4,13) (5,11) (5,8) (6,7) (6,10) (6,12) (6,13) (7,9) (7,14) (7,10) (7,13) (8,11) (10,14) (10,12) (10,13) (12,14) (12,13) (13,14)\nQ: Is there a path between node 2 and node 12?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "623"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,13) (0,8) (0,18) (0,25) (0,14) (0,17) (0,21) (1,13) (1,26) (1,14) (1,20) (1,17) (1,24) (1,6) (2,8) (2,18) (2,9) (2,26) (2,14) (2,10) (2,15) (3,16) (3,12) (4,13) (4,8) (4,18) (4,25) (4,6) (5,19) (5,13) (5,10) (5,20) (5,22) (5,17) (5,6) (6,8) (6,18) (6,9) (6,26) (6,14) (6,17) (6,21) (6,15) (6,23) (7,25) (7,14) (7,22) (7,24) (7,15) (7,23) (8,13) (8,25) (8,24) (8,23) (9,25) (9,27) (9,26) (9,14) (9,17) (9,24) (9,23) (10,19) (10,13) (10,25) (10,22) (11,12) (12,16) (13,19) (13,18) (13,21) (14,19) (14,18) (14,22) (15,19) (15,25) (15,23) (17,25) (17,22) (17,21) (17,24) (18,21) (18,24) (19,26) (19,22) (19,24) (19,23) (20,25) (20,26) (20,24) (20,23) (21,27) (21,23) (22,25) (22,26) (22,23) (25,27) (25,26)\nQ: Is there a path between node 1 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "624"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,8) (0,11) (0,17) (0,1) (0,2) (0,12) (0,6) (0,18) (0,7) (0,15) (1,19) (1,8) (1,9) (1,11) (1,2) (1,12) (1,6) (1,7) (1,15) (2,19) (2,4) (2,9) (2,11) (2,17) (2,12) (2,6) (2,18) (2,15) (3,5) (3,13) (3,10) (4,19) (4,8) (4,9) (4,11) (4,17) (4,12) (4,6) (4,7) (4,15) (5,13) (5,10) (6,9) (6,11) (6,12) (6,18) (7,19) (7,8) (7,9) (7,11) (7,17) (7,15) (8,19) (8,11) (8,17) (8,12) (9,17) (9,12) (9,18) (10,13) (11,17) (11,15) (12,19) (12,17) (12,18) (12,15) (14,20) (14,21) (15,17) (15,18) (17,19) (17,18) (18,19) (20,21)\nQ: Is there a path between node 1 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "625"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,19) (0,17) (0,3) (0,10) (0,14) (1,7) (1,8) (1,15) (1,13) (2,9) (2,12) (2,18) (2,4) (3,6) (3,19) (3,17) (3,16) (3,10) (3,14) (4,12) (4,18) (5,9) (5,18) (6,19) (6,17) (6,16) (6,14) (6,20) (7,8) (7,15) (7,13) (9,12) (9,18) (10,16) (10,14) (10,20) (11,15) (12,18) (13,15) (14,19) (14,17) (14,20) (16,19) (16,17) (17,20) (19,20)\nQ: Is there a path between node 6 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "626"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (1,2) (1,5) (5,6)\nQ: Is there a path between node 3 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "627"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,2) (3,5)\nQ: Is there a path between node 3 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "628"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (1,24) (1,13) (1,7) (2,24) (2,15) (2,18) (2,8) (2,13) (2,7) (3,23) (3,6) (5,20) (5,14) (6,11) (6,23) (7,12) (7,10) (7,21) (7,8) (7,13) (8,10) (8,15) (8,18) (8,22) (8,13) (9,21) (9,13) (10,12) (10,15) (10,13) (12,24) (13,24) (13,22) (14,20) (15,24) (17,24) (19,20) (21,24)\nQ: Is there a path between node 7 and node 22?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "629"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,5) (3,5)\nQ: Is there a path between node 0 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "630"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,24) (0,2) (0,7) (0,15) (0,14) (0,22) (0,10) (0,18) (0,5) (0,9) (0,4) (0,11) (0,8) (0,20) (0,13) (1,2) (1,7) (1,15) (1,14) (1,18) (1,5) (1,16) (1,9) (1,4) (1,11) (1,8) (1,13) (2,24) (2,7) (2,15) (2,14) (2,22) (2,18) (2,16) (2,9) (2,4) (2,11) (2,8) (2,20) (2,23) (3,21) (4,7) (4,14) (4,22) (4,18) (4,16) (4,13) (4,23) (5,24) (5,7) (5,15) (5,14) (5,22) (5,10) (5,18) (5,20) (5,23) (6,12) (7,24) (7,15) (7,14) (7,10) (7,18) (7,16) (7,9) (7,11) (7,8) (7,20) (7,13) (7,23) (8,24) (8,14) (8,10) (8,18) (8,9) (8,13) (8,23) (9,24) (9,15) (9,14) (9,22) (9,10) (9,16) (9,20) (9,23) (10,24) (10,15) (10,14) (10,22) (10,18) (10,16) (10,20) (11,15) (11,14) (11,18) (11,16) (11,20) (11,13) (11,23) (13,24) (13,15) (13,18) (13,16) (13,23) (14,24) (14,15) (14,22) (14,18) (14,16) (14,23) (15,24) (15,22) (15,18) (15,16) (15,20) (15,23) (16,24) (16,20) (16,23) (18,22) (18,20) (18,23) (19,21) (20,22) (22,24) (22,23) (23,24)\nQ: Is there a path between node 14 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "631"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,6) (0,3) (0,18) (0,1) (0,15) (0,12) (0,14) (0,9) (0,16) (0,8) (0,2) (0,11) (0,19) (1,7) (1,6) (1,3) (1,18) (1,15) (1,9) (1,8) (1,2) (1,20) (2,7) (2,3) (2,18) (2,15) (2,12) (2,14) (2,9) (2,16) (2,8) (2,11) (2,19) (2,20) (3,18) (3,15) (3,12) (3,9) (3,16) (3,8) (3,19) (3,20) (4,13) (4,17) (5,17) (6,7) (6,18) (6,15) (6,14) (6,9) (6,16) (6,11) (6,19) (6,20) (7,15) (7,12) (7,14) (7,9) (7,16) (8,18) (8,12) (8,14) (8,9) (8,16) (8,11) (8,19) (8,20) (9,18) (9,15) (9,12) (9,11) (9,19) (9,20) (10,13) (11,18) (11,12) (11,14) (11,16) (11,19) (11,20) (12,18) (12,15) (12,14) (12,19) (12,20) (13,17) (14,19) (16,18) (16,19) (18,20)\nQ: Is there a path between node 13 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "632"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,3) (0,2) (1,5) (1,3) (2,5) (2,3) (3,5)\nQ: Is there a path between node 0 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "633"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,1) (2,3) (4,6) (5,6) (5,7)\nQ: Is there a path between node 5 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "634"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (0,1) (0,19) (0,15) (0,20) (0,9) (0,21) (0,3) (0,22) (0,32) (0,24) (0,14) (0,11) (0,17) (0,5) (0,34) (0,4) (0,26) (0,10) (0,8) (1,27) (1,23) (1,30) (1,6) (1,19) (1,20) (1,2) (1,9) (1,21) (1,3) (1,22) (1,24) (1,14) (1,11) (1,17) (1,5) (1,4) (1,26) (1,8) (2,27) (2,30) (2,6) (2,19) (2,20) (2,9) (2,21) (2,3) (2,22) (2,32) (2,7) (2,11) (2,17) (2,5) (2,34) (2,4) (2,26) (2,12) (2,10) (3,27) (3,23) (3,30) (3,6) (3,19) (3,15) (3,20) (3,9) (3,22) (3,24) (3,14) (3,34) (3,4) (3,12) (3,10) (3,8) (3,28) (4,27) (4,23) (4,30) (4,19) (4,15) (4,20) (4,9) (4,21) (4,32) (4,24) (4,14) (4,7) (4,11) (4,17) (4,5) (4,26) (4,12) (4,8) (4,28) (5,30) (5,19) (5,9) (5,21) (5,24) (5,7) (5,11) (5,17) (5,34) (5,12) (6,27) (6,23) (6,30) (6,19) (6,20) (6,9) (6,21) (6,22) (6,32) (6,24) (6,14) (6,7) (6,11) (6,17) (6,34) (6,26) (6,8) (6,28) (7,23) (7,30) (7,19) (7,15) (7,20) (7,21) (7,32) (7,24) (7,11) (7,17) (7,34) (7,12) (7,10) (7,8) (7,28) (8,23) (8,15) (8,20) (8,24) (8,14) (8,11) (8,17) (8,34) (8,26) (8,12) (8,10) (8,28) (9,30) (9,19) (9,15) (9,20) (9,22) (9,32) (9,24) (9,11) (9,34) (9,12) (9,10) (9,28) (10,27) (10,23) (10,30) (10,19) (10,21) (10,32) (10,24) (10,26) (10,12) (11,27) (11,30) (11,19) (11,20) (11,21) (11,22) (11,32) (11,24) (11,14) (11,17) (11,34) (11,12) (12,27) (12,30) (12,19) (12,20) (12,22) (12,32) (12,24) (12,14) (12,17) (12,34) (12,28) (14,27) (14,23) (14,30) (14,19) (14,15) (14,21) (14,22) (14,32) (14,17) (14,34) (14,28) (15,19) (15,20) (15,21) (15,22) (15,32) (15,24) (15,34) (15,26) (15,28) (16,33) (16,29) (16,18) (16,31) (17,27) (17,23) (17,30) (17,19) (17,20) (17,21) (17,22) (17,32) (17,24) (17,34) (17,28) (18,33) (18,31) (18,25) (19,27) (19,23) (19,30) (19,20) (19,22) (19,32) (19,34) (19,26) (19,28) (20,23) (20,30) (20,21) (20,22) (20,32) (20,24) (20,34) (20,26) (21,27) (21,23) (21,30) (21,22) (21,32) (21,24) (21,34) (21,26) (21,28) (22,27) (22,23) (22,24) (22,34) (22,26) (22,28) (23,32) (23,26) (23,28) (24,27) (24,32) (24,34) (24,26) (25,33) (26,30) (26,32) (26,34) (27,30) (27,32) (27,28) (28,30) (28,32) (28,34) (29,33) (29,31) (31,33) (32,34)\nQ: Is there a path between node 31 and node 34?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "635"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,18) (0,1) (0,8) (0,10) (0,11) (0,7) (0,4) (0,2) (0,6) (0,17) (0,14) (1,19) (1,18) (1,8) (1,10) (1,11) (1,7) (1,4) (1,2) (1,6) (1,17) (1,14) (2,19) (2,18) (2,8) (2,10) (2,11) (2,7) (2,4) (2,6) (2,17) (2,14) (3,13) (3,9) (3,15) (4,19) (4,18) (4,8) (4,10) (4,11) (4,7) (4,6) (4,17) (4,14) (5,12) (5,16) (6,19) (6,18) (6,8) (6,10) (6,11) (6,7) (6,17) (6,14) (7,19) (7,18) (7,8) (7,10) (7,11) (7,17) (7,14) (8,19) (8,18) (8,10) (8,11) (8,17) (8,14) (9,13) (9,15) (10,19) (10,18) (10,11) (10,17) (10,14) (11,19) (11,18) (11,17) (11,14) (12,16) (13,15) (14,19) (14,18) (14,17) (17,19) (17,18) (18,19)\nQ: Is there a path between node 5 and node 12?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "636"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,6) (0,4) (1,3) (1,7) (1,2) (2,3) (3,9) (4,6) (5,9) (6,8) (7,9)\nQ: Is there a path between node 8 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "637"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,32) (0,29) (0,7) (0,15) (1,30) (1,10) (1,8) (2,27) (2,18) (2,20) (2,7) (2,26) (3,14) (3,9) (4,18) (4,11) (4,13) (4,15) (5,30) (5,21) (6,14) (6,21) (6,17) (7,18) (7,22) (7,31) (7,29) (7,26) (8,14) (8,10) (9,21) (10,12) (10,21) (10,17) (11,19) (11,22) (11,28) (11,32) (11,29) (11,15) (11,26) (12,30) (12,21) (13,27) (13,20) (13,28) (13,31) (14,17) (15,20) (15,31) (15,26) (16,27) (16,32) (17,30) (18,27) (18,28) (18,32) (18,26) (18,24) (18,23) (19,27) (19,20) (19,31) (19,29) (19,26) (19,24) (20,25) (20,28) (20,32) (20,26) (22,31) (22,23) (23,27) (23,28) (23,26) (25,26) (26,27) (26,28) (26,29) (28,32) (28,31) (29,31)\nQ: Is there a path between node 9 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "638"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,3) (0,13) (0,15) (0,7) (1,4) (1,6) (2,9) (2,18) (2,13) (3,12) (4,11) (6,8) (6,17) (7,16) (7,12) (7,13) (7,14) (8,11) (8,17) (8,20) (9,18) (9,21) (9,14) (9,15) (10,12) (12,16) (12,15) (13,18) (13,15) (14,16) (14,21) (15,16) (15,18) (16,18)\nQ: Is there a path between node 8 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "639"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,9) (0,14) (0,18) (0,3) (0,1) (0,17) (0,4) (0,8) (0,7) (0,15) (0,11) (0,10) (0,13) (1,5) (1,9) (1,14) (1,18) (1,3) (1,17) (1,4) (1,8) (1,7) (1,15) (1,11) (1,10) (1,13) (3,5) (3,9) (3,14) (3,18) (3,17) (3,4) (3,8) (3,7) (3,15) (3,11) (3,10) (3,13) (4,5) (4,9) (4,14) (4,18) (4,17) (4,8) (4,7) (4,15) (4,11) (4,10) (4,13) (5,9) (5,14) (5,18) (5,17) (5,8) (5,7) (5,15) (5,11) (5,10) (5,13) (6,12) (6,16) (7,9) (7,14) (7,18) (7,17) (7,8) (7,15) (7,11) (7,10) (7,13) (8,9) (8,14) (8,18) (8,17) (8,15) (8,11) (8,10) (8,13) (9,14) (9,18) (9,17) (9,15) (9,11) (9,10) (9,13) (10,14) (10,18) (10,17) (10,15) (10,11) (10,13) (11,14) (11,18) (11,17) (11,15) (11,13) (12,16) (13,14) (13,18) (13,17) (13,15) (14,18) (14,17) (14,15) (15,18) (15,17) (17,18)\nQ: Is there a path between node 8 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "640"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,14) (0,12) (1,20) (1,12) (2,13) (2,18) (3,17) (4,20) (7,21) (8,18) (9,20) (9,15) (10,13) (10,19) (13,18) (14,16) (14,15) (15,20)\nQ: Is there a path between node 13 and node 17?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "641"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,21) (0,7) (0,6) (0,3) (0,17) (0,20) (0,22) (0,16) (0,23) (0,25) (0,27) (1,5) (1,21) (1,4) (1,7) (1,15) (1,18) (1,2) (1,24) (1,20) (1,11) (1,16) (1,25) (1,27) (2,14) (2,5) (2,21) (2,4) (2,15) (2,24) (2,22) (2,11) (2,23) (2,25) (2,27) (3,14) (3,13) (3,21) (3,7) (3,15) (3,6) (3,17) (3,24) (3,22) (3,11) (3,16) (3,23) (4,14) (4,13) (4,5) (4,19) (4,7) (4,18) (4,17) (4,22) (4,11) (4,23) (4,25) (4,27) (5,13) (5,19) (5,15) (5,18) (5,24) (5,20) (5,22) (5,11) (5,23) (5,27) (6,14) (6,21) (6,19) (6,7) (6,15) (6,18) (6,17) (6,24) (6,20) (6,11) (6,16) (6,25) (6,27) (7,14) (7,13) (7,21) (7,19) (7,15) (7,18) (7,17) (7,20) (7,22) (7,11) (7,23) (7,27) (8,30) (8,28) (9,31) (9,10) (9,26) (9,29) (10,31) (10,26) (10,29) (11,13) (11,21) (11,19) (11,15) (11,24) (11,22) (11,25) (11,27) (12,28) (13,14) (13,21) (13,15) (13,18) (13,17) (13,24) (13,20) (13,16) (13,23) (13,25) (13,27) (14,21) (14,19) (14,24) (14,20) (14,22) (14,16) (14,23) (14,25) (15,21) (15,18) (15,17) (15,24) (15,20) (15,22) (15,16) (15,25) (15,27) (16,21) (16,18) (16,17) (16,24) (16,20) (16,22) (16,25) (17,21) (17,19) (17,18) (17,24) (17,20) (17,22) (17,23) (17,25) (17,27) (18,21) (18,24) (18,20) (18,25) (18,27) (19,21) (19,20) (19,22) (19,27) (20,21) (20,24) (20,22) (20,23) (20,27) (21,24) (21,22) (21,25) (21,27) (22,25) (23,25) (23,27) (25,27) (26,31) (26,29) (29,31)\nQ: Is there a path between node 19 and node 16?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "642"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,1) (0,15) (0,6) (0,9) (0,4) (0,16) (0,19) (1,20) (1,15) (1,6) (1,9) (1,4) (1,16) (1,19) (2,14) (2,10) (2,3) (2,11) (2,7) (2,18) (2,5) (2,12) (2,17) (2,8) (3,14) (3,10) (3,11) (3,7) (3,18) (3,5) (3,12) (3,17) (3,8) (4,20) (4,15) (4,6) (4,9) (4,16) (4,19) (5,14) (5,10) (5,11) (5,7) (5,18) (5,12) (5,17) (5,8) (6,20) (6,15) (6,9) (6,16) (6,19) (7,14) (7,10) (7,11) (7,18) (7,12) (7,17) (7,8) (8,14) (8,10) (8,11) (8,18) (8,12) (8,17) (9,20) (9,15) (9,16) (9,19) (10,14) (10,11) (10,18) (10,12) (10,17) (11,14) (11,18) (11,12) (11,17) (12,14) (12,18) (12,17) (14,18) (14,17) (15,20) (15,16) (15,19) (16,20) (16,19) (17,18) (19,20)\nQ: Is there a path between node 13 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "643"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,13) (0,8) (0,18) (0,25) (0,14) (0,17) (0,21) (1,13) (1,26) (1,14) (1,20) (1,17) (1,24) (1,6) (2,8) (2,18) (2,9) (2,26) (2,14) (2,10) (2,15) (3,16) (3,12) (4,13) (4,8) (4,18) (4,25) (4,6) (5,19) (5,13) (5,10) (5,20) (5,22) (5,17) (5,6) (6,8) (6,18) (6,9) (6,26) (6,14) (6,17) (6,21) (6,15) (6,23) (7,25) (7,14) (7,22) (7,24) (7,15) (7,23) (8,13) (8,25) (8,24) (8,23) (9,25) (9,27) (9,26) (9,14) (9,17) (9,24) (9,23) (10,19) (10,13) (10,25) (10,22) (11,12) (12,16) (13,19) (13,18) (13,21) (14,19) (14,18) (14,22) (15,19) (15,25) (15,23) (17,25) (17,22) (17,21) (17,24) (18,21) (18,24) (19,26) (19,22) (19,24) (19,23) (20,25) (20,26) (20,24) (20,23) (21,27) (21,23) (22,25) (22,26) (22,23) (25,27) (25,26)\nQ: Is there a path between node 26 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "644"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,13) (0,17) (0,10) (0,5) (0,4) (0,16) (0,19) (0,20) (0,7) (0,8) (0,15) (0,1) (0,18) (0,9) (0,12) (1,13) (1,17) (1,10) (1,5) (1,4) (1,16) (1,19) (1,20) (1,7) (1,8) (1,15) (1,18) (1,9) (1,12) (2,11) (2,21) (2,3) (2,14) (3,11) (3,21) (3,14) (4,13) (4,17) (4,10) (4,5) (4,16) (4,19) (4,20) (4,7) (4,8) (4,15) (4,18) (4,9) (4,12) (5,13) (5,17) (5,10) (5,16) (5,19) (5,20) (5,7) (5,8) (5,15) (5,18) (5,9) (5,12) (7,13) (7,17) (7,10) (7,16) (7,19) (7,20) (7,8) (7,15) (7,18) (7,9) (7,12) (8,13) (8,17) (8,10) (8,16) (8,19) (8,20) (8,15) (8,18) (8,9) (8,12) (9,13) (9,17) (9,10) (9,16) (9,19) (9,20) (9,15) (9,18) (9,12) (10,13) (10,17) (10,16) (10,19) (10,20) (10,15) (10,18) (10,12) (11,21) (11,14) (12,13) (12,17) (12,16) (12,19) (12,20) (12,15) (12,18) (13,17) (13,16) (13,19) (13,20) (13,15) (13,18) (14,21) (15,17) (15,16) (15,19) (15,20) (15,18) (16,17) (16,19) (16,20) (16,18) (17,19) (17,20) (17,18) (18,19) (18,20) (19,20)\nQ: Is there a path between node 1 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "645"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,3) (0,7) (0,10) (0,13) (0,12) (0,16) (1,14) (1,2) (1,5) (1,9) (1,8) (1,15) (1,4) (1,6) (2,14) (2,5) (2,9) (2,8) (2,15) (2,4) (2,6) (3,11) (3,7) (3,10) (3,13) (3,12) (3,16) (4,14) (4,5) (4,9) (4,8) (4,15) (4,6) (5,14) (5,9) (5,8) (5,15) (5,6) (6,14) (6,9) (6,8) (6,15) (7,11) (7,10) (7,13) (7,12) (7,16) (8,14) (8,9) (8,15) (9,14) (9,15) (10,11) (10,13) (10,12) (10,16) (11,13) (11,12) (11,16) (12,13) (12,16) (13,16) (14,15)\nQ: Is there a path between node 0 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "646"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,11) (0,15) (0,25) (0,31) (0,23) (0,14) (1,28) (1,20) (1,12) (1,21) (1,19) (1,24) (1,27) (1,13) (1,6) (2,20) (2,22) (2,21) (2,19) (2,13) (2,6) (3,15) (3,4) (3,25) (3,23) (4,9) (4,15) (4,14) (5,8) (5,17) (5,10) (5,26) (5,7) (5,16) (6,20) (6,21) (6,19) (6,27) (6,13) (7,17) (7,16) (7,29) (8,17) (9,11) (9,15) (9,31) (9,23) (9,14) (10,17) (11,15) (11,30) (11,23) (11,14) (12,20) (12,22) (12,19) (12,27) (12,13) (12,18) (13,28) (13,22) (13,21) (13,24) (13,27) (13,18) (14,15) (14,25) (14,31) (14,23) (15,25) (15,30) (15,23) (16,26) (17,26) (17,29) (18,28) (18,20) (18,22) (18,21) (18,19) (18,24) (18,27) (19,22) (19,21) (19,24) (19,27) (20,28) (20,22) (20,21) (20,24) (20,27) (21,28) (21,22) (21,24) (22,24) (22,27) (23,30) (23,31) (24,28) (25,31) (27,28) (30,31)\nQ: Is there a path between node 18 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "647"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (2,8) (2,4) (2,3) (3,8) (5,7) (6,7)\nQ: Is there a path between node 0 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "648"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,17) (0,23) (0,22) (0,1) (0,9) (0,11) (0,14) (0,19) (0,12) (0,18) (0,8) (0,4) (0,16) (0,15) (0,10) (0,6) (1,20) (1,17) (1,23) (1,22) (1,9) (1,11) (1,14) (1,19) (1,12) (1,18) (1,8) (1,4) (1,16) (1,15) (1,10) (1,6) (2,13) (2,5) (2,3) (2,21) (2,7) (3,13) (3,5) (3,21) (3,7) (4,20) (4,17) (4,23) (4,22) (4,9) (4,11) (4,14) (4,19) (4,12) (4,18) (4,8) (4,16) (4,15) (4,10) (4,6) (5,13) (5,21) (5,7) (6,20) (6,17) (6,23) (6,22) (6,9) (6,11) (6,14) (6,19) (6,12) (6,18) (6,8) (6,16) (6,15) (6,10) (7,13) (7,21) (8,20) (8,17) (8,23) (8,22) (8,9) (8,11) (8,14) (8,19) (8,12) (8,18) (8,16) (8,15) (8,10) (9,20) (9,17) (9,23) (9,22) (9,11) (9,14) (9,19) (9,12) (9,18) (9,16) (9,15) (9,10) (10,20) (10,17) (10,23) (10,22) (10,11) (10,14) (10,19) (10,12) (10,18) (10,16) (10,15) (11,20) (11,17) (11,23) (11,22) (11,14) (11,19) (11,12) (11,18) (11,16) (11,15) (12,20) (12,17) (12,23) (12,22) (12,14) (12,19) (12,18) (12,16) (12,15) (13,21) (14,20) (14,17) (14,23) (14,22) (14,19) (14,18) (14,16) (14,15) (15,20) (15,17) (15,23) (15,22) (15,19) (15,18) (15,16) (16,20) (16,17) (16,23) (16,22) (16,19) (16,18) (17,20) (17,23) (17,22) (17,19) (17,18) (18,20) (18,23) (18,22) (18,19) (19,20) (19,23) (19,22) (20,23) (20,22) (22,23)\nQ: Is there a path between node 20 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "649"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (1,11) (1,9) (1,14) (2,5) (2,6) (3,11) (3,13) (4,11) (4,13) (4,15) (5,7) (5,6) (7,10) (8,11) (8,9) (9,14) (9,12) (11,13) (13,14) (13,15)\nQ: Is there a path between node 4 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "650"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,9) (1,10) (1,3) (2,6) (2,4) (2,7) (3,6) (3,10) (3,9) (3,12) (4,8) (5,9) (5,12) (6,9) (6,12) (6,7) (7,10) (7,9) (7,14) (8,10) (8,9) (8,14) (12,14)\nQ: Is there a path between node 11 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "651"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,13) (0,30) (0,1) (0,4) (0,2) (0,22) (1,30) (1,17) (1,5) (1,4) (1,25) (1,29) (2,3) (2,5) (2,23) (3,28) (3,24) (3,4) (3,6) (3,8) (3,12) (4,15) (4,24) (4,25) (4,7) (4,6) (4,29) (5,21) (5,23) (5,7) (5,12) (6,20) (6,28) (6,23) (7,13) (7,15) (7,16) (7,8) (7,12) (8,20) (8,30) (8,24) (8,17) (8,23) (10,19) (11,19) (11,26) (12,20) (12,16) (12,25) (12,18) (13,28) (13,18) (14,20) (15,28) (15,24) (15,23) (16,20) (16,30) (16,24) (16,29) (17,21) (17,28) (17,25) (18,21) (18,23) (18,29) (20,24) (20,23) (20,22) (20,29) (21,25) (21,23) (21,22) (22,25) (23,24) (23,29) (24,28) (24,29) (25,28) (26,27) (29,30)\nQ: Is there a path between node 29 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "652"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,13) (0,5) (0,11) (0,15) (0,10) (0,16) (0,14) (0,8) (0,9) (1,18) (1,12) (1,7) (1,6) (2,13) (2,11) (2,15) (2,17) (2,16) (2,14) (2,3) (2,8) (2,9) (3,5) (3,11) (3,4) (3,15) (3,10) (3,14) (3,8) (3,9) (4,13) (4,5) (4,17) (4,16) (4,14) (4,8) (5,17) (5,16) (5,14) (6,12) (6,19) (6,20) (6,7) (7,18) (8,15) (8,17) (8,16) (8,14) (8,9) (9,13) (9,11) (9,17) (9,16) (9,14) (10,11) (10,15) (10,17) (10,16) (10,14) (11,13) (11,15) (11,16) (12,18) (12,19) (12,20) (13,17) (13,14) (14,15) (14,17) (14,16) (15,17) (16,17) (18,19) (18,20) (19,20)\nQ: Is there a path between node 10 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "653"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (2,8) (2,4) (2,3) (3,8) (5,7) (6,7)\nQ: Is there a path between node 6 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "654"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,3) (0,2) (0,1) (1,6) (1,3) (1,2) (2,6) (2,3) (3,6) (4,5)\nQ: Is there a path between node 0 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "655"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,9) (0,8) (0,19) (0,13) (0,11) (1,15) (1,6) (1,3) (1,12) (1,4) (1,2) (1,23) (1,5) (1,16) (1,22) (1,17) (1,18) (1,21) (1,24) (1,25) (2,15) (2,3) (2,4) (2,20) (2,23) (2,22) (2,27) (2,18) (2,21) (2,24) (3,15) (3,4) (3,26) (3,20) (3,23) (3,5) (3,16) (3,14) (3,22) (3,27) (3,18) (3,21) (3,24) (3,25) (4,15) (4,6) (4,12) (4,26) (4,20) (4,5) (4,22) (4,27) (4,17) (4,21) (4,25) (5,15) (5,6) (5,12) (5,20) (5,16) (5,14) (5,22) (5,27) (5,18) (5,21) (5,25) (6,15) (6,12) (6,27) (6,17) (6,21) (6,24) (6,25) (7,19) (7,13) (8,9) (8,19) (8,13) (9,19) (9,10) (10,19) (10,13) (10,11) (11,13) (12,15) (12,26) (12,20) (12,14) (12,22) (12,21) (12,24) (13,19) (14,15) (14,26) (14,20) (14,16) (14,22) (14,17) (14,21) (14,24) (14,25) (15,26) (15,20) (15,23) (15,16) (15,22) (15,17) (15,18) (15,24) (16,26) (16,27) (16,18) (16,25) (17,26) (17,23) (17,18) (17,21) (17,24) (17,25) (18,26) (18,20) (18,22) (18,27) (18,24) (18,25) (20,26) (20,23) (20,22) (20,27) (20,24) (20,25) (21,22) (21,27) (21,24) (21,25) (22,23) (22,27) (22,24) (22,25) (23,27) (23,25) (24,26) (24,27) (25,26) (25,27) (26,27)\nQ: Is there a path between node 25 and node 17?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "656"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,19) (0,25) (0,2) (0,13) (0,1) (1,17) (1,24) (1,25) (1,11) (2,17) (2,25) (2,16) (2,13) (3,17) (4,23) (4,7) (4,14) (4,8) (5,18) (5,16) (6,18) (6,16) (6,21) (7,14) (7,15) (7,10) (8,23) (8,10) (9,14) (9,10) (10,23) (10,20) (11,17) (11,18) (11,25) (11,16) (11,13) (12,16) (13,17) (13,24) (13,25) (13,21) (14,15) (16,21) (17,19) (17,18) (17,25) (19,25) (19,21) (21,25)\nQ: Is there a path between node 4 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "657"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (2,3) (2,5) (3,5) (4,6)\nQ: Is there a path between node 2 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "658"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,6) (0,2) (0,5) (1,7) (1,16) (1,14) (1,17) (1,3) (1,9) (1,13) (1,10) (2,11) (2,6) (2,5) (3,7) (3,16) (3,14) (3,17) (3,9) (3,13) (3,10) (4,8) (4,15) (4,12) (5,11) (5,6) (6,11) (7,16) (7,14) (7,17) (7,9) (7,13) (7,10) (8,15) (8,12) (9,16) (9,14) (9,17) (9,13) (9,10) (10,16) (10,14) (10,17) (10,13) (12,15) (13,16) (13,14) (13,17) (14,16) (14,17) (16,17)\nQ: Is there a path between node 13 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "659"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,23) (1,6) (1,19) (1,7) (2,17) (2,24) (2,10) (2,20) (3,22) (3,27) (4,17) (4,15) (5,19) (5,12) (5,25) (6,19) (6,7) (7,18) (7,23) (8,16) (8,13) (9,27) (9,13) (10,21) (10,15) (10,11) (11,17) (11,26) (11,24) (11,14) (12,25) (12,23) (14,17) (14,26) (15,21) (17,26) (17,21) (17,24) (20,21) (20,24) (21,26) (21,24) (23,25)\nQ: Is there a path between node 22 and node 13?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "660"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (1,5) (1,18) (1,7) (1,22) (1,11) (1,20) (1,4) (1,23) (2,14) (2,10) (2,21) (2,15) (2,16) (2,3) (3,14) (3,10) (3,15) (3,16) (3,6) (3,19) (4,18) (4,7) (4,22) (4,11) (4,20) (4,23) (5,13) (5,7) (5,22) (5,11) (5,20) (5,23) (6,10) (6,21) (6,15) (6,16) (6,9) (6,8) (6,19) (7,13) (7,22) (7,20) (7,23) (8,10) (8,9) (8,19) (9,21) (9,15) (9,19) (10,21) (10,16) (10,19) (11,18) (11,13) (11,22) (11,23) (12,17) (13,22) (13,20) (14,15) (14,16) (14,19) (15,16) (15,19) (16,21) (16,19) (18,20) (18,23) (19,21) (20,22) (20,23) (22,23)\nQ: Is there a path between node 6 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "661"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,4) (0,12) (0,11) (0,10) (0,3) (0,17) (0,21) (0,27) (0,15) (0,23) (0,31) (0,29) (0,2) (0,8) (0,9) (0,14) (0,18) (1,5) (1,26) (1,13) (1,20) (1,32) (1,7) (2,19) (2,4) (2,28) (2,22) (2,16) (2,12) (2,10) (2,3) (2,17) (2,21) (2,27) (2,15) (2,23) (2,31) (2,29) (2,8) (2,9) (2,14) (2,18) (3,4) (3,22) (3,16) (3,12) (3,10) (3,17) (3,21) (3,27) (3,23) (3,31) (3,29) (3,6) (3,9) (3,14) (3,18) (4,16) (4,12) (4,11) (4,17) (4,21) (4,15) (4,30) (4,23) (4,29) (4,6) (4,8) (4,9) (4,18) (5,26) (5,13) (5,25) (5,24) (5,32) (5,7) (6,19) (6,22) (6,12) (6,11) (6,10) (6,17) (6,21) (6,27) (6,15) (6,30) (6,23) (6,31) (6,29) (6,9) (6,14) (7,26) (7,25) (7,32) (8,19) (8,28) (8,10) (8,17) (8,27) (8,15) (8,30) (8,23) (9,19) (9,28) (9,22) (9,16) (9,12) (9,10) (9,17) (9,21) (9,15) (9,30) (9,23) (9,29) (9,18) (10,19) (10,28) (10,22) (10,12) (10,11) (10,17) (10,21) (10,27) (10,15) (10,30) (10,23) (10,31) (10,29) (10,14) (10,18) (11,16) (11,12) (11,17) (11,21) (11,27) (11,15) (11,30) (11,31) (11,29) (11,14) (11,18) (12,19) (12,28) (12,22) (12,17) (12,27) (12,15) (12,30) (12,23) (12,31) (12,29) (12,14) (12,18) (13,26) (13,25) (13,20) (13,32) (14,28) (14,16) (14,17) (14,21) (14,27) (14,15) (14,31) (14,29) (14,18) (15,19) (15,22) (15,16) (15,17) (15,21) (15,27) (15,30) (15,23) (15,31) (15,29) (15,18) (16,19) (16,28) (16,22) (16,17) (16,21) (16,27) (16,30) (16,31) (16,18) (17,22) (17,21) (17,30) (17,31) (17,29) (17,18) (18,19) (18,28) (18,22) (18,21) (18,27) (18,29) (19,28) (19,22) (19,21) (19,30) (19,31) (19,29) (20,32) (21,28) (21,22) (21,27) (21,29) (22,28) (22,30) (22,23) (22,31) (22,29) (23,28) (23,27) (23,30) (23,31) (23,29) (24,26) (24,25) (25,26) (25,32) (26,32) (27,28) (27,30) (27,29) (28,30) (28,31) (28,29) (29,30) (29,31)\nQ: Is there a path between node 7 and node 28?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "662"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (1,2) (1,5) (5,6)\nQ: Is there a path between node 2 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "663"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,7) (0,13) (0,24) (0,19) (0,5) (0,10) (0,4) (0,2) (0,21) (0,17) (0,23) (0,9) (0,20) (0,15) (0,22) (1,3) (1,18) (1,6) (1,14) (1,8) (1,11) (2,12) (2,7) (2,13) (2,24) (2,19) (2,5) (2,10) (2,4) (2,21) (2,17) (2,23) (2,9) (2,20) (2,15) (2,22) (3,18) (3,6) (3,14) (3,8) (3,11) (4,12) (4,7) (4,13) (4,24) (4,19) (4,5) (4,10) (4,21) (4,17) (4,23) (4,9) (4,20) (4,15) (4,22) (5,12) (5,7) (5,13) (5,24) (5,19) (5,10) (5,21) (5,17) (5,23) (5,9) (5,20) (5,15) (5,22) (6,18) (6,14) (6,8) (6,11) (7,12) (7,13) (7,24) (7,19) (7,10) (7,21) (7,17) (7,23) (7,9) (7,20) (7,15) (7,22) (8,18) (8,14) (8,11) (9,12) (9,13) (9,24) (9,19) (9,10) (9,21) (9,17) (9,23) (9,20) (9,15) (9,22) (10,12) (10,13) (10,24) (10,19) (10,21) (10,17) (10,23) (10,20) (10,15) (10,22) (11,18) (11,14) (12,13) (12,24) (12,19) (12,21) (12,17) (12,23) (12,20) (12,15) (12,22) (13,24) (13,19) (13,21) (13,17) (13,23) (13,20) (13,15) (13,22) (14,18) (15,24) (15,19) (15,21) (15,17) (15,23) (15,20) (15,22) (17,24) (17,19) (17,21) (17,23) (17,20) (17,22) (19,24) (19,21) (19,23) (19,20) (19,22) (20,24) (20,21) (20,23) (20,22) (21,24) (21,23) (21,22) (22,24) (22,23) (23,24)\nQ: Is there a path between node 3 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "664"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,14) (0,20) (0,13) (1,2) (1,8) (1,9) (2,9) (4,10) (4,20) (5,21) (5,17) (5,9) (6,10) (6,14) (6,13) (7,21) (7,22) (8,9) (10,19) (10,18) (10,12) (10,13) (11,16) (11,18) (12,16) (12,19) (12,18) (13,19) (14,19) (16,18) (17,22) (18,19)\nQ: Is there a path between node 19 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "665"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,17) (1,4) (2,10) (3,19) (3,30) (3,13) (3,25) (3,8) (4,31) (5,16) (6,29) (6,11) (6,32) (7,14) (7,17) (8,21) (8,30) (8,13) (8,28) (9,20) (9,25) (11,29) (11,26) (11,22) (13,21) (13,15) (13,28) (13,23) (15,31) (15,16) (15,28) (15,23) (16,21) (16,25) (16,23) (18,29) (18,24) (20,31) (20,30) (20,25) (21,25) (22,24) (23,25) (23,28) (24,29) (24,32) (25,30) (26,32) (28,30)\nQ: Is there a path between node 20 and node 16?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "666"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,27) (0,23) (0,4) (0,20) (0,17) (0,6) (1,5) (1,22) (1,11) (1,19) (1,24) (1,2) (1,15) (1,8) (1,30) (1,9) (1,28) (1,18) (2,5) (2,22) (2,24) (2,15) (2,8) (2,30) (2,9) (2,28) (2,18) (3,26) (3,13) (4,21) (4,29) (4,23) (4,20) (4,17) (4,6) (5,22) (5,19) (5,24) (5,14) (5,30) (5,28) (5,18) (6,21) (6,29) (6,27) (6,23) (6,20) (6,17) (7,26) (7,10) (7,13) (7,16) (7,12) (8,11) (8,24) (8,14) (8,30) (8,9) (8,28) (8,18) (9,22) (9,11) (9,19) (9,15) (9,28) (10,16) (10,12) (11,15) (11,30) (11,28) (11,18) (12,13) (12,16) (13,26) (13,16) (13,25) (14,22) (14,19) (14,15) (14,30) (15,19) (15,30) (15,28) (15,18) (16,26) (16,25) (17,29) (17,23) (18,19) (18,24) (18,28) (19,30) (19,28) (20,21) (20,27) (21,29) (21,27) (21,23) (22,24) (22,28) (23,27) (24,30) (24,28) (25,26) (28,30)\nQ: Is there a path between node 11 and node 19?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "667"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,11) (0,15) (0,25) (0,31) (0,23) (0,14) (1,28) (1,20) (1,12) (1,21) (1,19) (1,24) (1,27) (1,13) (1,6) (2,20) (2,22) (2,21) (2,19) (2,13) (2,6) (3,15) (3,4) (3,25) (3,23) (4,9) (4,15) (4,14) (5,8) (5,17) (5,10) (5,26) (5,7) (5,16) (6,20) (6,21) (6,19) (6,27) (6,13) (7,17) (7,16) (7,29) (8,17) (9,11) (9,15) (9,31) (9,23) (9,14) (10,17) (11,15) (11,30) (11,23) (11,14) (12,20) (12,22) (12,19) (12,27) (12,13) (12,18) (13,28) (13,22) (13,21) (13,24) (13,27) (13,18) (14,15) (14,25) (14,31) (14,23) (15,25) (15,30) (15,23) (16,26) (17,26) (17,29) (18,28) (18,20) (18,22) (18,21) (18,19) (18,24) (18,27) (19,22) (19,21) (19,24) (19,27) (20,28) (20,22) (20,21) (20,24) (20,27) (21,28) (21,22) (21,24) (22,24) (22,27) (23,30) (23,31) (24,28) (25,31) (27,28) (30,31)\nQ: Is there a path between node 18 and node 17?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "668"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,21) (0,8) (0,11) (0,16) (0,13) (0,10) (0,20) (0,6) (0,4) (1,14) (1,17) (1,18) (1,5) (1,19) (1,2) (2,22) (2,14) (2,5) (3,8) (3,11) (3,10) (3,12) (3,6) (4,11) (4,13) (4,20) (4,12) (5,22) (5,14) (5,17) (5,18) (5,9) (5,19) (6,8) (6,11) (6,16) (6,13) (6,10) (6,20) (6,12) (7,15) (8,11) (8,13) (8,10) (8,20) (8,12) (9,22) (9,14) (9,17) (9,18) (9,19) (10,21) (10,13) (11,16) (11,13) (11,20) (11,12) (12,21) (12,16) (12,13) (12,20) (13,21) (13,16) (13,20) (14,22) (14,18) (16,21) (16,20) (17,22) (17,18) (17,19) (18,19) (20,21)\nQ: Is there a path between node 11 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "669"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (3,8) (3,9) (4,5) (8,9)\nQ: Is there a path between node 8 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "670"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,6) (1,4) (1,3) (1,2) (1,7) (2,10) (2,4) (2,8) (3,10) (3,6) (3,4) (3,8) (3,5) (4,6) (4,8) (4,5) (4,7) (5,10) (5,8) (6,10) (6,8) (7,10)\nQ: Is there a path between node 4 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "671"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,8) (0,18) (0,6) (0,1) (0,12) (0,3) (0,7) (0,14) (0,10) (0,19) (0,16) (0,13) (1,17) (1,8) (1,18) (1,2) (1,19) (2,8) (2,6) (2,20) (2,14) (3,17) (3,18) (3,6) (3,14) (3,10) (3,19) (4,17) (4,18) (4,6) (4,19) (4,13) (5,15) (6,17) (6,8) (6,18) (6,13) (7,17) (7,14) (7,10) (8,20) (9,15) (9,11) (10,17) (10,18) (11,15) (12,17) (12,18) (12,14) (12,19) (13,17) (13,18) (13,20) (14,17) (14,18) (14,20) (18,20) (19,20)\nQ: Is there a path between node 5 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "672"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (1,18) (1,8) (1,4) (2,15) (2,18) (2,11) (2,23) (2,4) (3,12) (3,5) (4,23) (4,25) (5,12) (5,17) (6,22) (6,13) (7,18) (7,23) (7,8) (9,17) (10,19) (10,17) (11,15) (12,24) (14,20) (14,22) (15,18) (16,20) (16,22) (20,22) (21,22) (23,25)\nQ: Is there a path between node 7 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "673"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,11) (0,5) (0,9) (0,6) (1,2) (1,7) (1,3) (1,10) (1,8) (2,7) (2,3) (2,10) (2,8) (3,7) (3,10) (3,8) (4,11) (4,5) (4,9) (4,6) (5,11) (5,9) (5,6) (6,11) (6,9) (7,10) (7,8) (8,10) (9,11)\nQ: Is there a path between node 1 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "674"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,17) (0,23) (0,22) (0,1) (0,9) (0,11) (0,14) (0,19) (0,12) (0,18) (0,8) (0,4) (0,16) (0,15) (0,10) (0,6) (1,20) (1,17) (1,23) (1,22) (1,9) (1,11) (1,14) (1,19) (1,12) (1,18) (1,8) (1,4) (1,16) (1,15) (1,10) (1,6) (2,13) (2,5) (2,3) (2,21) (2,7) (3,13) (3,5) (3,21) (3,7) (4,20) (4,17) (4,23) (4,22) (4,9) (4,11) (4,14) (4,19) (4,12) (4,18) (4,8) (4,16) (4,15) (4,10) (4,6) (5,13) (5,21) (5,7) (6,20) (6,17) (6,23) (6,22) (6,9) (6,11) (6,14) (6,19) (6,12) (6,18) (6,8) (6,16) (6,15) (6,10) (7,13) (7,21) (8,20) (8,17) (8,23) (8,22) (8,9) (8,11) (8,14) (8,19) (8,12) (8,18) (8,16) (8,15) (8,10) (9,20) (9,17) (9,23) (9,22) (9,11) (9,14) (9,19) (9,12) (9,18) (9,16) (9,15) (9,10) (10,20) (10,17) (10,23) (10,22) (10,11) (10,14) (10,19) (10,12) (10,18) (10,16) (10,15) (11,20) (11,17) (11,23) (11,22) (11,14) (11,19) (11,12) (11,18) (11,16) (11,15) (12,20) (12,17) (12,23) (12,22) (12,14) (12,19) (12,18) (12,16) (12,15) (13,21) (14,20) (14,17) (14,23) (14,22) (14,19) (14,18) (14,16) (14,15) (15,20) (15,17) (15,23) (15,22) (15,19) (15,18) (15,16) (16,20) (16,17) (16,23) (16,22) (16,19) (16,18) (17,20) (17,23) (17,22) (17,19) (17,18) (18,20) (18,23) (18,22) (18,19) (19,20) (19,23) (19,22) (20,23) (20,22) (22,23)\nQ: Is there a path between node 3 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "675"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,10) (0,17) (0,4) (0,21) (0,1) (0,2) (0,18) (0,7) (0,19) (0,11) (0,3) (0,5) (0,14) (1,6) (1,10) (1,17) (1,21) (1,16) (1,18) (1,7) (1,8) (1,11) (2,6) (2,10) (2,17) (2,4) (2,21) (2,16) (2,13) (2,18) (2,7) (2,8) (2,19) (2,3) (2,5) (3,6) (3,10) (3,17) (3,4) (3,21) (3,16) (3,13) (3,18) (3,7) (3,19) (4,10) (4,16) (4,18) (4,7) (4,8) (4,19) (4,5) (5,6) (5,16) (5,13) (5,18) (5,7) (5,8) (5,19) (5,14) (6,10) (6,17) (6,21) (6,16) (6,13) (6,18) (6,7) (6,19) (6,11) (6,14) (7,10) (7,17) (7,21) (7,16) (7,13) (7,18) (7,8) (7,19) (7,11) (7,14) (8,10) (8,17) (8,21) (8,16) (8,13) (8,18) (8,19) (8,11) (9,20) (10,17) (10,21) (10,13) (10,18) (10,19) (10,11) (10,14) (11,17) (11,16) (11,13) (11,18) (11,19) (12,15) (13,21) (13,16) (13,18) (13,19) (13,14) (14,17) (14,21) (14,16) (14,18) (14,19) (16,17) (16,21) (16,18) (17,18) (18,21) (18,19) (19,21)\nQ: Is there a path between node 21 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "676"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,21) (0,14) (0,1) (0,22) (0,16) (0,19) (0,5) (0,10) (0,20) (0,11) (0,24) (0,13) (1,21) (1,9) (1,3) (1,14) (1,22) (1,10) (1,20) (1,12) (1,11) (1,24) (1,13) (1,23) (2,8) (2,4) (2,18) (2,15) (3,9) (3,14) (3,16) (3,19) (3,7) (3,6) (3,5) (3,10) (3,11) (4,8) (4,17) (4,18) (4,15) (5,9) (5,14) (5,22) (5,7) (5,6) (5,10) (5,20) (5,12) (5,11) (5,13) (5,23) (6,21) (6,9) (6,22) (6,19) (6,7) (6,20) (6,12) (6,11) (6,13) (6,23) (7,21) (7,9) (7,14) (7,16) (7,19) (7,10) (7,20) (7,12) (7,11) (7,24) (7,13) (7,23) (8,17) (8,18) (8,15) (9,21) (9,16) (9,10) (9,20) (9,12) (9,11) (9,24) (9,13) (9,23) (10,22) (10,19) (10,12) (10,11) (10,13) (10,23) (11,21) (11,22) (11,19) (11,20) (11,12) (11,24) (11,13) (11,23) (12,21) (12,14) (12,22) (12,20) (12,24) (12,13) (12,23) (13,21) (13,14) (13,22) (13,16) (13,20) (13,23) (14,21) (14,16) (14,20) (14,24) (14,23) (15,18) (16,21) (16,22) (16,19) (16,20) (16,24) (16,23) (17,18) (19,21) (19,20) (19,24) (19,23) (20,21) (20,24) (20,23) (21,24) (21,23) (22,23) (23,24)\nQ: Is there a path between node 2 and node 23?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "677"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,30) (0,27) (0,33) (0,11) (0,5) (0,12) (0,20) (0,7) (0,28) (0,17) (0,6) (0,4) (0,32) (0,13) (0,3) (0,22) (0,31) (1,25) (1,29) (1,30) (1,27) (1,33) (1,2) (1,5) (1,12) (1,20) (1,28) (1,18) (1,16) (1,24) (1,6) (1,13) (1,3) (1,22) (1,31) (2,25) (2,23) (2,29) (2,30) (2,27) (2,33) (2,11) (2,5) (2,12) (2,7) (2,18) (2,16) (2,17) (2,24) (2,13) (2,22) (2,15) (3,25) (3,23) (3,29) (3,30) (3,12) (3,7) (3,18) (3,16) (3,24) (3,4) (3,13) (3,22) (3,31) (4,23) (4,29) (4,27) (4,33) (4,11) (4,5) (4,7) (4,18) (4,24) (4,32) (4,15) (4,31) (5,25) (5,23) (5,30) (5,27) (5,33) (5,11) (5,12) (5,20) (5,7) (5,28) (5,24) (5,6) (5,32) (5,13) (5,22) (5,15) (5,31) (6,25) (6,23) (6,30) (6,27) (6,33) (6,12) (6,20) (6,7) (6,18) (6,24) (6,32) (6,13) (7,25) (7,30) (7,27) (7,33) (7,20) (7,28) (7,18) (7,24) (7,32) (7,13) (7,22) (7,15) (7,31) (8,14) (8,26) (8,19) (9,14) (9,26) (9,19) (9,21) (9,10) (10,14) (10,26) (10,19) (11,23) (11,29) (11,30) (11,27) (11,33) (11,20) (11,18) (11,16) (11,17) (11,32) (11,13) (11,22) (11,15) (11,31) (12,25) (12,23) (12,29) (12,27) (12,33) (12,28) (12,16) (12,24) (12,13) (12,22) (12,15) (12,31) (13,25) (13,23) (13,29) (13,27) (13,33) (13,20) (13,28) (13,18) (13,16) (13,17) (13,24) (13,32) (13,15) (13,31) (14,26) (15,25) (15,23) (15,29) (15,30) (15,33) (15,16) (15,17) (15,24) (15,22) (15,31) (16,25) (16,23) (16,29) (16,30) (16,27) (16,28) (16,17) (16,24) (16,32) (16,22) (17,25) (17,23) (17,29) (17,33) (17,20) (17,18) (17,24) (17,31) (18,25) (18,29) (18,30) (18,33) (18,28) (18,24) (18,31) (20,25) (20,23) (20,30) (20,24) (20,32) (20,22) (20,31) (21,26) (22,25) (22,29) (22,30) (22,28) (22,24) (23,25) (23,29) (23,27) (23,28) (23,24) (23,32) (24,25) (24,29) (24,27) (24,33) (24,28) (24,31) (25,29) (25,30) (25,27) (25,28) (25,32) (25,31) (27,29) (27,30) (27,33) (27,28) (28,29) (28,30) (28,33) (28,32) (28,31) (29,30) (29,33) (29,32) (29,31) (30,33) (30,32) (30,31) (31,33) (31,32) (32,33)\nQ: Is there a path between node 26 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "678"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,8) (1,5) (2,3) (3,5) (3,11) (4,8) (5,9) (5,7) (5,10) (6,11)\nQ: Is there a path between node 2 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "679"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,1) (2,3) (4,6) (5,6) (5,7)\nQ: Is there a path between node 1 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "680"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,9) (0,13) (0,3) (0,1) (0,2) (0,7) (0,8) (0,11) (1,14) (1,13) (1,8) (1,10) (1,11) (1,5) (2,9) (2,13) (2,3) (2,7) (2,8) (2,10) (3,14) (3,9) (3,13) (3,8) (3,11) (3,5) (4,6) (4,12) (5,14) (5,9) (5,7) (5,8) (5,10) (5,11) (6,12) (7,14) (7,13) (7,8) (7,10) (8,14) (8,9) (8,10) (9,14) (9,13) (10,14) (10,13) (11,14) (13,14)\nQ: Is there a path between node 12 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "681"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,10) (0,15) (0,21) (0,1) (0,7) (0,29) (0,24) (0,16) (0,23) (0,17) (1,26) (1,10) (1,15) (1,7) (1,28) (1,29) (1,12) (1,24) (1,16) (1,3) (1,23) (2,14) (2,27) (2,34) (3,26) (3,32) (3,15) (3,21) (3,7) (3,28) (3,29) (3,12) (3,24) (3,23) (3,17) (4,9) (4,14) (4,27) (4,31) (5,19) (5,22) (5,13) (5,20) (5,25) (5,30) (5,8) (5,33) (6,9) (6,27) (6,34) (6,31) (7,26) (7,32) (7,10) (7,15) (7,21) (7,29) (7,12) (7,24) (7,16) (7,23) (7,17) (8,19) (8,22) (8,13) (8,20) (8,25) (8,18) (8,30) (8,33) (9,14) (9,34) (10,32) (10,15) (10,21) (10,29) (10,24) (10,23) (10,17) (11,19) (11,22) (11,13) (11,25) (11,18) (11,30) (12,26) (12,32) (12,15) (12,21) (12,24) (12,16) (12,23) (13,19) (13,20) (13,25) (13,18) (13,33) (14,27) (14,31) (15,26) (15,21) (15,28) (15,24) (15,16) (15,23) (15,17) (16,26) (16,32) (16,23) (16,17) (17,26) (17,32) (17,21) (17,28) (17,24) (18,19) (18,22) (18,20) (18,30) (19,22) (19,20) (19,25) (19,30) (20,25) (20,30) (20,33) (21,26) (21,32) (21,28) (21,29) (22,25) (22,30) (22,33) (23,32) (23,28) (23,29) (23,24) (24,32) (24,28) (25,30) (25,33) (26,32) (26,28) (27,31) (28,29) (30,33)\nQ: Is there a path between node 32 and node 17?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "682"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,13) (0,19) (0,11) (0,16) (0,20) (0,8) (0,5) (0,3) (0,2) (0,7) (0,6) (0,17) (0,14) (0,12) (0,1) (0,18) (0,10) (0,23) (0,9) (1,4) (1,13) (1,19) (1,11) (1,16) (1,20) (1,8) (1,5) (1,3) (1,2) (1,7) (1,6) (1,17) (1,14) (1,12) (1,18) (1,10) (1,23) (1,9) (2,4) (2,13) (2,19) (2,11) (2,16) (2,20) (2,8) (2,5) (2,3) (2,7) (2,6) (2,17) (2,14) (2,12) (2,18) (2,10) (2,23) (2,9) (3,4) (3,13) (3,19) (3,11) (3,16) (3,20) (3,8) (3,5) (3,7) (3,6) (3,17) (3,14) (3,12) (3,18) (3,10) (3,23) (3,9) (4,13) (4,19) (4,11) (4,16) (4,20) (4,8) (4,5) (4,7) (4,6) (4,17) (4,14) (4,12) (4,18) (4,10) (4,23) (4,9) (5,13) (5,19) (5,11) (5,16) (5,20) (5,8) (5,7) (5,6) (5,17) (5,14) (5,12) (5,18) (5,10) (5,23) (5,9) (6,13) (6,19) (6,11) (6,16) (6,20) (6,8) (6,7) (6,17) (6,14) (6,12) (6,18) (6,10) (6,23) (6,9) (7,13) (7,19) (7,11) (7,16) (7,20) (7,8) (7,17) (7,14) (7,12) (7,18) (7,10) (7,23) (7,9) (8,13) (8,19) (8,11) (8,16) (8,20) (8,17) (8,14) (8,12) (8,18) (8,10) (8,23) (8,9) (9,13) (9,19) (9,11) (9,16) (9,20) (9,17) (9,14) (9,12) (9,18) (9,10) (9,23) (10,13) (10,19) (10,11) (10,16) (10,20) (10,17) (10,14) (10,12) (10,18) (10,23) (11,13) (11,19) (11,16) (11,20) (11,17) (11,14) (11,12) (11,18) (11,23) (12,13) (12,19) (12,16) (12,20) (12,17) (12,14) (12,18) (12,23) (13,19) (13,16) (13,20) (13,17) (13,14) (13,18) (13,23) (14,19) (14,16) (14,20) (14,17) (14,18) (14,23) (15,21) (15,22) (16,19) (16,20) (16,17) (16,18) (16,23) (17,19) (17,20) (17,18) (17,23) (18,19) (18,20) (18,23) (19,20) (19,23) (20,23) (21,22)\nQ: Is there a path between node 3 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "683"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,5) (0,20) (0,7) (0,19) (0,1) (0,14) (0,12) (0,15) (0,18) (0,4) (1,10) (1,5) (1,7) (1,2) (1,14) (1,12) (1,3) (1,15) (1,16) (1,4) (2,10) (2,5) (2,20) (2,7) (2,19) (2,14) (2,12) (2,15) (2,16) (2,17) (2,18) (2,4) (3,5) (3,20) (3,7) (3,19) (3,14) (3,16) (3,17) (3,18) (4,10) (4,5) (4,20) (4,7) (4,19) (4,14) (4,12) (4,15) (4,16) (4,17) (5,20) (5,7) (5,19) (5,14) (5,12) (5,16) (5,17) (5,18) (6,11) (6,8) (7,10) (7,19) (7,14) (7,12) (7,15) (7,16) (7,17) (7,18) (8,11) (9,21) (9,13) (10,19) (10,14) (10,12) (10,16) (10,18) (12,20) (12,19) (12,14) (12,15) (12,16) (12,17) (14,20) (14,19) (14,15) (14,16) (14,17) (15,20) (15,19) (15,16) (15,17) (15,18) (16,20) (16,19) (16,17) (16,18) (17,20) (17,19) (17,18) (18,19) (19,20)\nQ: Is there a path between node 2 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "684"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (3,7) (4,6) (5,6)\nQ: Is there a path between node 5 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "685"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,18) (0,24) (0,5) (0,12) (0,26) (0,14) (0,16) (0,21) (0,9) (0,1) (0,28) (0,25) (1,3) (1,18) (1,24) (1,5) (1,12) (1,26) (1,14) (1,16) (1,21) (1,2) (1,23) (1,20) (1,28) (1,25) (2,3) (2,18) (2,10) (2,24) (2,5) (2,12) (2,26) (2,14) (2,16) (2,9) (2,23) (2,20) (2,28) (2,7) (2,25) (2,22) (2,13) (3,18) (3,24) (3,12) (3,26) (3,16) (3,9) (3,19) (3,7) (3,25) (3,22) (4,11) (4,27) (4,17) (4,15) (4,8) (5,18) (5,24) (5,12) (5,26) (5,14) (5,16) (5,21) (5,9) (5,23) (5,19) (5,20) (5,7) (5,13) (6,11) (6,27) (6,29) (6,15) (6,8) (7,18) (7,10) (7,12) (7,26) (7,14) (7,16) (7,21) (7,9) (7,20) (7,25) (7,22) (7,13) (8,11) (8,27) (8,29) (8,17) (8,15) (9,18) (9,10) (9,24) (9,16) (9,21) (9,19) (9,20) (9,28) (9,25) (9,13) (10,18) (10,24) (10,12) (10,26) (10,14) (10,16) (10,23) (10,20) (10,28) (10,25) (10,22) (10,13) (11,27) (11,29) (12,18) (12,24) (12,16) (12,21) (12,23) (12,20) (12,28) (12,22) (12,13) (13,18) (13,24) (13,26) (13,14) (13,16) (13,21) (13,23) (13,20) (13,28) (13,25) (13,22) (14,26) (14,16) (14,21) (14,23) (14,19) (14,20) (14,28) (14,25) (15,27) (15,17) (16,18) (16,24) (16,26) (16,20) (16,25) (16,22) (17,29) (18,24) (18,26) (18,23) (18,19) (18,20) (18,25) (18,22) (19,21) (19,23) (19,28) (19,25) (20,26) (20,23) (20,28) (20,25) (20,22) (21,26) (21,23) (21,28) (21,22) (22,26) (22,23) (22,25) (23,24) (23,26) (24,26) (24,28) (25,26)\nQ: Is there a path between node 20 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "686"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,24) (0,2) (0,7) (0,15) (0,14) (0,22) (0,10) (0,18) (0,5) (0,9) (0,4) (0,11) (0,8) (0,20) (0,13) (1,2) (1,7) (1,15) (1,14) (1,18) (1,5) (1,16) (1,9) (1,4) (1,11) (1,8) (1,13) (2,24) (2,7) (2,15) (2,14) (2,22) (2,18) (2,16) (2,9) (2,4) (2,11) (2,8) (2,20) (2,23) (3,21) (4,7) (4,14) (4,22) (4,18) (4,16) (4,13) (4,23) (5,24) (5,7) (5,15) (5,14) (5,22) (5,10) (5,18) (5,20) (5,23) (6,12) (7,24) (7,15) (7,14) (7,10) (7,18) (7,16) (7,9) (7,11) (7,8) (7,20) (7,13) (7,23) (8,24) (8,14) (8,10) (8,18) (8,9) (8,13) (8,23) (9,24) (9,15) (9,14) (9,22) (9,10) (9,16) (9,20) (9,23) (10,24) (10,15) (10,14) (10,22) (10,18) (10,16) (10,20) (11,15) (11,14) (11,18) (11,16) (11,20) (11,13) (11,23) (13,24) (13,15) (13,18) (13,16) (13,23) (14,24) (14,15) (14,22) (14,18) (14,16) (14,23) (15,24) (15,22) (15,18) (15,16) (15,20) (15,23) (16,24) (16,20) (16,23) (18,22) (18,20) (18,23) (19,21) (20,22) (22,24) (22,23) (23,24)\nQ: Is there a path between node 7 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "687"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,12) (0,11) (0,4) (2,10) (2,8) (2,4) (4,6) (4,11) (5,9) (6,7) (6,10) (6,11) (7,8) (8,10) (8,9) (9,12) (10,11)\nQ: Is there a path between node 6 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "688"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,8) (0,10) (0,12) (0,13) (1,10) (2,5) (2,16) (3,13) (4,16) (5,7) (5,14) (6,7) (7,16) (7,14) (9,13) (10,15) (11,12) (12,15)\nQ: Is there a path between node 15 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "689"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,3) (0,7) (0,10) (0,13) (0,12) (0,16) (1,14) (1,2) (1,5) (1,9) (1,8) (1,15) (1,4) (1,6) (2,14) (2,5) (2,9) (2,8) (2,15) (2,4) (2,6) (3,11) (3,7) (3,10) (3,13) (3,12) (3,16) (4,14) (4,5) (4,9) (4,8) (4,15) (4,6) (5,14) (5,9) (5,8) (5,15) (5,6) (6,14) (6,9) (6,8) (6,15) (7,11) (7,10) (7,13) (7,12) (7,16) (8,14) (8,9) (8,15) (9,14) (9,15) (10,11) (10,13) (10,12) (10,16) (11,13) (11,12) (11,16) (12,13) (12,16) (13,16) (14,15)\nQ: Is there a path between node 2 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "690"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,10) (0,25) (0,16) (0,24) (0,4) (0,8) (0,27) (0,19) (1,5) (1,28) (2,15) (3,12) (3,13) (3,21) (3,24) (3,4) (3,8) (4,26) (4,20) (4,21) (4,11) (4,9) (6,13) (6,14) (6,22) (6,21) (6,7) (6,23) (6,11) (7,12) (7,26) (7,20) (7,17) (7,14) (7,10) (7,25) (7,24) (7,8) (7,11) (7,19) (7,9) (8,25) (8,27) (8,11) (9,17) (9,14) (9,21) (9,23) (9,27) (9,11) (10,26) (10,20) (10,14) (10,25) (10,23) (10,24) (11,13) (11,17) (11,21) (11,25) (11,23) (11,19) (12,20) (12,17) (12,24) (13,26) (13,20) (13,17) (13,22) (13,25) (13,24) (13,19) (14,20) (14,16) (15,28) (15,18) (16,26) (16,21) (16,23) (17,26) (17,22) (17,23) (17,27) (18,28) (19,22) (20,23) (20,24) (20,27) (21,26) (21,27) (23,25) (24,25) (24,27) (25,27)\nQ: Is there a path between node 28 and node 22?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "691"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,8) (0,18) (0,6) (0,1) (0,12) (0,3) (0,7) (0,14) (0,10) (0,19) (0,16) (0,13) (1,17) (1,8) (1,18) (1,2) (1,19) (2,8) (2,6) (2,20) (2,14) (3,17) (3,18) (3,6) (3,14) (3,10) (3,19) (4,17) (4,18) (4,6) (4,19) (4,13) (5,15) (6,17) (6,8) (6,18) (6,13) (7,17) (7,14) (7,10) (8,20) (9,15) (9,11) (10,17) (10,18) (11,15) (12,17) (12,18) (12,14) (12,19) (13,17) (13,18) (13,20) (14,17) (14,18) (14,20) (18,20) (19,20)\nQ: Is there a path between node 5 and node 14?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "692"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,12) (0,1) (0,13) (0,14) (0,11) (0,20) (0,7) (0,21) (1,4) (1,13) (1,14) (1,16) (1,7) (1,21) (2,5) (2,22) (2,8) (2,15) (2,25) (2,9) (2,17) (2,26) (3,11) (3,20) (3,7) (4,13) (4,14) (4,11) (4,20) (4,21) (5,22) (5,18) (5,15) (5,23) (5,25) (5,17) (5,26) (5,24) (6,19) (7,12) (7,13) (7,14) (7,11) (7,20) (7,21) (8,22) (8,15) (8,23) (8,9) (8,17) (8,24) (9,18) (9,15) (9,23) (9,25) (9,17) (11,13) (11,14) (11,16) (11,20) (12,13) (12,14) (12,16) (12,20) (12,21) (13,16) (13,20) (14,16) (14,20) (14,21) (15,22) (15,18) (15,23) (15,25) (15,26) (15,24) (16,21) (17,22) (17,18) (17,23) (17,25) (18,25) (18,24) (20,21) (22,23) (22,25) (22,26) (22,24) (23,26) (23,24) (24,25) (25,26)\nQ: Is there a path between node 2 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "693"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,11) (0,15) (0,25) (0,31) (0,23) (0,14) (1,28) (1,20) (1,12) (1,21) (1,19) (1,24) (1,27) (1,13) (1,6) (2,20) (2,22) (2,21) (2,19) (2,13) (2,6) (3,15) (3,4) (3,25) (3,23) (4,9) (4,15) (4,14) (5,8) (5,17) (5,10) (5,26) (5,7) (5,16) (6,20) (6,21) (6,19) (6,27) (6,13) (7,17) (7,16) (7,29) (8,17) (9,11) (9,15) (9,31) (9,23) (9,14) (10,17) (11,15) (11,30) (11,23) (11,14) (12,20) (12,22) (12,19) (12,27) (12,13) (12,18) (13,28) (13,22) (13,21) (13,24) (13,27) (13,18) (14,15) (14,25) (14,31) (14,23) (15,25) (15,30) (15,23) (16,26) (17,26) (17,29) (18,28) (18,20) (18,22) (18,21) (18,19) (18,24) (18,27) (19,22) (19,21) (19,24) (19,27) (20,28) (20,22) (20,21) (20,24) (20,27) (21,28) (21,22) (21,24) (22,24) (22,27) (23,30) (23,31) (24,28) (25,31) (27,28) (30,31)\nQ: Is there a path between node 31 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "694"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,4) (1,5)\nQ: Is there a path between node 6 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "695"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,32) (0,29) (0,7) (0,15) (1,30) (1,10) (1,8) (2,27) (2,18) (2,20) (2,7) (2,26) (3,14) (3,9) (4,18) (4,11) (4,13) (4,15) (5,30) (5,21) (6,14) (6,21) (6,17) (7,18) (7,22) (7,31) (7,29) (7,26) (8,14) (8,10) (9,21) (10,12) (10,21) (10,17) (11,19) (11,22) (11,28) (11,32) (11,29) (11,15) (11,26) (12,30) (12,21) (13,27) (13,20) (13,28) (13,31) (14,17) (15,20) (15,31) (15,26) (16,27) (16,32) (17,30) (18,27) (18,28) (18,32) (18,26) (18,24) (18,23) (19,27) (19,20) (19,31) (19,29) (19,26) (19,24) (20,25) (20,28) (20,32) (20,26) (22,31) (22,23) (23,27) (23,28) (23,26) (25,26) (26,27) (26,28) (26,29) (28,32) (28,31) (29,31)\nQ: Is there a path between node 24 and node 22?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "696"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,3) (0,4) (1,3) (1,4) (3,4)\nQ: Is there a path between node 0 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "697"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,9) (1,10) (1,3) (2,6) (2,4) (2,7) (3,6) (3,10) (3,9) (3,12) (4,8) (5,9) (5,12) (6,9) (6,12) (6,7) (7,10) (7,9) (7,14) (8,10) (8,9) (8,14) (12,14)\nQ: Is there a path between node 4 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "698"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,6) (1,4) (1,3) (1,2) (1,7) (2,10) (2,4) (2,8) (3,10) (3,6) (3,4) (3,8) (3,5) (4,6) (4,8) (4,5) (4,7) (5,10) (5,8) (6,10) (6,8) (7,10)\nQ: Is there a path between node 9 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "699"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,13) (0,11) (0,21) (0,8) (0,18) (0,3) (0,7) (0,15) (0,20) (0,17) (0,10) (0,22) (0,1) (0,9) (0,6) (0,19) (1,23) (1,14) (1,5) (1,13) (1,11) (1,12) (1,21) (1,8) (1,18) (1,3) (1,25) (1,7) (1,28) (1,15) (1,20) (1,17) (1,10) (1,22) (1,9) (1,6) (1,16) (1,19) (3,27) (3,14) (3,5) (3,13) (3,4) (3,21) (3,18) (3,25) (3,28) (3,15) (3,20) (3,17) (3,22) (3,6) (3,16) (3,19) (4,27) (4,23) (4,5) (4,13) (4,11) (4,12) (4,8) (4,28) (4,15) (4,20) (4,17) (4,10) (4,24) (4,6) (5,27) (5,23) (5,14) (5,13) (5,11) (5,12) (5,21) (5,8) (5,18) (5,25) (5,7) (5,15) (5,10) (5,22) (5,24) (5,9) (5,6) (5,16) (5,19) (6,27) (6,14) (6,11) (6,12) (6,18) (6,25) (6,7) (6,20) (6,17) (6,10) (6,22) (6,24) (6,9) (6,16) (6,19) (7,23) (7,14) (7,13) (7,12) (7,21) (7,8) (7,25) (7,28) (7,20) (7,10) (7,22) (7,16) (7,19) (8,27) (8,13) (8,18) (8,25) (8,15) (8,17) (8,10) (8,22) (8,24) (8,9) (8,16) (8,19) (9,27) (9,23) (9,11) (9,21) (9,25) (9,28) (9,15) (9,20) (9,17) (9,10) (9,22) (9,24) (9,16) (9,19) (10,27) (10,14) (10,11) (10,12) (10,25) (10,28) (10,15) (10,20) (10,17) (10,24) (10,16) (10,19) (11,23) (11,21) (11,18) (11,25) (11,28) (11,15) (11,17) (11,22) (11,24) (11,19) (12,27) (12,23) (12,13) (12,21) (12,18) (12,25) (12,28) (12,15) (12,17) (12,22) (12,24) (12,16) (13,27) (13,14) (13,21) (13,18) (13,28) (13,15) (13,17) (13,24) (13,16) (13,19) (14,27) (14,25) (14,28) (14,15) (14,17) (14,22) (14,24) (14,16) (15,23) (15,21) (15,18) (15,25) (15,20) (15,24) (16,27) (16,23) (16,17) (16,24) (16,19) (17,27) (17,23) (17,18) (17,25) (17,28) (17,20) (17,22) (17,24) (17,19) (18,23) (18,21) (18,25) (18,28) (18,20) (18,22) (18,24) (18,19) (19,27) (19,23) (19,21) (19,25) (19,24) (20,27) (20,23) (20,21) (20,25) (20,24) (21,23) (21,22) (23,27) (23,24) (25,27) (25,28) (27,28)\nQ: Is there a path between node 10 and node 21?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "700"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (1,12) (1,19) (2,13) (3,20) (3,11) (4,7) (4,16) (4,18) (5,17) (5,7) (6,15) (6,20) (6,11) (7,20) (7,11) (8,12) (8,13) (8,19) (11,17) (11,15) (12,19) (16,17) (16,20) (17,20) (18,20)\nQ: Is there a path between node 1 and node 19?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "701"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,1) (0,13) (0,15) (0,16) (0,9) (0,14) (0,3) (0,12) (0,17) (0,2) (0,18) (1,11) (1,13) (1,15) (1,16) (1,9) (1,8) (1,14) (1,3) (1,4) (1,17) (1,18) (2,11) (2,13) (2,15) (2,9) (2,8) (2,14) (2,3) (2,12) (2,17) (2,18) (3,11) (3,13) (3,15) (3,16) (3,9) (3,8) (3,14) (3,12) (3,17) (3,18) (4,13) (4,15) (4,16) (4,8) (4,14) (4,12) (4,18) (5,6) (5,7) (5,10) (6,7) (6,10) (7,10) (8,11) (8,15) (8,16) (8,18) (9,11) (9,13) (9,15) (9,16) (9,14) (9,12) (9,17) (9,18) (11,13) (11,16) (11,17) (11,18) (12,15) (12,16) (12,17) (12,18) (13,15) (13,18) (14,15) (14,17) (15,16) (16,17) (16,18) (17,18)\nQ: Is there a path between node 15 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "702"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,2) (0,1) (0,4) (1,3) (1,2) (1,4) (1,6) (2,3) (2,4) (2,5) (3,4) (3,6) (4,6) (5,6)\nQ: Is there a path between node 6 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "703"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,2) (0,14) (0,7) (0,13) (1,17) (1,3) (1,10) (1,6) (2,11) (2,12) (2,14) (2,13) (3,17) (3,10) (3,6) (4,9) (4,5) (5,9) (5,16) (6,17) (6,8) (6,10) (7,11) (7,12) (7,14) (7,13) (8,17) (8,15) (9,18) (9,16) (10,17) (12,14) (12,13) (13,14) (15,17)\nQ: Is there a path between node 2 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "704"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,34) (0,1) (0,10) (0,12) (1,12) (2,24) (3,31) (3,30) (3,25) (4,19) (4,6) (5,8) (7,26) (10,20) (10,28) (10,17) (10,18) (12,20) (12,32) (12,17) (13,14) (13,15) (13,21) (13,26) (13,23) (14,15) (14,21) (15,26) (15,23) (16,21) (16,30) (17,20) (17,27) (17,32) (18,27) (18,34) (19,33) (20,27) (21,31) (21,22) (22,26) (22,31) (23,31) (26,31) (28,34) (30,31)\nQ: Is there a path between node 6 and node 21?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "705"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (1,8) (1,4) (1,5) (1,7) (1,2) (1,9) (1,6) (2,8) (2,4) (2,5) (2,7) (2,9) (2,6) (4,8) (4,5) (4,7) (4,9) (4,6) (5,8) (5,7) (5,9) (5,6) (6,8) (6,7) (6,9) (7,8) (7,9) (8,9)\nQ: Is there a path between node 7 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "706"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,22) (0,6) (0,11) (0,10) (0,4) (0,5) (0,9) (0,1) (0,13) (0,21) (0,20) (0,12) (1,22) (1,11) (1,10) (1,5) (1,16) (1,9) (1,13) (1,21) (1,20) (2,8) (2,19) (2,3) (2,18) (2,24) (3,19) (3,17) (3,24) (3,23) (4,22) (4,6) (4,16) (4,9) (4,21) (4,20) (5,22) (5,6) (5,14) (5,11) (5,16) (5,15) (5,9) (5,13) (5,21) (5,20) (6,22) (6,11) (6,10) (6,16) (6,13) (6,21) (6,12) (7,8) (7,17) (7,18) (7,24) (7,23) (8,17) (8,24) (9,14) (9,11) (9,10) (9,16) (9,15) (9,21) (9,20) (9,12) (10,22) (10,14) (10,11) (10,16) (10,15) (10,21) (10,20) (11,22) (11,16) (11,15) (11,20) (12,22) (12,14) (12,15) (12,13) (12,21) (12,20) (13,14) (13,16) (13,15) (13,21) (13,20) (14,22) (14,16) (14,15) (14,21) (15,16) (15,21) (16,22) (16,21) (16,20) (17,19) (17,18) (17,24) (17,23) (18,23) (19,24) (23,24)\nQ: Is there a path between node 14 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "707"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,17) (0,24) (1,11) (1,9) (1,3) (2,19) (2,29) (2,27) (3,7) (3,20) (4,23) (4,25) (5,17) (6,22) (7,29) (7,27) (7,9) (8,16) (8,30) (8,26) (8,18) (8,31) (9,11) (9,27) (10,13) (10,12) (11,19) (11,27) (12,26) (12,18) (14,28) (15,27) (16,30) (17,23) (18,26) (19,28) (20,29) (21,22) (23,24) (24,25) (27,28) (30,31)\nQ: Is there a path between node 12 and node 16?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "708"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,30) (0,6) (0,12) (1,15) (2,17) (2,4) (3,25) (3,30) (3,12) (4,18) (4,16) (4,20) (4,22) (4,28) (4,8) (4,17) (5,12) (5,11) (6,19) (7,9) (7,10) (8,22) (8,28) (8,21) (9,23) (10,12) (10,11) (11,30) (11,19) (11,12) (12,25) (12,19) (13,27) (13,26) (15,26) (16,18) (16,29) (16,20) (16,24) (16,22) (16,28) (16,17) (17,22) (17,28) (17,21) (18,29) (18,20) (18,24) (18,22) (19,30) (20,22) (20,28) (21,24) (24,28) (25,30)\nQ: Is there a path between node 20 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "709"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,7) (0,8) (0,9) (0,13) (0,14) (0,15) (0,5) (1,2) (1,12) (1,16) (1,11) (1,3) (1,6) (1,14) (1,4) (2,12) (2,7) (2,9) (2,13) (2,14) (3,16) (3,11) (3,7) (3,8) (3,14) (3,15) (3,5) (3,4) (4,12) (4,11) (4,8) (4,9) (4,13) (4,14) (4,5) (5,12) (5,16) (5,11) (5,7) (5,8) (5,13) (5,14) (5,15) (6,12) (6,16) (6,11) (6,7) (6,14) (6,15) (7,12) (7,16) (7,11) (7,8) (7,9) (7,13) (8,12) (8,16) (8,11) (8,9) (8,13) (8,14) (9,12) (9,16) (9,11) (9,14) (9,15) (11,12) (11,16) (11,14) (12,13) (12,15) (13,16) (13,15) (14,16)\nQ: Is there a path between node 1 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "710"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,14) (1,21) (1,3) (1,15) (1,7) (3,12) (4,10) (5,10) (6,22) (7,21) (7,15) (9,12) (11,13) (11,21) (14,20) (15,17) (15,21) (16,18) (18,22)\nQ: Is there a path between node 21 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "711"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,31) (0,11) (0,27) (0,18) (1,4) (1,12) (1,31) (1,7) (1,25) (1,8) (1,18) (2,17) (2,14) (2,6) (2,10) (2,19) (3,17) (3,22) (3,9) (4,12) (4,30) (4,31) (4,13) (4,27) (4,18) (5,29) (5,16) (5,22) (5,21) (5,20) (5,28) (5,19) (6,29) (6,9) (6,10) (6,28) (7,11) (7,27) (7,15) (7,18) (8,30) (8,23) (8,11) (9,14) (9,21) (9,10) (11,23) (11,18) (12,30) (12,31) (12,27) (12,25) (12,15) (12,18) (13,23) (13,25) (13,15) (14,29) (14,17) (16,24) (16,17) (16,20) (17,29) (18,30) (18,26) (20,29) (21,24) (22,24) (23,27) (23,25) (25,26) (25,27) (26,31) (27,31) (28,29)\nQ: Is there a path between node 24 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "712"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,2) (0,1) (1,5) (1,6) (2,6) (3,7) (4,7) (5,6)\nQ: Is there a path between node 2 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "713"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,12) (0,1) (0,7) (0,16) (0,13) (0,9) (0,2) (0,10) (0,21) (0,19) (0,3) (0,20) (0,8) (0,23) (0,5) (0,4) (0,6) (0,22) (1,15) (1,12) (1,7) (1,16) (1,13) (1,9) (1,2) (1,10) (1,21) (1,19) (1,3) (1,20) (1,8) (1,23) (1,5) (1,4) (1,6) (1,22) (2,15) (2,12) (2,7) (2,16) (2,13) (2,9) (2,10) (2,21) (2,19) (2,3) (2,20) (2,8) (2,23) (2,5) (2,4) (2,6) (2,22) (3,15) (3,12) (3,7) (3,16) (3,13) (3,9) (3,10) (3,21) (3,19) (3,20) (3,8) (3,23) (3,5) (3,4) (3,6) (3,22) (4,15) (4,12) (4,7) (4,16) (4,13) (4,9) (4,10) (4,21) (4,19) (4,20) (4,8) (4,23) (4,5) (4,6) (4,22) (5,15) (5,12) (5,7) (5,16) (5,13) (5,9) (5,10) (5,21) (5,19) (5,20) (5,8) (5,23) (5,6) (5,22) (6,15) (6,12) (6,7) (6,16) (6,13) (6,9) (6,10) (6,21) (6,19) (6,20) (6,8) (6,23) (6,22) (7,15) (7,12) (7,16) (7,13) (7,9) (7,10) (7,21) (7,19) (7,20) (7,8) (7,23) (7,22) (8,15) (8,12) (8,16) (8,13) (8,9) (8,10) (8,21) (8,19) (8,20) (8,23) (8,22) (9,15) (9,12) (9,16) (9,13) (9,10) (9,21) (9,19) (9,20) (9,23) (9,22) (10,15) (10,12) (10,16) (10,13) (10,21) (10,19) (10,20) (10,23) (10,22) (11,17) (11,14) (11,18) (12,15) (12,16) (12,13) (12,21) (12,19) (12,20) (12,23) (12,22) (13,15) (13,16) (13,21) (13,19) (13,20) (13,23) (13,22) (14,17) (14,18) (15,16) (15,21) (15,19) (15,20) (15,23) (15,22) (16,21) (16,19) (16,20) (16,23) (16,22) (17,18) (19,21) (19,20) (19,23) (19,22) (20,21) (20,23) (20,22) (21,23) (21,22) (22,23)\nQ: Is there a path between node 5 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "714"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,21) (0,11) (0,15) (0,4) (0,22) (0,5) (0,3) (0,6) (0,20) (0,13) (0,18) (0,9) (0,1) (0,12) (0,24) (0,16) (0,8) (0,23) (0,2) (1,21) (1,11) (1,15) (1,4) (1,22) (1,5) (1,3) (1,6) (1,20) (1,13) (1,18) (1,9) (1,12) (1,24) (1,16) (1,8) (1,23) (1,2) (2,21) (2,11) (2,15) (2,4) (2,22) (2,5) (2,3) (2,6) (2,20) (2,13) (2,18) (2,9) (2,12) (2,24) (2,16) (2,8) (2,23) (3,21) (3,11) (3,15) (3,4) (3,22) (3,5) (3,6) (3,20) (3,13) (3,18) (3,9) (3,12) (3,24) (3,16) (3,8) (3,23) (4,21) (4,11) (4,15) (4,22) (4,5) (4,6) (4,20) (4,13) (4,18) (4,9) (4,12) (4,24) (4,16) (4,8) (4,23) (5,21) (5,11) (5,15) (5,22) (5,6) (5,20) (5,13) (5,18) (5,9) (5,12) (5,24) (5,16) (5,8) (5,23) (6,21) (6,11) (6,15) (6,22) (6,20) (6,13) (6,18) (6,9) (6,12) (6,24) (6,16) (6,8) (6,23) (7,10) (7,14) (7,17) (7,19) (8,21) (8,11) (8,15) (8,22) (8,20) (8,13) (8,18) (8,9) (8,12) (8,24) (8,16) (8,23) (9,21) (9,11) (9,15) (9,22) (9,20) (9,13) (9,18) (9,12) (9,24) (9,16) (9,23) (10,14) (10,17) (10,19) (11,21) (11,15) (11,22) (11,20) (11,13) (11,18) (11,12) (11,24) (11,16) (11,23) (12,21) (12,15) (12,22) (12,20) (12,13) (12,18) (12,24) (12,16) (12,23) (13,21) (13,15) (13,22) (13,20) (13,18) (13,24) (13,16) (13,23) (14,17) (14,19) (15,21) (15,22) (15,20) (15,18) (15,24) (15,16) (15,23) (16,21) (16,22) (16,20) (16,18) (16,24) (16,23) (17,19) (18,21) (18,22) (18,20) (18,24) (18,23) (20,21) (20,22) (20,24) (20,23) (21,22) (21,24) (21,23) (22,24) (22,23) (23,24)\nQ: Is there a path between node 19 and node 18?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "715"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,3) (0,12) (0,6) (0,11) (1,16) (1,3) (1,12) (1,6) (1,11) (1,14) (1,10) (2,15) (2,7) (2,13) (2,5) (2,9) (2,4) (2,18) (3,17) (3,12) (3,11) (3,14) (4,15) (4,7) (4,5) (4,9) (4,8) (5,15) (5,13) (5,9) (5,8) (5,18) (6,16) (6,17) (6,12) (6,14) (6,10) (7,15) (7,13) (7,9) (7,18) (8,15) (8,9) (8,18) (9,13) (9,18) (10,16) (10,17) (10,12) (10,11) (11,16) (11,17) (11,12) (12,16) (12,17) (12,14) (13,15) (13,18) (14,16) (14,17) (15,18) (16,17)\nQ: Is there a path between node 16 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "716"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,10) (0,12) (0,20) (0,14) (0,8) (0,3) (0,6) (0,5) (0,15) (0,19) (0,7) (0,9) (0,22) (0,2) (0,21) (0,18) (1,4) (1,10) (1,12) (1,20) (1,8) (1,5) (1,15) (1,16) (1,19) (1,7) (1,9) (1,22) (1,2) (1,18) (2,4) (2,10) (2,12) (2,14) (2,3) (2,5) (2,15) (2,19) (2,7) (2,22) (2,21) (2,18) (3,4) (3,12) (3,20) (3,14) (3,6) (3,5) (3,15) (3,16) (3,19) (3,7) (3,9) (3,22) (3,21) (3,18) (4,10) (4,12) (4,8) (4,6) (4,5) (4,15) (4,16) (4,19) (4,7) (4,9) (4,21) (4,18) (5,12) (5,14) (5,8) (5,6) (5,15) (5,16) (5,19) (5,7) (5,9) (5,22) (5,18) (6,10) (6,12) (6,20) (6,14) (6,16) (6,19) (6,7) (6,9) (6,22) (6,21) (6,18) (7,10) (7,12) (7,14) (7,8) (7,16) (7,9) (7,22) (7,21) (7,18) (8,10) (8,12) (8,14) (8,15) (8,16) (8,19) (8,9) (8,21) (9,12) (9,20) (9,15) (9,16) (9,22) (9,21) (9,18) (10,12) (10,20) (10,14) (10,15) (10,16) (10,18) (12,16) (12,19) (13,17) (14,20) (14,16) (15,16) (15,22) (15,21) (16,20) (16,21) (16,18) (18,22) (18,21) (19,20) (19,22) (19,21) (21,22)\nQ: Is there a path between node 7 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "717"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,20) (0,27) (0,29) (0,26) (0,17) (0,3) (0,1) (0,16) (1,6) (1,7) (1,20) (1,19) (1,3) (1,33) (1,4) (2,27) (2,34) (2,26) (2,19) (2,17) (2,3) (2,21) (2,4) (3,6) (3,7) (3,11) (3,28) (3,29) (4,6) (4,28) (4,27) (4,29) (4,26) (4,19) (4,33) (4,23) (5,7) (5,11) (5,28) (5,19) (5,33) (5,16) (6,7) (6,28) (6,27) (6,26) (6,21) (7,34) (8,13) (8,12) (8,22) (8,15) (9,24) (9,12) (9,10) (10,25) (11,16) (11,23) (12,32) (12,18) (12,22) (12,15) (13,14) (14,18) (14,15) (15,30) (15,18) (16,27) (16,17) (16,23) (17,29) (17,19) (17,33) (17,23) (18,31) (18,24) (19,28) (19,27) (19,34) (19,29) (19,33) (19,21) (20,21) (21,26) (21,33) (22,30) (22,25) (25,30) (25,31) (26,28) (26,34) (26,29) (27,28) (30,32) (31,32)\nQ: Is there a path between node 7 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "718"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,15) (1,3) (1,20) (2,11) (3,12) (3,6) (3,16) (3,20) (5,14) (5,7) (6,20) (6,21) (7,13) (7,18) (8,14) (8,13) (9,12) (9,16) (9,21) (10,21) (11,17) (12,16) (14,18) (15,16) (15,21) (16,20) (20,21)\nQ: Is there a path between node 10 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "719"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,4) (0,11) (0,13) (1,8) (1,21) (1,10) (1,7) (1,2) (2,24) (2,8) (2,9) (2,10) (2,22) (3,5) (3,11) (3,13) (4,15) (4,6) (4,16) (4,11) (5,12) (5,15) (5,19) (5,18) (5,27) (6,19) (6,11) (7,26) (7,23) (7,9) (8,23) (8,9) (8,10) (8,22) (9,25) (9,14) (10,25) (10,17) (10,23) (11,20) (11,27) (12,15) (12,16) (12,18) (14,22) (15,19) (15,27) (16,19) (17,26) (17,24) (17,28) (17,23) (17,22) (19,20) (19,27) (21,26) (21,25) (21,29) (21,22) (22,29) (23,24) (23,29) (26,28)\nQ: Is there a path between node 10 and node 29?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "720"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,6) (1,4) (1,3) (1,2) (1,7) (2,10) (2,4) (2,8) (3,10) (3,6) (3,4) (3,8) (3,5) (4,6) (4,8) (4,5) (4,7) (5,10) (5,8) (6,10) (6,8) (7,10)\nQ: Is there a path between node 9 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "721"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,8) (0,10) (0,12) (0,13) (1,10) (2,5) (2,16) (3,13) (4,16) (5,7) (5,14) (6,7) (7,16) (7,14) (9,13) (10,15) (11,12) (12,15)\nQ: Is there a path between node 10 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "722"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (0,1) (0,19) (0,15) (0,20) (0,9) (0,21) (0,3) (0,22) (0,32) (0,24) (0,14) (0,11) (0,17) (0,5) (0,34) (0,4) (0,26) (0,10) (0,8) (1,27) (1,23) (1,30) (1,6) (1,19) (1,20) (1,2) (1,9) (1,21) (1,3) (1,22) (1,24) (1,14) (1,11) (1,17) (1,5) (1,4) (1,26) (1,8) (2,27) (2,30) (2,6) (2,19) (2,20) (2,9) (2,21) (2,3) (2,22) (2,32) (2,7) (2,11) (2,17) (2,5) (2,34) (2,4) (2,26) (2,12) (2,10) (3,27) (3,23) (3,30) (3,6) (3,19) (3,15) (3,20) (3,9) (3,22) (3,24) (3,14) (3,34) (3,4) (3,12) (3,10) (3,8) (3,28) (4,27) (4,23) (4,30) (4,19) (4,15) (4,20) (4,9) (4,21) (4,32) (4,24) (4,14) (4,7) (4,11) (4,17) (4,5) (4,26) (4,12) (4,8) (4,28) (5,30) (5,19) (5,9) (5,21) (5,24) (5,7) (5,11) (5,17) (5,34) (5,12) (6,27) (6,23) (6,30) (6,19) (6,20) (6,9) (6,21) (6,22) (6,32) (6,24) (6,14) (6,7) (6,11) (6,17) (6,34) (6,26) (6,8) (6,28) (7,23) (7,30) (7,19) (7,15) (7,20) (7,21) (7,32) (7,24) (7,11) (7,17) (7,34) (7,12) (7,10) (7,8) (7,28) (8,23) (8,15) (8,20) (8,24) (8,14) (8,11) (8,17) (8,34) (8,26) (8,12) (8,10) (8,28) (9,30) (9,19) (9,15) (9,20) (9,22) (9,32) (9,24) (9,11) (9,34) (9,12) (9,10) (9,28) (10,27) (10,23) (10,30) (10,19) (10,21) (10,32) (10,24) (10,26) (10,12) (11,27) (11,30) (11,19) (11,20) (11,21) (11,22) (11,32) (11,24) (11,14) (11,17) (11,34) (11,12) (12,27) (12,30) (12,19) (12,20) (12,22) (12,32) (12,24) (12,14) (12,17) (12,34) (12,28) (14,27) (14,23) (14,30) (14,19) (14,15) (14,21) (14,22) (14,32) (14,17) (14,34) (14,28) (15,19) (15,20) (15,21) (15,22) (15,32) (15,24) (15,34) (15,26) (15,28) (16,33) (16,29) (16,18) (16,31) (17,27) (17,23) (17,30) (17,19) (17,20) (17,21) (17,22) (17,32) (17,24) (17,34) (17,28) (18,33) (18,31) (18,25) (19,27) (19,23) (19,30) (19,20) (19,22) (19,32) (19,34) (19,26) (19,28) (20,23) (20,30) (20,21) (20,22) (20,32) (20,24) (20,34) (20,26) (21,27) (21,23) (21,30) (21,22) (21,32) (21,24) (21,34) (21,26) (21,28) (22,27) (22,23) (22,24) (22,34) (22,26) (22,28) (23,32) (23,26) (23,28) (24,27) (24,32) (24,34) (24,26) (25,33) (26,30) (26,32) (26,34) (27,30) (27,32) (27,28) (28,30) (28,32) (28,34) (29,33) (29,31) (31,33) (32,34)\nQ: Is there a path between node 31 and node 26?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "723"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,2) (0,1) (1,5) (1,6) (2,6) (3,7) (4,7) (5,6)\nQ: Is there a path between node 5 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "724"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,3) (0,2) (1,5) (1,3) (2,5) (2,3) (3,5)\nQ: Is there a path between node 2 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "725"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,24) (0,1) (0,6) (0,14) (1,10) (2,25) (2,5) (2,20) (2,18) (3,22) (3,6) (3,19) (3,23) (4,9) (4,18) (5,15) (5,25) (5,17) (5,20) (6,11) (6,24) (6,14) (6,7) (6,21) (7,24) (8,25) (8,17) (8,20) (8,18) (9,25) (10,24) (10,22) (10,21) (11,22) (11,19) (11,23) (12,15) (12,16) (12,17) (13,19) (13,14) (14,22) (14,19) (15,16) (15,18) (16,17) (17,20) (18,25) (19,24) (19,22) (20,25) (21,23) (22,24) (22,23)\nQ: Is there a path between node 23 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "726"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,3) (0,14) (1,8) (1,6) (1,14) (2,6) (2,12) (2,18) (3,8) (3,6) (3,12) (3,18) (4,12) (4,9) (4,14) (5,15) (5,16) (5,7) (6,8) (6,12) (6,14) (7,10) (9,11) (9,18) (15,17) (15,16)\nQ: Is there a path between node 5 and node 18?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "727"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,18) (0,1) (0,8) (0,10) (0,11) (0,7) (0,4) (0,2) (0,6) (0,17) (0,14) (1,19) (1,18) (1,8) (1,10) (1,11) (1,7) (1,4) (1,2) (1,6) (1,17) (1,14) (2,19) (2,18) (2,8) (2,10) (2,11) (2,7) (2,4) (2,6) (2,17) (2,14) (3,13) (3,9) (3,15) (4,19) (4,18) (4,8) (4,10) (4,11) (4,7) (4,6) (4,17) (4,14) (5,12) (5,16) (6,19) (6,18) (6,8) (6,10) (6,11) (6,7) (6,17) (6,14) (7,19) (7,18) (7,8) (7,10) (7,11) (7,17) (7,14) (8,19) (8,18) (8,10) (8,11) (8,17) (8,14) (9,13) (9,15) (10,19) (10,18) (10,11) (10,17) (10,14) (11,19) (11,18) (11,17) (11,14) (12,16) (13,15) (14,19) (14,18) (14,17) (17,19) (17,18) (18,19)\nQ: Is there a path between node 14 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "728"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,5) (0,7) (0,6) (0,2) (0,4) (0,8) (0,9) (1,10) (2,3) (2,5) (2,7) (2,6) (2,4) (2,8) (2,9) (2,11) (3,5) (3,4) (3,8) (3,11) (4,5) (4,6) (4,9) (4,11) (5,6) (5,8) (5,9) (6,7) (6,8) (6,9) (6,11) (7,8) (7,11) (8,9) (9,11)\nQ: Is there a path between node 10 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "729"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (1,3) (1,2) (1,6) (2,5) (2,6) (3,5) (5,6)\nQ: Is there a path between node 5 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "730"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,3) (0,11) (0,8) (0,2) (0,12) (0,9) (0,1) (1,4) (1,3) (1,6) (1,11) (1,8) (1,7) (1,10) (1,2) (1,12) (2,3) (2,6) (2,11) (2,8) (2,9) (3,6) (3,11) (3,8) (3,7) (3,10) (3,9) (4,6) (4,11) (4,8) (4,7) (4,10) (4,12) (4,9) (6,8) (6,10) (7,10) (7,12) (7,9) (8,11) (8,10) (8,12) (9,10) (10,12)\nQ: Is there a path between node 1 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "731"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,20) (0,27) (0,29) (0,26) (0,17) (0,3) (0,1) (0,16) (1,6) (1,7) (1,20) (1,19) (1,3) (1,33) (1,4) (2,27) (2,34) (2,26) (2,19) (2,17) (2,3) (2,21) (2,4) (3,6) (3,7) (3,11) (3,28) (3,29) (4,6) (4,28) (4,27) (4,29) (4,26) (4,19) (4,33) (4,23) (5,7) (5,11) (5,28) (5,19) (5,33) (5,16) (6,7) (6,28) (6,27) (6,26) (6,21) (7,34) (8,13) (8,12) (8,22) (8,15) (9,24) (9,12) (9,10) (10,25) (11,16) (11,23) (12,32) (12,18) (12,22) (12,15) (13,14) (14,18) (14,15) (15,30) (15,18) (16,27) (16,17) (16,23) (17,29) (17,19) (17,33) (17,23) (18,31) (18,24) (19,28) (19,27) (19,34) (19,29) (19,33) (19,21) (20,21) (21,26) (21,33) (22,30) (22,25) (25,30) (25,31) (26,28) (26,34) (26,29) (27,28) (30,32) (31,32)\nQ: Is there a path between node 15 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "732"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,4) (0,9) (0,5) (0,13) (1,14) (1,15) (1,12) (1,5) (1,7) (2,4) (2,6) (2,9) (2,12) (2,13) (4,11) (4,6) (4,15) (4,7) (4,8) (4,13) (5,11) (5,10) (5,14) (5,6) (5,9) (5,15) (5,12) (5,7) (5,13) (6,14) (7,14) (7,8) (9,13) (10,14) (12,15)\nQ: Is there a path between node 10 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "733"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,18) (0,17) (0,10) (1,7) (1,24) (1,27) (2,4) (2,8) (2,13) (2,19) (2,27) (3,16) (3,28) (3,9) (4,18) (4,6) (4,10) (4,11) (4,27) (6,20) (6,8) (6,7) (6,27) (7,8) (7,18) (7,17) (7,23) (7,24) (7,10) (7,13) (7,19) (7,11) (7,14) (8,17) (8,22) (8,24) (8,10) (8,11) (10,18) (10,17) (10,12) (10,11) (10,27) (11,17) (11,12) (12,20) (12,18) (12,17) (12,14) (13,20) (13,18) (13,24) (13,27) (13,26) (14,18) (15,28) (15,25) (16,25) (17,20) (17,18) (17,26) (18,22) (18,23) (18,19) (18,27) (19,23) (19,27) (19,26) (20,24) (22,23) (22,24) (22,26) (26,27)\nQ: Is there a path between node 5 and node 15?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "734"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,6) (3,4) (4,5) (5,10) (6,8) (8,9)\nQ: Is there a path between node 6 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "735"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,30) (0,27) (0,33) (0,11) (0,5) (0,12) (0,20) (0,7) (0,28) (0,17) (0,6) (0,4) (0,32) (0,13) (0,3) (0,22) (0,31) (1,25) (1,29) (1,30) (1,27) (1,33) (1,2) (1,5) (1,12) (1,20) (1,28) (1,18) (1,16) (1,24) (1,6) (1,13) (1,3) (1,22) (1,31) (2,25) (2,23) (2,29) (2,30) (2,27) (2,33) (2,11) (2,5) (2,12) (2,7) (2,18) (2,16) (2,17) (2,24) (2,13) (2,22) (2,15) (3,25) (3,23) (3,29) (3,30) (3,12) (3,7) (3,18) (3,16) (3,24) (3,4) (3,13) (3,22) (3,31) (4,23) (4,29) (4,27) (4,33) (4,11) (4,5) (4,7) (4,18) (4,24) (4,32) (4,15) (4,31) (5,25) (5,23) (5,30) (5,27) (5,33) (5,11) (5,12) (5,20) (5,7) (5,28) (5,24) (5,6) (5,32) (5,13) (5,22) (5,15) (5,31) (6,25) (6,23) (6,30) (6,27) (6,33) (6,12) (6,20) (6,7) (6,18) (6,24) (6,32) (6,13) (7,25) (7,30) (7,27) (7,33) (7,20) (7,28) (7,18) (7,24) (7,32) (7,13) (7,22) (7,15) (7,31) (8,14) (8,26) (8,19) (9,14) (9,26) (9,19) (9,21) (9,10) (10,14) (10,26) (10,19) (11,23) (11,29) (11,30) (11,27) (11,33) (11,20) (11,18) (11,16) (11,17) (11,32) (11,13) (11,22) (11,15) (11,31) (12,25) (12,23) (12,29) (12,27) (12,33) (12,28) (12,16) (12,24) (12,13) (12,22) (12,15) (12,31) (13,25) (13,23) (13,29) (13,27) (13,33) (13,20) (13,28) (13,18) (13,16) (13,17) (13,24) (13,32) (13,15) (13,31) (14,26) (15,25) (15,23) (15,29) (15,30) (15,33) (15,16) (15,17) (15,24) (15,22) (15,31) (16,25) (16,23) (16,29) (16,30) (16,27) (16,28) (16,17) (16,24) (16,32) (16,22) (17,25) (17,23) (17,29) (17,33) (17,20) (17,18) (17,24) (17,31) (18,25) (18,29) (18,30) (18,33) (18,28) (18,24) (18,31) (20,25) (20,23) (20,30) (20,24) (20,32) (20,22) (20,31) (21,26) (22,25) (22,29) (22,30) (22,28) (22,24) (23,25) (23,29) (23,27) (23,28) (23,24) (23,32) (24,25) (24,29) (24,27) (24,33) (24,28) (24,31) (25,29) (25,30) (25,27) (25,28) (25,32) (25,31) (27,29) (27,30) (27,33) (27,28) (28,29) (28,30) (28,33) (28,32) (28,31) (29,30) (29,33) (29,32) (29,31) (30,33) (30,32) (30,31) (31,33) (31,32) (32,33)\nQ: Is there a path between node 9 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "736"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,4) (1,23) (1,7) (1,18) (1,24) (1,32) (1,31) (1,21) (1,27) (1,11) (1,6) (1,29) (1,17) (1,20) (2,23) (2,7) (2,18) (2,33) (2,24) (2,31) (2,21) (2,8) (2,27) (2,11) (2,29) (2,17) (2,26) (3,9) (3,22) (3,13) (3,5) (3,30) (3,28) (3,16) (3,14) (3,15) (4,19) (4,10) (5,9) (5,22) (5,13) (5,28) (5,16) (5,14) (6,18) (6,32) (6,25) (6,21) (6,8) (6,11) (6,17) (6,20) (6,26) (7,18) (7,33) (7,24) (7,32) (7,25) (7,31) (7,21) (7,17) (7,20) (7,26) (8,18) (8,33) (8,32) (8,25) (8,31) (8,27) (8,11) (8,29) (8,20) (8,26) (9,22) (9,13) (9,30) (9,28) (9,14) (9,15) (10,19) (10,12) (11,18) (11,33) (11,24) (11,25) (11,31) (11,27) (11,29) (11,26) (12,19) (13,28) (13,15) (14,30) (14,28) (14,16) (14,15) (15,22) (15,30) (15,16) (16,22) (17,23) (17,18) (17,33) (17,25) (17,31) (17,21) (17,27) (17,29) (17,20) (17,26) (18,23) (18,32) (18,25) (18,21) (18,29) (18,20) (18,26) (20,23) (20,33) (20,32) (20,25) (20,31) (20,21) (20,27) (20,29) (20,26) (21,23) (21,33) (21,24) (21,25) (21,29) (23,33) (23,24) (23,25) (23,31) (23,27) (23,29) (23,26) (24,33) (24,32) (24,25) (24,27) (24,29) (24,26) (25,32) (25,31) (25,27) (25,29) (25,26) (26,33) (26,31) (26,27) (27,31) (27,29) (28,30) (31,32) (32,33)\nQ: Is there a path between node 11 and node 20?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "737"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (0,13) (0,3) (0,14) (0,15) (0,19) (0,7) (0,9) (0,10) (1,5) (1,18) (1,12) (1,13) (1,14) (1,6) (1,17) (1,16) (1,9) (1,10) (1,11) (2,18) (2,12) (2,13) (2,6) (2,15) (2,19) (2,7) (2,17) (2,16) (2,9) (2,10) (2,11) (3,18) (3,12) (3,13) (3,14) (3,6) (3,19) (3,17) (3,9) (3,10) (3,11) (5,18) (5,12) (5,13) (5,14) (5,6) (5,15) (5,19) (5,7) (5,16) (5,11) (6,18) (6,12) (6,7) (6,17) (6,16) (6,9) (6,10) (7,18) (7,12) (7,13) (7,15) (7,19) (7,17) (7,16) (7,10) (7,11) (9,18) (9,13) (9,15) (9,19) (9,16) (9,10) (10,18) (10,13) (10,14) (10,19) (10,17) (10,11) (11,12) (11,13) (11,14) (11,15) (11,19) (11,17) (11,16) (12,14) (12,19) (12,17) (12,16) (13,18) (13,15) (13,19) (13,17) (14,18) (14,15) (14,19) (14,17) (14,16) (15,18) (15,19) (15,16) (16,18) (17,18) (17,19) (18,19)\nQ: Is there a path between node 17 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "738"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,11) (0,1) (0,3) (0,10) (0,4) (1,11) (1,3) (1,10) (1,4) (2,7) (3,11) (3,4) (4,5) (4,11) (5,11) (6,9) (6,8) (7,9) (7,8) (8,9) (10,11)\nQ: Is there a path between node 2 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "739"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,12) (0,5) (0,6) (0,4) (0,8) (0,2) (0,9) (0,1) (0,7) (1,12) (1,5) (1,6) (1,4) (1,8) (1,2) (1,9) (1,10) (1,7) (2,8) (2,10) (2,7) (4,11) (4,12) (4,5) (4,6) (4,8) (4,9) (4,7) (5,11) (5,6) (5,8) (5,10) (5,7) (6,11) (6,12) (6,8) (6,9) (7,11) (7,12) (7,9) (7,10) (8,12) (8,9) (8,10) (9,11) (9,12) (9,10) (10,11) (10,12) (11,12)\nQ: Is there a path between node 0 and node 12?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "740"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,4) (0,15) (0,19) (0,8) (0,17) (0,13) (0,3) (0,14) (0,5) (0,2) (0,16) (0,1) (0,10) (1,20) (1,4) (1,15) (1,19) (1,8) (1,17) (1,13) (1,3) (1,14) (1,5) (1,2) (1,16) (1,10) (2,20) (2,4) (2,15) (2,19) (2,8) (2,17) (2,13) (2,3) (2,14) (2,5) (2,16) (2,10) (3,20) (3,4) (3,15) (3,19) (3,8) (3,17) (3,13) (3,14) (3,5) (3,16) (3,10) (4,20) (4,15) (4,19) (4,8) (4,17) (4,13) (4,14) (4,5) (4,16) (4,10) (5,20) (5,15) (5,19) (5,8) (5,17) (5,13) (5,14) (5,16) (5,10) (6,12) (6,22) (6,9) (6,18) (6,21) (6,7) (6,11) (7,12) (7,22) (7,9) (7,18) (7,21) (7,11) (8,20) (8,15) (8,19) (8,17) (8,13) (8,14) (8,16) (8,10) (9,12) (9,22) (9,18) (9,21) (9,11) (10,20) (10,15) (10,19) (10,17) (10,13) (10,14) (10,16) (11,12) (11,22) (11,18) (11,21) (12,22) (12,18) (12,21) (13,20) (13,15) (13,19) (13,17) (13,14) (13,16) (14,20) (14,15) (14,19) (14,17) (14,16) (15,20) (15,19) (15,17) (15,16) (16,20) (16,19) (16,17) (17,20) (17,19) (18,22) (18,21) (19,20) (21,22)\nQ: Is there a path between node 9 and node 12?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "741"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,6) (1,2) (3,7) (3,5)\nQ: Is there a path between node 3 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "742"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,8) (0,4) (0,5) (0,13) (0,2) (0,17) (1,15) (1,8) (1,3) (1,4) (1,5) (1,13) (1,17) (2,15) (2,8) (2,3) (2,4) (2,5) (2,13) (3,8) (3,5) (3,17) (4,15) (4,13) (4,17) (5,15) (5,8) (5,17) (6,14) (6,7) (6,10) (6,16) (6,9) (6,12) (7,14) (7,16) (7,9) (8,13) (9,14) (9,10) (9,11) (9,16) (9,12) (10,14) (10,12) (11,14) (11,12) (12,14) (12,16) (13,17) (15,17)\nQ: Is there a path between node 14 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "743"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,8) (0,2) (0,20) (0,16) (0,14) (0,15) (0,7) (1,18) (1,24) (1,22) (1,5) (1,19) (1,11) (1,17) (2,6) (2,4) (2,23) (2,8) (2,20) (2,16) (2,21) (2,14) (2,15) (2,10) (3,6) (3,4) (3,23) (3,8) (3,16) (3,14) (3,25) (3,15) (3,7) (4,6) (4,23) (4,8) (4,20) (4,16) (4,21) (4,14) (4,15) (4,10) (4,7) (5,18) (5,24) (5,22) (5,13) (5,9) (5,11) (5,12) (6,23) (6,8) (6,20) (6,16) (6,14) (6,25) (6,15) (7,23) (7,20) (7,16) (7,21) (7,14) (7,25) (7,15) (7,10) (8,20) (8,16) (8,14) (8,25) (8,15) (9,18) (9,24) (9,22) (9,19) (9,11) (9,17) (9,12) (10,23) (10,20) (10,16) (10,21) (10,14) (10,25) (11,22) (11,19) (11,17) (11,12) (12,18) (12,13) (12,19) (13,18) (13,24) (13,22) (13,17) (14,23) (14,20) (14,16) (14,25) (15,20) (15,16) (15,21) (15,25) (16,23) (16,20) (16,25) (17,18) (17,22) (17,19) (18,24) (18,22) (18,19) (19,24) (19,22) (20,21) (20,25) (21,23) (21,25) (22,24) (23,25)\nQ: Is there a path between node 24 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "744"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,22) (0,15) (0,8) (0,12) (0,14) (0,2) (0,9) (0,1) (1,15) (1,20) (1,12) (2,20) (2,12) (2,7) (2,16) (3,15) (3,7) (3,16) (3,13) (3,14) (3,17) (3,21) (4,22) (4,8) (4,12) (4,17) (4,11) (6,23) (7,15) (7,17) (7,11) (7,21) (7,18) (8,22) (8,15) (8,20) (8,16) (8,9) (9,22) (9,13) (9,11) (9,21) (9,18) (10,22) (10,13) (10,21) (11,22) (11,15) (11,20) (11,12) (11,21) (11,18) (12,15) (12,13) (13,20) (13,18) (14,20) (17,22) (17,18) (18,20) (19,23) (20,22) (21,22)\nQ: Is there a path between node 13 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "745"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,17) (0,1) (0,4) (0,15) (0,2) (0,13) (0,10) (0,6) (0,18) (0,11) (0,12) (0,5) (1,19) (1,17) (1,4) (1,15) (1,2) (1,13) (1,10) (1,6) (1,18) (1,11) (1,12) (1,5) (2,19) (2,17) (2,4) (2,15) (2,13) (2,10) (2,6) (2,18) (2,11) (2,12) (2,5) (3,20) (3,16) (3,14) (3,8) (4,19) (4,17) (4,15) (4,13) (4,10) (4,6) (4,18) (4,11) (4,12) (4,5) (5,19) (5,17) (5,15) (5,13) (5,10) (5,6) (5,18) (5,11) (5,12) (6,19) (6,17) (6,15) (6,13) (6,10) (6,18) (6,11) (6,12) (7,9) (8,20) (8,16) (8,14) (10,19) (10,17) (10,15) (10,13) (10,18) (10,11) (10,12) (11,19) (11,17) (11,15) (11,13) (11,18) (11,12) (12,19) (12,17) (12,15) (12,13) (12,18) (13,19) (13,17) (13,15) (13,18) (14,20) (14,16) (15,19) (15,17) (15,18) (16,20) (17,19) (17,18) (18,19)\nQ: Is there a path between node 7 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "746"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,8) (1,5) (2,3) (3,5) (3,11) (4,8) (5,9) (5,7) (5,10) (6,11)\nQ: Is there a path between node 5 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "747"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,11) (0,17) (0,3) (0,19) (0,9) (0,16) (0,15) (0,7) (0,12) (0,2) (1,11) (1,10) (1,3) (1,4) (1,8) (1,19) (1,13) (1,9) (1,16) (1,15) (1,7) (1,12) (1,2) (2,17) (2,5) (2,16) (2,15) (3,17) (3,10) (3,5) (3,6) (3,8) (3,13) (3,9) (3,16) (3,15) (3,7) (3,12) (4,11) (4,5) (4,8) (4,19) (4,13) (4,9) (4,7) (4,12) (5,11) (5,10) (5,6) (5,8) (5,19) (5,13) (5,7) (6,11) (6,17) (6,10) (6,8) (6,19) (6,13) (6,16) (6,15) (6,7) (6,12) (7,11) (7,17) (7,10) (7,19) (7,9) (7,16) (7,15) (8,11) (8,17) (8,10) (8,19) (8,13) (8,15) (8,12) (9,11) (9,17) (9,10) (9,13) (9,16) (9,15) (10,11) (10,17) (10,19) (10,13) (10,15) (10,12) (11,19) (11,15) (11,12) (12,17) (12,19) (12,13) (13,19) (13,16) (13,15) (14,18) (15,19) (15,16) (16,17) (17,19)\nQ: Is there a path between node 9 and node 18?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "748"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,22) (0,15) (0,8) (0,12) (0,14) (0,2) (0,9) (0,1) (1,15) (1,20) (1,12) (2,20) (2,12) (2,7) (2,16) (3,15) (3,7) (3,16) (3,13) (3,14) (3,17) (3,21) (4,22) (4,8) (4,12) (4,17) (4,11) (6,23) (7,15) (7,17) (7,11) (7,21) (7,18) (8,22) (8,15) (8,20) (8,16) (8,9) (9,22) (9,13) (9,11) (9,21) (9,18) (10,22) (10,13) (10,21) (11,22) (11,15) (11,20) (11,12) (11,21) (11,18) (12,15) (12,13) (13,20) (13,18) (14,20) (17,22) (17,18) (18,20) (19,23) (20,22) (21,22)\nQ: Is there a path between node 4 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "749"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,5) (3,5)\nQ: Is there a path between node 3 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "750"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,4) (0,11) (0,13) (1,8) (1,21) (1,10) (1,7) (1,2) (2,24) (2,8) (2,9) (2,10) (2,22) (3,5) (3,11) (3,13) (4,15) (4,6) (4,16) (4,11) (5,12) (5,15) (5,19) (5,18) (5,27) (6,19) (6,11) (7,26) (7,23) (7,9) (8,23) (8,9) (8,10) (8,22) (9,25) (9,14) (10,25) (10,17) (10,23) (11,20) (11,27) (12,15) (12,16) (12,18) (14,22) (15,19) (15,27) (16,19) (17,26) (17,24) (17,28) (17,23) (17,22) (19,20) (19,27) (21,26) (21,25) (21,29) (21,22) (22,29) (23,24) (23,29) (26,28)\nQ: Is there a path between node 28 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "751"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,6) (0,21) (0,18) (1,24) (1,3) (3,24) (3,14) (4,6) (4,5) (4,23) (6,14) (6,21) (6,23) (7,11) (8,19) (8,13) (9,15) (9,19) (10,11) (10,12) (10,16) (10,17) (11,12) (11,16) (12,17) (13,15) (13,22) (14,23) (15,22) (16,17) (18,24) (18,21)\nQ: Is there a path between node 0 and node 22?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "752"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,10) (0,26) (0,13) (0,23) (0,14) (0,27) (0,30) (0,31) (0,28) (0,2) (0,8) (0,12) (0,9) (0,24) (0,5) (1,19) (1,15) (1,6) (1,11) (1,29) (1,17) (1,21) (1,4) (1,25) (1,7) (2,3) (2,14) (2,31) (2,28) (2,18) (2,8) (2,12) (2,9) (2,24) (2,5) (3,10) (3,13) (3,23) (3,27) (3,30) (3,31) (3,28) (3,18) (3,8) (3,12) (3,9) (3,24) (3,5) (4,20) (4,19) (4,15) (4,11) (4,29) (4,16) (4,22) (4,7) (5,10) (5,13) (5,23) (5,14) (5,27) (5,31) (5,18) (5,8) (5,12) (5,9) (6,20) (6,15) (6,11) (6,29) (6,17) (6,21) (6,16) (6,25) (6,7) (7,20) (7,15) (7,11) (7,29) (7,17) (7,21) (7,25) (8,10) (8,26) (8,13) (8,23) (8,14) (8,27) (8,30) (8,12) (8,24) (9,10) (9,26) (9,13) (9,14) (9,27) (9,30) (9,31) (9,18) (9,24) (10,26) (10,13) (10,23) (10,14) (10,27) (10,30) (10,31) (10,18) (11,20) (11,19) (11,15) (11,29) (11,17) (11,21) (11,16) (11,25) (11,22) (12,13) (12,23) (12,14) (12,27) (12,28) (13,26) (13,23) (13,14) (13,27) (13,31) (13,28) (14,23) (14,30) (14,28) (14,18) (14,24) (15,19) (15,29) (15,21) (15,16) (15,22) (16,20) (16,19) (16,29) (16,17) (16,21) (16,25) (17,20) (17,19) (17,29) (17,21) (17,25) (17,22) (18,26) (18,27) (18,30) (18,31) (18,28) (19,29) (19,21) (19,25) (19,22) (20,29) (20,22) (21,29) (21,25) (21,22) (22,25) (23,26) (23,27) (23,30) (23,31) (23,24) (24,27) (24,30) (24,31) (25,29) (26,27) (26,30) (26,28) (27,30) (27,31) (28,30) (28,31) (30,31)\nQ: Is there a path between node 18 and node 30?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "753"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,6) (0,1) (0,5) (1,7) (1,6) (1,8) (1,5) (2,7) (2,8) (2,5) (3,4) (5,7) (5,6) (5,8)\nQ: Is there a path between node 2 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "754"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,16) (0,9) (0,3) (0,4) (0,8) (0,17) (1,6) (1,12) (1,13) (1,18) (1,2) (1,4) (1,8) (1,17) (2,6) (2,12) (2,15) (2,9) (2,13) (2,18) (2,4) (2,8) (2,17) (3,6) (3,16) (3,12) (3,9) (3,13) (3,18) (3,8) (3,17) (3,5) (4,6) (4,16) (4,12) (4,9) (4,18) (4,17) (4,5) (5,6) (5,12) (5,15) (5,9) (5,17) (6,12) (6,15) (6,9) (6,13) (6,18) (6,8) (7,10) (7,11) (7,19) (8,16) (8,15) (8,9) (8,18) (9,16) (9,12) (9,15) (9,13) (9,18) (9,17) (10,19) (11,14) (11,19) (12,16) (12,15) (12,13) (12,17) (13,18) (14,19) (15,17) (16,17) (17,18)\nQ: Is there a path between node 14 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "755"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,12) (1,25) (1,2) (1,10) (1,12) (1,3) (2,8) (2,22) (2,25) (2,26) (2,19) (2,11) (2,12) (2,7) (2,21) (3,25) (3,26) (3,10) (3,27) (3,21) (5,24) (5,6) (6,23) (6,9) (7,22) (7,25) (7,11) (8,20) (8,22) (8,25) (8,26) (8,27) (9,24) (10,14) (10,25) (10,13) (10,27) (10,21) (11,22) (11,12) (11,17) (11,21) (12,19) (12,18) (12,17) (12,27) (12,21) (13,17) (13,21) (14,17) (14,21) (15,23) (15,24) (16,22) (17,22) (17,25) (17,19) (18,20) (18,26) (18,21) (19,22) (19,26) (19,27) (20,27) (22,25) (25,26)\nQ: Is there a path between node 18 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "756"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,10) (0,12) (0,20) (0,14) (0,8) (0,3) (0,6) (0,5) (0,15) (0,19) (0,7) (0,9) (0,22) (0,2) (0,21) (0,18) (1,4) (1,10) (1,12) (1,20) (1,8) (1,5) (1,15) (1,16) (1,19) (1,7) (1,9) (1,22) (1,2) (1,18) (2,4) (2,10) (2,12) (2,14) (2,3) (2,5) (2,15) (2,19) (2,7) (2,22) (2,21) (2,18) (3,4) (3,12) (3,20) (3,14) (3,6) (3,5) (3,15) (3,16) (3,19) (3,7) (3,9) (3,22) (3,21) (3,18) (4,10) (4,12) (4,8) (4,6) (4,5) (4,15) (4,16) (4,19) (4,7) (4,9) (4,21) (4,18) (5,12) (5,14) (5,8) (5,6) (5,15) (5,16) (5,19) (5,7) (5,9) (5,22) (5,18) (6,10) (6,12) (6,20) (6,14) (6,16) (6,19) (6,7) (6,9) (6,22) (6,21) (6,18) (7,10) (7,12) (7,14) (7,8) (7,16) (7,9) (7,22) (7,21) (7,18) (8,10) (8,12) (8,14) (8,15) (8,16) (8,19) (8,9) (8,21) (9,12) (9,20) (9,15) (9,16) (9,22) (9,21) (9,18) (10,12) (10,20) (10,14) (10,15) (10,16) (10,18) (12,16) (12,19) (13,17) (14,20) (14,16) (15,16) (15,22) (15,21) (16,20) (16,21) (16,18) (18,22) (18,21) (19,20) (19,22) (19,21) (21,22)\nQ: Is there a path between node 22 and node 17?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "757"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,9) (1,10) (1,3) (2,6) (2,4) (2,7) (3,6) (3,10) (3,9) (3,12) (4,8) (5,9) (5,12) (6,9) (6,12) (6,7) (7,10) (7,9) (7,14) (8,10) (8,9) (8,14) (12,14)\nQ: Is there a path between node 11 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "758"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (0,13) (0,22) (1,12) (1,6) (2,20) (2,14) (2,11) (3,5) (3,23) (3,6) (5,17) (6,19) (7,23) (8,13) (8,15) (9,21) (9,18) (12,24) (12,17) (12,19) (13,21) (13,18) (13,25) (13,15) (13,16) (15,16) (16,21) (16,25) (17,23) (17,19) (19,26) (21,22) (22,25)\nQ: Is there a path between node 18 and node 22?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "759"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,12) (0,5) (0,6) (0,4) (0,8) (0,2) (0,9) (0,1) (0,7) (1,12) (1,5) (1,6) (1,4) (1,8) (1,2) (1,9) (1,10) (1,7) (2,8) (2,10) (2,7) (4,11) (4,12) (4,5) (4,6) (4,8) (4,9) (4,7) (5,11) (5,6) (5,8) (5,10) (5,7) (6,11) (6,12) (6,8) (6,9) (7,11) (7,12) (7,9) (7,10) (8,12) (8,9) (8,10) (9,11) (9,12) (9,10) (10,11) (10,12) (11,12)\nQ: Is there a path between node 3 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "760"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,22) (0,12) (0,24) (0,18) (0,19) (0,30) (0,1) (0,21) (0,9) (0,5) (0,6) (0,7) (0,2) (1,22) (1,24) (1,18) (1,19) (1,30) (1,21) (1,9) (1,5) (1,6) (1,11) (1,7) (1,31) (1,2) (2,12) (2,24) (2,18) (2,19) (2,21) (2,5) (2,6) (2,11) (2,7) (2,31) (3,26) (3,16) (3,4) (3,28) (3,13) (3,20) (4,26) (4,16) (4,8) (4,28) (5,12) (5,24) (5,30) (5,21) (5,9) (5,11) (5,7) (5,31) (6,22) (6,12) (6,24) (6,30) (6,21) (6,9) (6,11) (6,7) (7,12) (7,18) (7,30) (7,9) (7,11) (7,31) (8,26) (8,16) (8,28) (9,22) (9,12) (9,24) (9,18) (9,19) (9,30) (9,11) (9,31) (10,25) (10,14) (10,29) (10,32) (10,15) (10,23) (11,22) (11,12) (11,24) (11,18) (11,30) (11,21) (12,24) (12,30) (12,21) (12,31) (13,26) (13,28) (14,27) (14,17) (14,29) (14,32) (14,15) (15,25) (15,27) (15,17) (15,29) (15,32) (15,23) (16,26) (17,29) (18,22) (18,24) (18,19) (18,21) (19,22) (19,30) (19,21) (20,26) (21,22) (21,24) (21,31) (22,24) (23,25) (23,27) (23,32) (24,30) (24,31) (25,27) (25,29) (25,32) (26,28) (27,29) (27,32) (30,31)\nQ: Is there a path between node 4 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "761"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,2) (0,4) (0,5) (0,15) (0,7) (1,9) (1,13) (1,12) (1,3) (2,14) (2,10) (2,4) (2,8) (2,15) (2,7) (3,9) (3,13) (3,12) (3,11) (4,14) (4,6) (4,10) (4,8) (4,15) (5,6) (5,8) (5,7) (6,14) (6,8) (6,15) (7,14) (7,10) (7,8) (7,15) (8,14) (8,10) (8,15) (9,13) (9,12) (9,11) (10,14) (10,15) (11,13) (11,12) (12,13) (14,15)\nQ: Is there a path between node 10 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "762"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (2,3) (2,5) (3,5) (4,6)\nQ: Is there a path between node 3 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "763"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,15) (0,22) (0,18) (1,5) (1,14) (1,21) (1,16) (1,19) (1,3) (1,17) (1,13) (1,11) (1,2) (1,20) (1,8) (1,6) (1,12) (1,9) (1,7) (2,5) (2,14) (2,21) (2,16) (2,19) (2,3) (2,17) (2,13) (2,11) (2,20) (2,8) (2,6) (2,12) (2,9) (2,7) (3,5) (3,14) (3,21) (3,16) (3,19) (3,17) (3,13) (3,11) (3,20) (3,8) (3,6) (3,12) (3,9) (3,7) (5,14) (5,21) (5,16) (5,19) (5,17) (5,13) (5,11) (5,20) (5,8) (5,6) (5,12) (5,9) (5,7) (6,14) (6,21) (6,16) (6,19) (6,17) (6,13) (6,11) (6,20) (6,8) (6,12) (6,9) (6,7) (7,14) (7,21) (7,16) (7,19) (7,17) (7,13) (7,11) (7,20) (7,8) (7,12) (7,9) (8,14) (8,21) (8,16) (8,19) (8,17) (8,13) (8,11) (8,20) (8,12) (8,9) (9,14) (9,21) (9,16) (9,19) (9,17) (9,13) (9,11) (9,20) (9,12) (10,15) (10,22) (10,18) (11,14) (11,21) (11,16) (11,19) (11,17) (11,13) (11,20) (11,12) (12,14) (12,21) (12,16) (12,19) (12,17) (12,13) (12,20) (13,14) (13,21) (13,16) (13,19) (13,17) (13,20) (14,21) (14,16) (14,19) (14,17) (14,20) (15,22) (15,18) (16,21) (16,19) (16,17) (16,20) (17,21) (17,19) (17,20) (18,22) (19,21) (19,20) (20,21)\nQ: Is there a path between node 14 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "764"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,13) (0,5) (0,11) (0,15) (0,10) (0,16) (0,14) (0,8) (0,9) (1,18) (1,12) (1,7) (1,6) (2,13) (2,11) (2,15) (2,17) (2,16) (2,14) (2,3) (2,8) (2,9) (3,5) (3,11) (3,4) (3,15) (3,10) (3,14) (3,8) (3,9) (4,13) (4,5) (4,17) (4,16) (4,14) (4,8) (5,17) (5,16) (5,14) (6,12) (6,19) (6,20) (6,7) (7,18) (8,15) (8,17) (8,16) (8,14) (8,9) (9,13) (9,11) (9,17) (9,16) (9,14) (10,11) (10,15) (10,17) (10,16) (10,14) (11,13) (11,15) (11,16) (12,18) (12,19) (12,20) (13,17) (13,14) (14,15) (14,17) (14,16) (15,17) (16,17) (18,19) (18,20) (19,20)\nQ: Is there a path between node 20 and node 14?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "765"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,18) (0,15) (0,12) (0,5) (1,24) (2,21) (2,23) (2,9) (2,15) (2,19) (3,23) (3,15) (3,8) (3,16) (5,21) (5,22) (5,6) (5,19) (5,8) (5,10) (5,16) (6,14) (6,22) (6,9) (6,12) (6,17) (9,23) (9,22) (9,20) (9,10) (10,22) (10,18) (10,19) (11,24) (12,14) (13,14) (13,21) (13,23) (13,18) (13,15) (14,21) (14,18) (14,15) (14,16) (15,20) (15,17) (17,23) (17,22) (17,18) (17,20) (17,19) (18,19) (19,20) (21,23)\nQ: Is there a path between node 14 and node 24?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "766"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,2) (0,14) (0,7) (0,13) (1,17) (1,3) (1,10) (1,6) (2,11) (2,12) (2,14) (2,13) (3,17) (3,10) (3,6) (4,9) (4,5) (5,9) (5,16) (6,17) (6,8) (6,10) (7,11) (7,12) (7,14) (7,13) (8,17) (8,15) (9,18) (9,16) (10,17) (12,14) (12,13) (13,14) (15,17)\nQ: Is there a path between node 6 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "767"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,28) (0,1) (0,22) (0,20) (0,15) (0,18) (0,2) (0,5) (0,10) (0,8) (0,14) (0,6) (1,27) (1,12) (1,19) (1,28) (1,25) (1,29) (1,22) (1,4) (1,7) (1,15) (1,18) (1,3) (1,2) (1,24) (1,5) (1,11) (1,14) (1,13) (1,6) (2,12) (2,19) (2,28) (2,29) (2,4) (2,15) (2,16) (2,18) (2,3) (2,10) (2,13) (2,21) (2,6) (3,27) (3,19) (3,28) (3,20) (3,4) (3,7) (3,16) (3,18) (3,9) (3,24) (3,5) (3,11) (3,10) (3,8) (3,14) (3,23) (3,21) (3,6) (4,27) (4,12) (4,19) (4,28) (4,25) (4,20) (4,7) (4,15) (4,16) (4,5) (4,8) (4,14) (4,13) (4,21) (4,6) (5,27) (5,12) (5,19) (5,28) (5,25) (5,29) (5,22) (5,20) (5,7) (5,15) (5,16) (5,24) (5,11) (5,10) (5,8) (5,14) (5,23) (5,13) (5,21) (5,6) (6,27) (6,12) (6,28) (6,25) (6,29) (6,22) (6,20) (6,7) (6,16) (6,18) (6,9) (6,24) (6,8) (6,14) (6,21) (7,19) (7,25) (7,29) (7,22) (7,20) (7,15) (7,16) (7,24) (7,11) (7,10) (7,14) (7,23) (7,21) (8,27) (8,12) (8,19) (8,29) (8,22) (8,20) (8,15) (8,16) (8,9) (8,24) (8,11) (8,10) (8,14) (8,13) (9,12) (9,19) (9,25) (9,22) (9,20) (9,18) (9,24) (9,11) (9,10) (9,14) (9,23) (9,13) (9,21) (10,27) (10,12) (10,19) (10,28) (10,25) (10,29) (10,16) (10,18) (10,24) (10,14) (10,23) (10,13) (10,21) (11,27) (11,12) (11,25) (11,22) (11,20) (11,18) (11,24) (12,19) (12,28) (12,29) (12,22) (12,15) (12,16) (12,18) (12,14) (12,23) (12,13) (12,21) (13,27) (13,28) (13,25) (13,29) (13,22) (13,20) (13,15) (13,18) (13,24) (14,19) (14,28) (14,25) (14,29) (14,15) (14,16) (14,18) (14,24) (14,23) (15,27) (15,28) (15,25) (15,29) (15,20) (15,18) (15,23) (15,21) (16,27) (16,19) (16,28) (16,25) (16,29) (16,22) (16,20) (16,18) (16,24) (16,21) (18,19) (18,28) (18,29) (18,22) (18,20) (18,24) (18,23) (18,21) (19,27) (19,28) (19,25) (19,29) (19,22) (19,20) (19,24) (19,23) (19,21) (20,27) (20,28) (20,29) (20,22) (20,23) (20,21) (21,27) (21,28) (21,24) (21,23) (22,27) (22,28) (22,29) (22,23) (23,27) (23,28) (23,25) (23,29) (24,27) (24,28) (24,25) (24,29) (25,27) (25,29) (27,28) (27,29)\nQ: Is there a path between node 2 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "768"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,3) (0,7) (0,10) (0,13) (0,12) (0,16) (1,14) (1,2) (1,5) (1,9) (1,8) (1,15) (1,4) (1,6) (2,14) (2,5) (2,9) (2,8) (2,15) (2,4) (2,6) (3,11) (3,7) (3,10) (3,13) (3,12) (3,16) (4,14) (4,5) (4,9) (4,8) (4,15) (4,6) (5,14) (5,9) (5,8) (5,15) (5,6) (6,14) (6,9) (6,8) (6,15) (7,11) (7,10) (7,13) (7,12) (7,16) (8,14) (8,9) (8,15) (9,14) (9,15) (10,11) (10,13) (10,12) (10,16) (11,13) (11,12) (11,16) (12,13) (12,16) (13,16) (14,15)\nQ: Is there a path between node 3 and node 13?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "769"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,1) (0,2) (0,7) (0,6) (1,2) (1,8) (1,7) (1,4) (1,6) (2,7) (2,4) (2,6) (3,5) (4,9) (4,8) (4,7) (6,9) (6,7) (7,8)\nQ: Is there a path between node 0 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "770"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,28) (0,26) (0,7) (0,22) (0,6) (0,1) (0,30) (0,3) (1,16) (1,28) (1,26) (1,22) (1,10) (1,30) (2,4) (2,29) (2,24) (2,14) (2,21) (2,25) (2,13) (2,12) (2,31) (2,19) (2,33) (2,27) (2,23) (2,8) (2,18) (3,16) (3,28) (3,26) (3,9) (3,7) (3,10) (4,29) (4,32) (4,24) (4,21) (4,25) (4,15) (4,12) (4,31) (4,19) (4,33) (4,27) (4,17) (4,23) (4,18) (5,32) (5,14) (5,21) (5,15) (5,12) (5,19) (5,33) (5,27) (5,23) (5,8) (6,28) (6,26) (6,7) (6,22) (6,10) (7,16) (7,9) (7,22) (7,10) (8,29) (8,32) (8,24) (8,21) (8,15) (8,13) (8,33) (8,27) (8,23) (8,18) (9,16) (9,28) (9,26) (9,22) (9,10) (10,28) (10,22) (10,30) (12,29) (12,14) (12,21) (12,25) (12,15) (12,13) (12,31) (12,19) (12,33) (12,17) (12,23) (12,18) (13,20) (13,29) (13,24) (13,21) (13,25) (13,15) (13,31) (13,19) (13,33) (13,27) (13,17) (13,23) (13,18) (14,20) (14,29) (14,32) (14,24) (14,21) (14,15) (14,31) (14,19) (14,33) (14,17) (14,18) (15,20) (15,29) (15,32) (15,24) (15,21) (15,25) (15,31) (15,19) (15,33) (15,27) (15,17) (15,23) (15,18) (16,28) (16,26) (16,22) (16,30) (17,20) (17,29) (17,32) (17,24) (17,21) (17,25) (17,31) (17,19) (17,18) (18,20) (18,29) (18,32) (18,24) (18,21) (18,25) (18,31) (18,19) (18,27) (18,23) (19,32) (19,24) (19,33) (19,27) (19,23) (20,29) (20,32) (20,24) (20,21) (20,25) (20,31) (20,33) (20,27) (20,23) (21,32) (21,24) (21,25) (21,31) (21,33) (21,27) (21,23) (22,26) (22,30) (23,29) (23,32) (23,24) (23,25) (23,31) (23,33) (23,27) (24,32) (24,25) (24,31) (24,27) (25,29) (25,33) (25,27) (26,28) (26,30) (27,29) (27,31) (27,33) (28,30) (29,32) (29,31) (29,33) (31,32) (31,33) (32,33)\nQ: Is there a path between node 3 and node 26?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "771"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,8) (0,18) (0,6) (0,1) (0,12) (0,3) (0,7) (0,14) (0,10) (0,19) (0,16) (0,13) (1,17) (1,8) (1,18) (1,2) (1,19) (2,8) (2,6) (2,20) (2,14) (3,17) (3,18) (3,6) (3,14) (3,10) (3,19) (4,17) (4,18) (4,6) (4,19) (4,13) (5,15) (6,17) (6,8) (6,18) (6,13) (7,17) (7,14) (7,10) (8,20) (9,15) (9,11) (10,17) (10,18) (11,15) (12,17) (12,18) (12,14) (12,19) (13,17) (13,18) (13,20) (14,17) (14,18) (14,20) (18,20) (19,20)\nQ: Is there a path between node 13 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "772"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,16) (0,9) (0,3) (0,4) (0,8) (0,17) (1,6) (1,12) (1,13) (1,18) (1,2) (1,4) (1,8) (1,17) (2,6) (2,12) (2,15) (2,9) (2,13) (2,18) (2,4) (2,8) (2,17) (3,6) (3,16) (3,12) (3,9) (3,13) (3,18) (3,8) (3,17) (3,5) (4,6) (4,16) (4,12) (4,9) (4,18) (4,17) (4,5) (5,6) (5,12) (5,15) (5,9) (5,17) (6,12) (6,15) (6,9) (6,13) (6,18) (6,8) (7,10) (7,11) (7,19) (8,16) (8,15) (8,9) (8,18) (9,16) (9,12) (9,15) (9,13) (9,18) (9,17) (10,19) (11,14) (11,19) (12,16) (12,15) (12,13) (12,17) (13,18) (14,19) (15,17) (16,17) (17,18)\nQ: Is there a path between node 18 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "773"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,6) (1,4) (1,3) (1,2) (1,7) (2,10) (2,4) (2,8) (3,10) (3,6) (3,4) (3,8) (3,5) (4,6) (4,8) (4,5) (4,7) (5,10) (5,8) (6,10) (6,8) (7,10)\nQ: Is there a path between node 7 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "774"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,14) (1,21) (1,3) (1,15) (1,7) (3,12) (4,10) (5,10) (6,22) (7,21) (7,15) (9,12) (11,13) (11,21) (14,20) (15,17) (15,21) (16,18) (18,22)\nQ: Is there a path between node 7 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "775"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (1,14) (1,3) (1,9) (1,10) (1,4) (1,7) (1,6) (1,13) (1,12) (1,11) (2,15) (3,14) (3,8) (3,9) (3,10) (3,4) (3,12) (3,11) (4,8) (4,9) (4,10) (4,7) (4,5) (4,11) (5,9) (5,7) (5,13) (5,12) (5,11) (6,14) (6,8) (6,7) (6,13) (6,11) (7,8) (7,9) (7,10) (7,11) (8,14) (8,10) (8,12) (8,11) (9,14) (9,10) (9,13) (9,12) (10,14) (10,13) (10,12) (11,14) (11,13) (11,12) (12,14)\nQ: Is there a path between node 15 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "776"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,14) (0,12) (1,20) (1,12) (2,13) (2,18) (3,17) (4,20) (7,21) (8,18) (9,20) (9,15) (10,13) (10,19) (13,18) (14,16) (14,15) (15,20)\nQ: Is there a path between node 1 and node 20?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "777"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (0,10) (0,23) (0,3) (0,9) (0,26) (1,8) (1,20) (1,6) (1,4) (1,19) (1,16) (1,13) (1,24) (2,8) (2,20) (2,4) (2,19) (2,16) (2,13) (2,24) (2,12) (3,10) (3,9) (3,21) (3,22) (4,6) (4,19) (4,13) (4,24) (4,12) (5,15) (5,25) (5,11) (5,7) (6,8) (6,20) (6,19) (6,16) (6,13) (6,24) (7,15) (7,25) (7,14) (8,19) (8,13) (8,24) (8,12) (9,18) (9,23) (10,18) (10,23) (10,21) (10,26) (11,15) (11,17) (11,25) (12,20) (12,19) (12,16) (12,24) (13,20) (13,19) (13,16) (13,24) (14,17) (14,25) (15,17) (15,25) (16,20) (16,24) (17,25) (18,21) (18,22) (19,20) (19,24) (20,24) (21,23) (22,23) (22,26) (23,26)\nQ: Is there a path between node 14 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "778"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,9) (0,14) (0,18) (0,3) (0,1) (0,17) (0,4) (0,8) (0,7) (0,15) (0,11) (0,10) (0,13) (1,5) (1,9) (1,14) (1,18) (1,3) (1,17) (1,4) (1,8) (1,7) (1,15) (1,11) (1,10) (1,13) (3,5) (3,9) (3,14) (3,18) (3,17) (3,4) (3,8) (3,7) (3,15) (3,11) (3,10) (3,13) (4,5) (4,9) (4,14) (4,18) (4,17) (4,8) (4,7) (4,15) (4,11) (4,10) (4,13) (5,9) (5,14) (5,18) (5,17) (5,8) (5,7) (5,15) (5,11) (5,10) (5,13) (6,12) (6,16) (7,9) (7,14) (7,18) (7,17) (7,8) (7,15) (7,11) (7,10) (7,13) (8,9) (8,14) (8,18) (8,17) (8,15) (8,11) (8,10) (8,13) (9,14) (9,18) (9,17) (9,15) (9,11) (9,10) (9,13) (10,14) (10,18) (10,17) (10,15) (10,11) (10,13) (11,14) (11,18) (11,17) (11,15) (11,13) (12,16) (13,14) (13,18) (13,17) (13,15) (14,18) (14,17) (14,15) (15,18) (15,17) (17,18)\nQ: Is there a path between node 9 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "779"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,7) (0,10) (0,6) (0,2) (0,8) (0,4) (0,1) (1,3) (1,7) (1,10) (1,6) (1,2) (1,8) (1,4) (2,3) (2,7) (2,10) (2,6) (2,8) (2,4) (3,7) (3,10) (3,6) (3,8) (3,4) (4,7) (4,10) (4,6) (4,8) (5,9) (6,7) (6,10) (6,8) (7,10) (7,8) (8,10)\nQ: Is there a path between node 1 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "780"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,18) (0,25) (0,19) (0,16) (0,22) (0,8) (0,10) (0,31) (0,13) (0,5) (0,14) (0,24) (0,27) (0,1) (0,15) (0,23) (1,9) (1,30) (1,25) (1,19) (1,16) (1,17) (1,22) (1,8) (1,21) (1,4) (1,31) (1,13) (1,14) (1,24) (1,12) (1,27) (1,15) (2,11) (2,28) (2,29) (2,7) (3,9) (3,18) (3,25) (3,19) (3,16) (3,22) (3,10) (3,4) (3,31) (3,13) (3,5) (3,14) (3,24) (3,12) (3,20) (3,27) (3,15) (3,23) (4,18) (4,30) (4,19) (4,22) (4,8) (4,21) (4,31) (4,5) (4,24) (4,12) (4,27) (4,23) (5,18) (5,30) (5,25) (5,19) (5,17) (5,10) (5,21) (5,31) (5,12) (5,20) (5,15) (5,23) (6,28) (6,29) (6,7) (6,26) (7,28) (8,9) (8,25) (8,19) (8,16) (8,22) (8,10) (8,13) (8,14) (8,24) (8,12) (8,27) (8,15) (8,23) (9,18) (9,30) (9,19) (9,16) (9,17) (9,22) (9,10) (9,31) (9,13) (9,27) (9,15) (9,23) (10,18) (10,30) (10,25) (10,16) (10,22) (10,21) (10,31) (10,14) (10,24) (10,12) (10,20) (10,15) (11,28) (11,26) (12,19) (12,22) (12,21) (12,13) (12,24) (12,15) (12,23) (13,25) (13,19) (13,16) (13,17) (13,22) (13,31) (13,14) (13,27) (14,30) (14,25) (14,16) (14,17) (14,22) (14,31) (14,24) (14,20) (14,15) (14,23) (15,18) (15,30) (15,25) (15,19) (15,16) (15,22) (15,31) (15,24) (16,18) (16,30) (16,22) (16,21) (16,31) (16,20) (16,27) (17,18) (17,30) (17,25) (17,19) (17,22) (17,21) (17,31) (17,24) (17,27) (17,23) (18,30) (18,25) (18,19) (18,22) (18,21) (18,31) (18,24) (18,27) (18,23) (19,30) (19,25) (19,21) (19,24) (19,20) (19,27) (19,23) (20,21) (20,31) (20,24) (20,27) (20,23) (21,25) (21,22) (21,31) (21,24) (21,27) (21,23) (22,30) (22,31) (22,24) (22,23) (23,30) (23,25) (23,24) (23,27) (24,30) (24,25) (24,31) (24,27) (25,30) (25,27) (26,28) (27,30) (27,31) (28,29) (30,31)\nQ: Is there a path between node 10 and node 30?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "781"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,11) (0,17) (0,3) (0,19) (0,9) (0,16) (0,15) (0,7) (0,12) (0,2) (1,11) (1,10) (1,3) (1,4) (1,8) (1,19) (1,13) (1,9) (1,16) (1,15) (1,7) (1,12) (1,2) (2,17) (2,5) (2,16) (2,15) (3,17) (3,10) (3,5) (3,6) (3,8) (3,13) (3,9) (3,16) (3,15) (3,7) (3,12) (4,11) (4,5) (4,8) (4,19) (4,13) (4,9) (4,7) (4,12) (5,11) (5,10) (5,6) (5,8) (5,19) (5,13) (5,7) (6,11) (6,17) (6,10) (6,8) (6,19) (6,13) (6,16) (6,15) (6,7) (6,12) (7,11) (7,17) (7,10) (7,19) (7,9) (7,16) (7,15) (8,11) (8,17) (8,10) (8,19) (8,13) (8,15) (8,12) (9,11) (9,17) (9,10) (9,13) (9,16) (9,15) (10,11) (10,17) (10,19) (10,13) (10,15) (10,12) (11,19) (11,15) (11,12) (12,17) (12,19) (12,13) (13,19) (13,16) (13,15) (14,18) (15,19) (15,16) (16,17) (17,19)\nQ: Is there a path between node 12 and node 14?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "782"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,3) (0,5) (1,2) (1,10) (1,3) (1,5) (2,6) (2,10) (3,17) (3,14) (3,6) (3,9) (4,14) (4,7) (4,9) (5,17) (5,14) (5,6) (5,10) (5,7) (6,14) (6,16) (6,7) (9,17) (9,16) (9,10) (10,14) (11,15) (12,13) (14,17) (14,16) (14,15) (15,17)\nQ: Is there a path between node 7 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "783"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,1) (0,13) (0,15) (0,16) (0,9) (0,14) (0,3) (0,12) (0,17) (0,2) (0,18) (1,11) (1,13) (1,15) (1,16) (1,9) (1,8) (1,14) (1,3) (1,4) (1,17) (1,18) (2,11) (2,13) (2,15) (2,9) (2,8) (2,14) (2,3) (2,12) (2,17) (2,18) (3,11) (3,13) (3,15) (3,16) (3,9) (3,8) (3,14) (3,12) (3,17) (3,18) (4,13) (4,15) (4,16) (4,8) (4,14) (4,12) (4,18) (5,6) (5,7) (5,10) (6,7) (6,10) (7,10) (8,11) (8,15) (8,16) (8,18) (9,11) (9,13) (9,15) (9,16) (9,14) (9,12) (9,17) (9,18) (11,13) (11,16) (11,17) (11,18) (12,15) (12,16) (12,17) (12,18) (13,15) (13,18) (14,15) (14,17) (15,16) (16,17) (16,18) (17,18)\nQ: Is there a path between node 15 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "784"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,8) (1,5) (2,3) (3,5) (3,11) (4,8) (5,9) (5,7) (5,10) (6,11)\nQ: Is there a path between node 3 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "785"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,4) (0,1) (0,5) (0,24) (0,3) (0,21) (0,19) (0,9) (0,15) (0,20) (0,27) (0,13) (1,24) (1,21) (1,31) (1,10) (1,7) (1,20) (1,27) (1,13) (2,6) (2,5) (2,24) (2,3) (2,21) (2,19) (2,9) (2,31) (2,15) (2,7) (2,27) (2,13) (3,6) (3,4) (3,5) (3,22) (3,24) (3,21) (3,19) (3,9) (3,31) (3,18) (3,7) (3,20) (4,5) (4,21) (4,19) (4,9) (4,31) (4,7) (4,20) (4,27) (4,13) (5,6) (5,22) (5,24) (5,21) (5,9) (5,31) (5,10) (5,15) (5,18) (5,20) (5,27) (5,13) (6,22) (6,21) (6,19) (6,9) (6,31) (6,10) (6,15) (6,18) (6,7) (6,27) (6,13) (7,22) (7,9) (7,10) (7,15) (7,18) (7,20) (7,27) (7,13) (8,16) (8,11) (8,28) (8,12) (8,25) (8,30) (8,14) (8,32) (8,29) (9,22) (9,24) (9,21) (9,19) (9,31) (9,10) (9,15) (9,18) (9,20) (10,22) (10,19) (10,31) (10,15) (10,20) (10,27) (10,13) (11,16) (11,28) (11,26) (11,23) (11,30) (11,14) (11,32) (11,17) (12,16) (12,28) (12,23) (12,30) (12,14) (12,33) (12,32) (12,17) (12,29) (13,22) (13,24) (13,21) (13,19) (13,15) (13,18) (13,20) (14,28) (14,26) (14,23) (14,25) (14,33) (14,32) (14,29) (15,22) (15,24) (15,21) (15,19) (15,20) (15,27) (16,26) (16,25) (16,30) (16,33) (16,32) (16,17) (16,29) (17,28) (17,26) (17,25) (17,30) (17,33) (17,32) (17,29) (18,24) (18,19) (18,31) (19,22) (19,24) (19,31) (19,20) (19,27) (20,21) (20,31) (20,27) (21,31) (23,28) (23,26) (23,25) (23,30) (24,31) (24,27) (25,26) (25,30) (25,33) (25,32) (25,29) (26,28) (26,33) (26,32) (28,30) (28,29) (29,30) (29,33) (29,32) (30,32)\nQ: Is there a path between node 16 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "786"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,8) (0,10) (0,12) (0,13) (1,10) (2,5) (2,16) (3,13) (4,16) (5,7) (5,14) (6,7) (7,16) (7,14) (9,13) (10,15) (11,12) (12,15)\nQ: Is there a path between node 2 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "787"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,3) (0,5) (1,2) (1,8) (1,7) (2,8) (2,7) (3,11) (3,9) (3,13) (5,11) (5,12) (10,11) (11,12) (12,13)\nQ: Is there a path between node 13 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "788"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,10) (0,17) (0,4) (0,21) (0,1) (0,2) (0,18) (0,7) (0,19) (0,11) (0,3) (0,5) (0,14) (1,6) (1,10) (1,17) (1,21) (1,16) (1,18) (1,7) (1,8) (1,11) (2,6) (2,10) (2,17) (2,4) (2,21) (2,16) (2,13) (2,18) (2,7) (2,8) (2,19) (2,3) (2,5) (3,6) (3,10) (3,17) (3,4) (3,21) (3,16) (3,13) (3,18) (3,7) (3,19) (4,10) (4,16) (4,18) (4,7) (4,8) (4,19) (4,5) (5,6) (5,16) (5,13) (5,18) (5,7) (5,8) (5,19) (5,14) (6,10) (6,17) (6,21) (6,16) (6,13) (6,18) (6,7) (6,19) (6,11) (6,14) (7,10) (7,17) (7,21) (7,16) (7,13) (7,18) (7,8) (7,19) (7,11) (7,14) (8,10) (8,17) (8,21) (8,16) (8,13) (8,18) (8,19) (8,11) (9,20) (10,17) (10,21) (10,13) (10,18) (10,19) (10,11) (10,14) (11,17) (11,16) (11,13) (11,18) (11,19) (12,15) (13,21) (13,16) (13,18) (13,19) (13,14) (14,17) (14,21) (14,16) (14,18) (14,19) (16,17) (16,21) (16,18) (17,18) (18,21) (18,19) (19,21)\nQ: Is there a path between node 20 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "789"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,10) (0,15) (0,21) (0,1) (0,7) (0,29) (0,24) (0,16) (0,23) (0,17) (1,26) (1,10) (1,15) (1,7) (1,28) (1,29) (1,12) (1,24) (1,16) (1,3) (1,23) (2,14) (2,27) (2,34) (3,26) (3,32) (3,15) (3,21) (3,7) (3,28) (3,29) (3,12) (3,24) (3,23) (3,17) (4,9) (4,14) (4,27) (4,31) (5,19) (5,22) (5,13) (5,20) (5,25) (5,30) (5,8) (5,33) (6,9) (6,27) (6,34) (6,31) (7,26) (7,32) (7,10) (7,15) (7,21) (7,29) (7,12) (7,24) (7,16) (7,23) (7,17) (8,19) (8,22) (8,13) (8,20) (8,25) (8,18) (8,30) (8,33) (9,14) (9,34) (10,32) (10,15) (10,21) (10,29) (10,24) (10,23) (10,17) (11,19) (11,22) (11,13) (11,25) (11,18) (11,30) (12,26) (12,32) (12,15) (12,21) (12,24) (12,16) (12,23) (13,19) (13,20) (13,25) (13,18) (13,33) (14,27) (14,31) (15,26) (15,21) (15,28) (15,24) (15,16) (15,23) (15,17) (16,26) (16,32) (16,23) (16,17) (17,26) (17,32) (17,21) (17,28) (17,24) (18,19) (18,22) (18,20) (18,30) (19,22) (19,20) (19,25) (19,30) (20,25) (20,30) (20,33) (21,26) (21,32) (21,28) (21,29) (22,25) (22,30) (22,33) (23,32) (23,28) (23,29) (23,24) (24,32) (24,28) (25,30) (25,33) (26,32) (26,28) (27,31) (28,29) (30,33)\nQ: Is there a path between node 22 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "790"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,1) (3,4)\nQ: Is there a path between node 2 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "791"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,22) (0,12) (0,24) (0,18) (0,19) (0,30) (0,1) (0,21) (0,9) (0,5) (0,6) (0,7) (0,2) (1,22) (1,24) (1,18) (1,19) (1,30) (1,21) (1,9) (1,5) (1,6) (1,11) (1,7) (1,31) (1,2) (2,12) (2,24) (2,18) (2,19) (2,21) (2,5) (2,6) (2,11) (2,7) (2,31) (3,26) (3,16) (3,4) (3,28) (3,13) (3,20) (4,26) (4,16) (4,8) (4,28) (5,12) (5,24) (5,30) (5,21) (5,9) (5,11) (5,7) (5,31) (6,22) (6,12) (6,24) (6,30) (6,21) (6,9) (6,11) (6,7) (7,12) (7,18) (7,30) (7,9) (7,11) (7,31) (8,26) (8,16) (8,28) (9,22) (9,12) (9,24) (9,18) (9,19) (9,30) (9,11) (9,31) (10,25) (10,14) (10,29) (10,32) (10,15) (10,23) (11,22) (11,12) (11,24) (11,18) (11,30) (11,21) (12,24) (12,30) (12,21) (12,31) (13,26) (13,28) (14,27) (14,17) (14,29) (14,32) (14,15) (15,25) (15,27) (15,17) (15,29) (15,32) (15,23) (16,26) (17,29) (18,22) (18,24) (18,19) (18,21) (19,22) (19,30) (19,21) (20,26) (21,22) (21,24) (21,31) (22,24) (23,25) (23,27) (23,32) (24,30) (24,31) (25,27) (25,29) (25,32) (26,28) (27,29) (27,32) (30,31)\nQ: Is there a path between node 23 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "792"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,2) (3,5)\nQ: Is there a path between node 0 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "793"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,12) (0,2) (0,3) (1,13) (1,22) (1,7) (1,11) (1,19) (1,6) (1,8) (2,14) (2,20) (2,3) (3,14) (3,20) (4,21) (4,18) (4,5) (4,17) (4,9) (4,15) (4,10) (5,21) (5,17) (5,9) (5,15) (5,10) (6,16) (6,13) (6,22) (6,7) (6,11) (6,19) (6,8) (7,16) (7,13) (7,22) (7,8) (8,16) (8,13) (8,11) (8,19) (9,18) (9,17) (9,15) (9,10) (10,21) (10,18) (11,16) (11,13) (11,22) (11,19) (12,14) (12,20) (13,16) (13,19) (14,20) (15,21) (15,18) (15,17) (16,22) (17,21) (17,18) (19,22)\nQ: Is there a path between node 0 and node 15?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "794"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,8) (0,10) (0,12) (0,13) (1,10) (2,5) (2,16) (3,13) (4,16) (5,7) (5,14) (6,7) (7,16) (7,14) (9,13) (10,15) (11,12) (12,15)\nQ: Is there a path between node 9 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "795"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,20) (0,13) (0,24) (0,4) (1,21) (1,3) (1,11) (1,10) (1,23) (1,8) (1,2) (1,22) (1,19) (1,18) (2,21) (2,3) (2,11) (2,10) (2,23) (2,8) (2,22) (2,19) (2,18) (3,21) (3,11) (3,10) (3,23) (3,8) (3,22) (3,19) (3,18) (4,14) (4,20) (4,13) (4,24) (5,7) (5,9) (5,12) (5,16) (5,15) (5,17) (5,6) (6,7) (6,9) (6,12) (6,16) (6,15) (6,17) (7,9) (7,12) (7,16) (7,15) (7,17) (8,21) (8,11) (8,10) (8,23) (8,22) (8,19) (8,18) (9,12) (9,16) (9,15) (9,17) (10,21) (10,11) (10,23) (10,22) (10,19) (10,18) (11,21) (11,23) (11,22) (11,19) (11,18) (12,16) (12,15) (12,17) (13,14) (13,20) (13,24) (14,20) (14,24) (15,16) (15,17) (16,17) (18,21) (18,23) (18,22) (18,19) (19,21) (19,23) (19,22) (20,24) (21,23) (21,22) (22,23)\nQ: Is there a path between node 9 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "796"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,34) (0,4) (0,7) (0,28) (0,8) (0,15) (0,23) (0,13) (0,22) (0,32) (0,11) (0,18) (1,7) (1,2) (1,13) (1,27) (1,26) (1,9) (2,14) (2,31) (2,15) (2,23) (2,13) (2,9) (2,22) (2,17) (2,32) (2,18) (3,24) (4,7) (4,27) (4,17) (5,16) (5,12) (5,29) (5,20) (6,34) (6,7) (6,14) (6,31) (6,10) (6,23) (6,26) (6,21) (6,17) (6,18) (7,33) (7,14) (7,28) (7,15) (7,26) (7,19) (8,14) (8,28) (8,31) (8,10) (8,13) (8,25) (8,30) (8,18) (9,14) (9,21) (9,25) (9,22) (9,11) (10,31) (10,15) (10,27) (10,25) (10,17) (10,32) (11,28) (11,31) (11,15) (11,13) (11,27) (11,21) (11,25) (11,22) (12,16) (13,33) (13,14) (13,28) (13,26) (13,21) (13,17) (13,32) (13,18) (14,33) (14,31) (14,23) (14,27) (14,25) (15,34) (15,30) (15,17) (15,19) (16,24) (17,23) (17,26) (17,19) (18,34) (18,21) (18,30) (19,33) (19,21) (19,25) (19,30) (21,33) (21,28) (21,25) (21,30) (22,33) (22,23) (22,26) (22,25) (23,34) (23,25) (25,33) (25,32) (26,33) (26,28) (26,31) (26,32) (27,33) (27,32) (32,33)\nQ: Is there a path between node 25 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "797"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,10) (2,9) (2,5) (3,12) (3,14) (3,4) (3,8) (3,18) (4,19) (4,16) (4,11) (5,20) (5,12) (5,14) (5,11) (6,18) (6,16) (7,15) (8,20) (8,12) (8,18) (8,16) (9,20) (9,14) (9,19) (9,11) (11,13) (11,12) (11,18) (11,16) (12,18) (13,19) (13,18) (14,19) (16,20) (18,19)\nQ: Is there a path between node 20 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "798"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,13) (0,2) (0,15) (0,6) (0,17) (0,8) (0,16) (0,18) (0,9) (0,12) (0,11) (1,10) (1,14) (1,7) (1,5) (1,4) (2,3) (2,13) (2,15) (2,6) (2,17) (2,8) (2,16) (2,18) (2,9) (2,12) (2,11) (3,13) (3,15) (3,6) (3,17) (3,8) (3,16) (3,18) (3,9) (3,12) (3,11) (4,10) (4,14) (4,7) (4,5) (5,10) (5,14) (5,7) (6,13) (6,15) (6,17) (6,8) (6,16) (6,18) (6,9) (6,12) (6,11) (7,10) (7,14) (8,13) (8,15) (8,17) (8,16) (8,18) (8,9) (8,12) (8,11) (9,13) (9,15) (9,17) (9,16) (9,18) (9,12) (9,11) (10,14) (11,13) (11,15) (11,17) (11,16) (11,18) (11,12) (12,13) (12,15) (12,17) (12,16) (12,18) (13,15) (13,17) (13,16) (13,18) (15,17) (15,16) (15,18) (16,17) (16,18) (17,18)\nQ: Is there a path between node 14 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "799"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (0,10) (0,23) (0,3) (0,9) (0,26) (1,8) (1,20) (1,6) (1,4) (1,19) (1,16) (1,13) (1,24) (2,8) (2,20) (2,4) (2,19) (2,16) (2,13) (2,24) (2,12) (3,10) (3,9) (3,21) (3,22) (4,6) (4,19) (4,13) (4,24) (4,12) (5,15) (5,25) (5,11) (5,7) (6,8) (6,20) (6,19) (6,16) (6,13) (6,24) (7,15) (7,25) (7,14) (8,19) (8,13) (8,24) (8,12) (9,18) (9,23) (10,18) (10,23) (10,21) (10,26) (11,15) (11,17) (11,25) (12,20) (12,19) (12,16) (12,24) (13,20) (13,19) (13,16) (13,24) (14,17) (14,25) (15,17) (15,25) (16,20) (16,24) (17,25) (18,21) (18,22) (19,20) (19,24) (20,24) (21,23) (22,23) (22,26) (23,26)\nQ: Is there a path between node 10 and node 25?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "800"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,7) (0,12) (0,32) (0,22) (0,9) (0,20) (0,2) (0,5) (0,14) (0,4) (0,26) (0,21) (1,11) (1,8) (1,24) (1,3) (1,31) (1,28) (1,6) (2,16) (2,7) (2,32) (2,22) (2,9) (2,20) (2,14) (2,4) (2,21) (3,11) (3,8) (3,24) (3,31) (3,28) (4,16) (4,32) (4,22) (4,9) (4,20) (4,5) (4,14) (4,26) (5,16) (5,7) (5,12) (5,32) (5,22) (5,9) (5,20) (5,14) (5,26) (5,21) (6,8) (6,24) (6,31) (6,28) (7,12) (7,32) (7,22) (7,9) (7,14) (7,26) (7,21) (8,24) (8,31) (8,28) (9,16) (9,12) (9,32) (9,20) (9,26) (9,21) (10,23) (10,13) (10,29) (10,19) (10,25) (10,18) (12,32) (12,22) (12,20) (12,26) (12,21) (13,30) (13,27) (13,29) (13,19) (13,25) (13,18) (14,16) (14,32) (14,22) (14,20) (14,26) (15,30) (15,29) (15,25) (15,18) (16,32) (16,22) (16,20) (16,26) (16,21) (17,30) (17,27) (18,30) (18,29) (19,30) (19,23) (19,27) (19,25) (20,32) (20,22) (20,26) (21,32) (21,26) (22,32) (22,26) (23,30) (23,29) (23,25) (24,28) (26,32) (27,30) (27,29) (28,31) (29,30)\nQ: Is there a path between node 4 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "801"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,12) (0,11) (0,4) (2,10) (2,8) (2,4) (4,6) (4,11) (5,9) (6,7) (6,10) (6,11) (7,8) (8,10) (8,9) (9,12) (10,11)\nQ: Is there a path between node 7 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "802"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,3) (0,11) (0,8) (0,2) (0,12) (0,9) (0,1) (1,4) (1,3) (1,6) (1,11) (1,8) (1,7) (1,10) (1,2) (1,12) (2,3) (2,6) (2,11) (2,8) (2,9) (3,6) (3,11) (3,8) (3,7) (3,10) (3,9) (4,6) (4,11) (4,8) (4,7) (4,10) (4,12) (4,9) (6,8) (6,10) (7,10) (7,12) (7,9) (8,11) (8,10) (8,12) (9,10) (10,12)\nQ: Is there a path between node 1 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "803"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,4) (0,16) (0,21) (0,1) (0,25) (0,14) (0,9) (0,5) (0,6) (0,12) (0,17) (0,24) (0,23) (1,29) (1,4) (1,27) (1,16) (1,21) (1,14) (1,9) (1,6) (1,24) (1,23) (2,26) (2,10) (2,22) (2,15) (2,28) (2,8) (2,30) (2,19) (3,26) (3,10) (3,11) (3,22) (3,15) (3,28) (3,8) (3,30) (3,19) (3,20) (4,29) (4,27) (4,16) (4,21) (4,14) (4,9) (4,5) (4,6) (4,12) (4,24) (5,29) (5,27) (5,21) (5,7) (5,14) (5,12) (5,17) (5,24) (5,23) (6,29) (6,27) (6,7) (6,25) (6,14) (6,9) (6,12) (6,24) (6,23) (7,25) (7,14) (7,9) (7,12) (7,17) (7,23) (8,26) (8,10) (8,11) (8,13) (8,30) (8,19) (9,29) (9,27) (9,16) (9,14) (9,12) (9,24) (9,23) (10,26) (10,13) (10,15) (10,28) (10,19) (10,20) (11,26) (11,13) (11,15) (11,28) (11,30) (11,19) (11,20) (12,29) (12,27) (12,16) (12,21) (12,25) (12,17) (12,24) (12,23) (13,26) (13,28) (13,30) (14,29) (14,16) (14,21) (14,25) (14,17) (14,24) (14,23) (15,26) (15,28) (15,30) (15,20) (16,27) (16,21) (16,17) (16,24) (16,23) (17,29) (17,27) (17,21) (17,25) (17,24) (19,26) (19,22) (19,30) (19,20) (20,26) (20,22) (20,28) (21,29) (21,27) (21,25) (21,24) (21,23) (22,26) (22,28) (22,30) (23,29) (23,27) (23,25) (24,29) (24,27) (24,25) (25,29) (26,28) (28,30)\nQ: Is there a path between node 5 and node 16?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "804"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,20) (0,8) (0,31) (0,22) (1,4) (1,24) (1,19) (1,16) (1,5) (1,2) (1,8) (1,18) (1,27) (2,4) (2,19) (2,12) (2,17) (2,21) (2,31) (2,22) (3,25) (3,20) (3,14) (3,31) (3,22) (3,27) (4,7) (4,21) (4,26) (4,27) (5,11) (5,24) (5,20) (5,19) (5,12) (5,16) (5,17) (5,21) (5,9) (5,22) (6,15) (7,24) (7,20) (7,19) (7,16) (7,29) (7,17) (7,21) (7,14) (7,9) (7,8) (7,18) (7,22) (7,30) (8,20) (8,12) (8,14) (9,20) (9,16) (9,14) (9,18) (9,26) (9,23) (10,15) (11,25) (11,28) (11,20) (11,21) (11,26) (12,28) (12,24) (12,20) (12,29) (12,14) (12,18) (12,26) (12,22) (12,27) (12,23) (14,24) (14,16) (14,18) (14,31) (16,25) (16,26) (16,31) (16,23) (17,31) (17,27) (18,25) (18,28) (18,24) (18,21) (18,26) (18,27) (19,29) (19,21) (19,22) (20,25) (20,21) (20,26) (21,24) (21,29) (21,31) (21,23) (22,29) (22,26) (22,23) (23,25) (23,26) (24,25) (24,26) (24,30) (25,29) (25,31) (26,29) (26,31) (27,28) (27,31) (28,29) (29,31) (29,30) (30,31)\nQ: Is there a path between node 2 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "805"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,4) (0,11) (0,13) (1,8) (1,21) (1,10) (1,7) (1,2) (2,24) (2,8) (2,9) (2,10) (2,22) (3,5) (3,11) (3,13) (4,15) (4,6) (4,16) (4,11) (5,12) (5,15) (5,19) (5,18) (5,27) (6,19) (6,11) (7,26) (7,23) (7,9) (8,23) (8,9) (8,10) (8,22) (9,25) (9,14) (10,25) (10,17) (10,23) (11,20) (11,27) (12,15) (12,16) (12,18) (14,22) (15,19) (15,27) (16,19) (17,26) (17,24) (17,28) (17,23) (17,22) (19,20) (19,27) (21,26) (21,25) (21,29) (21,22) (22,29) (23,24) (23,29) (26,28)\nQ: Is there a path between node 5 and node 20?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "806"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,14) (0,20) (0,13) (1,2) (1,8) (1,9) (2,9) (4,10) (4,20) (5,21) (5,17) (5,9) (6,10) (6,14) (6,13) (7,21) (7,22) (8,9) (10,19) (10,18) (10,12) (10,13) (11,16) (11,18) (12,16) (12,19) (12,18) (13,19) (14,19) (16,18) (17,22) (18,19)\nQ: Is there a path between node 4 and node 20?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "807"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,12) (0,1) (0,13) (0,14) (0,11) (0,20) (0,7) (0,21) (1,4) (1,13) (1,14) (1,16) (1,7) (1,21) (2,5) (2,22) (2,8) (2,15) (2,25) (2,9) (2,17) (2,26) (3,11) (3,20) (3,7) (4,13) (4,14) (4,11) (4,20) (4,21) (5,22) (5,18) (5,15) (5,23) (5,25) (5,17) (5,26) (5,24) (6,19) (7,12) (7,13) (7,14) (7,11) (7,20) (7,21) (8,22) (8,15) (8,23) (8,9) (8,17) (8,24) (9,18) (9,15) (9,23) (9,25) (9,17) (11,13) (11,14) (11,16) (11,20) (12,13) (12,14) (12,16) (12,20) (12,21) (13,16) (13,20) (14,16) (14,20) (14,21) (15,22) (15,18) (15,23) (15,25) (15,26) (15,24) (16,21) (17,22) (17,18) (17,23) (17,25) (18,25) (18,24) (20,21) (22,23) (22,25) (22,26) (22,24) (23,26) (23,24) (24,25) (25,26)\nQ: Is there a path between node 2 and node 22?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "808"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,8) (0,2) (0,20) (0,16) (0,14) (0,15) (0,7) (1,18) (1,24) (1,22) (1,5) (1,19) (1,11) (1,17) (2,6) (2,4) (2,23) (2,8) (2,20) (2,16) (2,21) (2,14) (2,15) (2,10) (3,6) (3,4) (3,23) (3,8) (3,16) (3,14) (3,25) (3,15) (3,7) (4,6) (4,23) (4,8) (4,20) (4,16) (4,21) (4,14) (4,15) (4,10) (4,7) (5,18) (5,24) (5,22) (5,13) (5,9) (5,11) (5,12) (6,23) (6,8) (6,20) (6,16) (6,14) (6,25) (6,15) (7,23) (7,20) (7,16) (7,21) (7,14) (7,25) (7,15) (7,10) (8,20) (8,16) (8,14) (8,25) (8,15) (9,18) (9,24) (9,22) (9,19) (9,11) (9,17) (9,12) (10,23) (10,20) (10,16) (10,21) (10,14) (10,25) (11,22) (11,19) (11,17) (11,12) (12,18) (12,13) (12,19) (13,18) (13,24) (13,22) (13,17) (14,23) (14,20) (14,16) (14,25) (15,20) (15,16) (15,21) (15,25) (16,23) (16,20) (16,25) (17,18) (17,22) (17,19) (18,24) (18,22) (18,19) (19,24) (19,22) (20,21) (20,25) (21,23) (21,25) (22,24) (23,25)\nQ: Is there a path between node 21 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "809"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,5) (0,2) (0,3) (0,10) (0,6) (0,1) (0,4) (0,9) (0,7) (0,12) (1,8) (1,5) (1,2) (1,3) (1,10) (1,6) (1,4) (1,9) (1,7) (1,12) (2,8) (2,5) (2,3) (2,10) (2,6) (2,4) (2,9) (2,7) (2,12) (3,8) (3,5) (3,10) (3,6) (3,4) (3,9) (3,7) (3,12) (4,8) (4,5) (4,10) (4,6) (4,9) (4,7) (4,12) (5,8) (5,10) (5,6) (5,9) (5,7) (5,12) (6,8) (6,10) (6,9) (6,7) (6,12) (7,8) (7,10) (7,9) (7,12) (8,10) (8,9) (8,12) (9,10) (9,12) (10,12) (11,13)\nQ: Is there a path between node 8 and node 12?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "810"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,8) (1,5) (1,10) (1,8) (2,6) (2,7) (3,9) (3,10) (4,11) (4,8) (6,7) (8,9) (8,10) (11,12)\nQ: Is there a path between node 7 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "811"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,4) (0,9) (0,5) (0,13) (1,14) (1,15) (1,12) (1,5) (1,7) (2,4) (2,6) (2,9) (2,12) (2,13) (4,11) (4,6) (4,15) (4,7) (4,8) (4,13) (5,11) (5,10) (5,14) (5,6) (5,9) (5,15) (5,12) (5,7) (5,13) (6,14) (7,14) (7,8) (9,13) (10,14) (12,15)\nQ: Is there a path between node 13 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "812"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,15) (0,18) (0,27) (0,9) (0,13) (0,25) (0,3) (1,8) (1,5) (1,26) (1,12) (1,2) (1,16) (1,14) (2,8) (2,26) (2,12) (2,16) (2,14) (3,7) (3,4) (3,15) (3,18) (3,27) (3,13) (4,7) (4,15) (4,18) (4,27) (4,13) (5,8) (5,12) (5,11) (5,16) (5,14) (5,20) (6,17) (6,21) (6,29) (6,28) (7,15) (7,18) (7,27) (7,9) (7,13) (8,26) (8,23) (8,16) (8,14) (9,15) (10,29) (10,24) (11,12) (11,16) (11,14) (11,20) (12,22) (12,23) (12,14) (12,20) (13,18) (13,27) (14,26) (14,22) (14,23) (14,20) (15,18) (15,27) (15,25) (16,26) (16,22) (16,23) (16,20) (17,21) (17,19) (17,24) (17,28) (19,21) (19,29) (19,24) (19,28) (20,26) (20,22) (20,23) (21,29) (21,24) (22,26) (22,23) (24,29) (24,28) (25,27)\nQ: Is there a path between node 8 and node 18?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "813"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,4) (1,2) (3,4)\nQ: Is there a path between node 2 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "814"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,6) (1,4) (1,3) (1,2) (1,7) (2,10) (2,4) (2,8) (3,10) (3,6) (3,4) (3,8) (3,5) (4,6) (4,8) (4,5) (4,7) (5,10) (5,8) (6,10) (6,8) (7,10)\nQ: Is there a path between node 8 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "815"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,2) (0,8) (0,4) (0,7) (0,3) (0,1) (1,5) (1,2) (1,8) (1,4) (1,7) (1,3) (2,5) (2,8) (2,4) (2,7) (2,3) (3,5) (3,8) (3,4) (3,7) (4,5) (4,8) (4,7) (5,8) (5,7) (6,9) (7,8)\nQ: Is there a path between node 2 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "816"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,11) (0,13) (0,3) (0,15) (0,4) (0,2) (1,7) (1,8) (2,14) (2,23) (2,21) (2,6) (2,10) (3,9) (3,17) (3,13) (3,5) (3,19) (3,4) (3,16) (3,10) (4,9) (4,22) (4,6) (5,11) (5,18) (5,23) (6,9) (6,14) (6,17) (6,20) (6,15) (6,21) (7,8) (9,17) (9,15) (9,21) (10,18) (10,12) (10,16) (11,17) (11,15) (11,22) (11,16) (12,15) (12,22) (13,23) (13,16) (14,17) (14,18) (14,20) (14,21) (14,22) (14,16) (15,20) (17,20) (17,19) (17,23) (18,19) (18,23) (19,20) (19,23) (21,23) (21,22)\nQ: Is there a path between node 23 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "817"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,12) (0,1) (0,7) (0,16) (0,13) (0,9) (0,2) (0,10) (0,21) (0,19) (0,3) (0,20) (0,8) (0,23) (0,5) (0,4) (0,6) (0,22) (1,15) (1,12) (1,7) (1,16) (1,13) (1,9) (1,2) (1,10) (1,21) (1,19) (1,3) (1,20) (1,8) (1,23) (1,5) (1,4) (1,6) (1,22) (2,15) (2,12) (2,7) (2,16) (2,13) (2,9) (2,10) (2,21) (2,19) (2,3) (2,20) (2,8) (2,23) (2,5) (2,4) (2,6) (2,22) (3,15) (3,12) (3,7) (3,16) (3,13) (3,9) (3,10) (3,21) (3,19) (3,20) (3,8) (3,23) (3,5) (3,4) (3,6) (3,22) (4,15) (4,12) (4,7) (4,16) (4,13) (4,9) (4,10) (4,21) (4,19) (4,20) (4,8) (4,23) (4,5) (4,6) (4,22) (5,15) (5,12) (5,7) (5,16) (5,13) (5,9) (5,10) (5,21) (5,19) (5,20) (5,8) (5,23) (5,6) (5,22) (6,15) (6,12) (6,7) (6,16) (6,13) (6,9) (6,10) (6,21) (6,19) (6,20) (6,8) (6,23) (6,22) (7,15) (7,12) (7,16) (7,13) (7,9) (7,10) (7,21) (7,19) (7,20) (7,8) (7,23) (7,22) (8,15) (8,12) (8,16) (8,13) (8,9) (8,10) (8,21) (8,19) (8,20) (8,23) (8,22) (9,15) (9,12) (9,16) (9,13) (9,10) (9,21) (9,19) (9,20) (9,23) (9,22) (10,15) (10,12) (10,16) (10,13) (10,21) (10,19) (10,20) (10,23) (10,22) (11,17) (11,14) (11,18) (12,15) (12,16) (12,13) (12,21) (12,19) (12,20) (12,23) (12,22) (13,15) (13,16) (13,21) (13,19) (13,20) (13,23) (13,22) (14,17) (14,18) (15,16) (15,21) (15,19) (15,20) (15,23) (15,22) (16,21) (16,19) (16,20) (16,23) (16,22) (17,18) (19,21) (19,20) (19,23) (19,22) (20,21) (20,23) (20,22) (21,23) (21,22) (22,23)\nQ: Is there a path between node 12 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "818"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,12) (0,11) (0,8) (0,1) (0,13) (0,10) (0,3) (1,2) (1,5) (1,12) (1,11) (1,8) (1,13) (1,10) (1,3) (2,5) (2,12) (2,11) (2,8) (2,13) (2,10) (2,3) (3,5) (3,12) (3,11) (3,8) (3,13) (3,10) (4,9) (4,6) (4,7) (4,14) (5,12) (5,11) (5,8) (5,13) (5,10) (6,9) (6,7) (6,14) (7,9) (7,14) (8,12) (8,11) (8,13) (8,10) (9,14) (10,12) (10,11) (10,13) (11,12) (11,13) (12,13)\nQ: Is there a path between node 9 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "819"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,4) (0,1) (0,11) (0,9) (0,12) (1,2) (1,4) (1,11) (1,9) (1,13) (1,8) (1,12) (2,6) (2,3) (2,4) (2,11) (2,9) (2,13) (2,8) (3,6) (3,9) (3,13) (3,8) (3,12) (4,6) (4,11) (4,9) (4,13) (4,8) (4,12) (5,7) (5,10) (6,11) (6,9) (6,8) (6,12) (8,9) (8,12) (9,11) (9,12) (11,13) (12,13)\nQ: Is there a path between node 4 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "820"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,10) (0,13) (0,12) (0,9) (0,18) (0,24) (0,5) (0,20) (0,21) (0,7) (0,3) (0,23) (1,2) (1,13) (1,16) (1,12) (1,18) (1,24) (1,20) (1,4) (1,7) (1,3) (1,19) (1,23) (2,13) (2,16) (2,12) (2,9) (2,11) (2,18) (2,24) (2,5) (2,20) (2,4) (2,21) (2,7) (2,3) (2,23) (3,13) (3,16) (3,12) (3,9) (3,11) (3,24) (3,5) (3,20) (3,21) (3,7) (3,19) (3,23) (4,10) (4,16) (4,12) (4,11) (4,18) (4,24) (4,5) (4,20) (4,21) (4,7) (4,19) (4,23) (5,13) (5,12) (5,11) (5,18) (5,24) (5,20) (5,21) (5,7) (5,23) (6,15) (6,25) (6,22) (6,8) (7,13) (7,12) (7,9) (7,11) (7,18) (7,20) (7,21) (7,19) (8,17) (8,15) (8,22) (8,14) (9,10) (9,13) (9,16) (9,11) (9,18) (9,21) (9,19) (9,23) (10,13) (10,12) (10,11) (10,24) (10,20) (10,21) (10,19) (10,23) (11,13) (11,16) (11,24) (11,20) (11,21) (11,19) (11,23) (12,13) (12,16) (12,18) (12,24) (12,20) (12,21) (12,19) (12,23) (13,16) (13,24) (13,21) (13,23) (14,17) (14,15) (14,22) (15,17) (15,25) (15,22) (16,18) (16,24) (16,21) (16,23) (17,25) (17,22) (18,20) (18,21) (18,19) (18,23) (19,20) (19,23) (20,24) (20,21) (21,23) (22,25) (23,24)\nQ: Is there a path between node 21 and node 19?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "821"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,7) (0,10) (0,6) (0,2) (0,8) (0,4) (0,1) (1,3) (1,7) (1,10) (1,6) (1,2) (1,8) (1,4) (2,3) (2,7) (2,10) (2,6) (2,8) (2,4) (3,7) (3,10) (3,6) (3,8) (3,4) (4,7) (4,10) (4,6) (4,8) (5,9) (6,7) (6,10) (6,8) (7,10) (7,8) (8,10)\nQ: Is there a path between node 2 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "822"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,17) (0,23) (0,22) (0,1) (0,9) (0,11) (0,14) (0,19) (0,12) (0,18) (0,8) (0,4) (0,16) (0,15) (0,10) (0,6) (1,20) (1,17) (1,23) (1,22) (1,9) (1,11) (1,14) (1,19) (1,12) (1,18) (1,8) (1,4) (1,16) (1,15) (1,10) (1,6) (2,13) (2,5) (2,3) (2,21) (2,7) (3,13) (3,5) (3,21) (3,7) (4,20) (4,17) (4,23) (4,22) (4,9) (4,11) (4,14) (4,19) (4,12) (4,18) (4,8) (4,16) (4,15) (4,10) (4,6) (5,13) (5,21) (5,7) (6,20) (6,17) (6,23) (6,22) (6,9) (6,11) (6,14) (6,19) (6,12) (6,18) (6,8) (6,16) (6,15) (6,10) (7,13) (7,21) (8,20) (8,17) (8,23) (8,22) (8,9) (8,11) (8,14) (8,19) (8,12) (8,18) (8,16) (8,15) (8,10) (9,20) (9,17) (9,23) (9,22) (9,11) (9,14) (9,19) (9,12) (9,18) (9,16) (9,15) (9,10) (10,20) (10,17) (10,23) (10,22) (10,11) (10,14) (10,19) (10,12) (10,18) (10,16) (10,15) (11,20) (11,17) (11,23) (11,22) (11,14) (11,19) (11,12) (11,18) (11,16) (11,15) (12,20) (12,17) (12,23) (12,22) (12,14) (12,19) (12,18) (12,16) (12,15) (13,21) (14,20) (14,17) (14,23) (14,22) (14,19) (14,18) (14,16) (14,15) (15,20) (15,17) (15,23) (15,22) (15,19) (15,18) (15,16) (16,20) (16,17) (16,23) (16,22) (16,19) (16,18) (17,20) (17,23) (17,22) (17,19) (17,18) (18,20) (18,23) (18,22) (18,19) (19,20) (19,23) (19,22) (20,23) (20,22) (22,23)\nQ: Is there a path between node 16 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "823"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,6) (0,1) (0,5) (1,7) (1,6) (1,8) (1,5) (2,7) (2,8) (2,5) (3,4) (5,7) (5,6) (5,8)\nQ: Is there a path between node 8 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "824"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,2) (0,3) (1,5) (2,4) (2,3) (3,4)\nQ: Is there a path between node 1 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "825"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,14) (1,21) (1,3) (1,15) (1,7) (3,12) (4,10) (5,10) (6,22) (7,21) (7,15) (9,12) (11,13) (11,21) (14,20) (15,17) (15,21) (16,18) (18,22)\nQ: Is there a path between node 5 and node 17?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "826"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,9) (1,8) (1,4) (2,8) (2,4) (2,3) (3,7) (3,6) (3,10) (3,12) (3,11) (4,10) (4,12) (6,14) (6,8) (6,10) (7,14) (7,11) (8,14) (8,12) (10,14) (11,14) (12,14)\nQ: Is there a path between node 7 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "827"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,10) (0,18) (0,21) (0,30) (0,28) (0,15) (1,27) (1,24) (1,22) (1,32) (1,14) (1,5) (2,29) (2,10) (2,18) (2,21) (2,19) (2,30) (2,16) (2,28) (2,15) (3,24) (3,13) (3,22) (3,20) (3,5) (4,17) (4,11) (4,6) (4,26) (4,23) (4,31) (4,25) (5,27) (5,13) (5,22) (5,20) (5,32) (5,14) (6,17) (6,9) (6,23) (6,31) (6,25) (7,29) (7,10) (7,18) (7,19) (7,30) (7,16) (7,15) (8,17) (8,11) (8,26) (8,23) (8,31) (9,17) (9,26) (9,23) (9,31) (9,25) (10,29) (10,18) (10,21) (10,30) (10,28) (10,15) (11,17) (11,26) (11,23) (12,27) (12,24) (12,13) (12,22) (12,32) (13,27) (13,24) (13,22) (13,20) (13,32) (13,14) (14,27) (14,22) (14,32) (15,29) (15,18) (15,21) (15,19) (15,28) (16,29) (16,21) (16,19) (16,28) (17,23) (18,29) (18,21) (18,30) (18,28) (19,29) (19,21) (19,30) (19,28) (20,24) (20,22) (20,32) (21,29) (21,30) (21,28) (22,27) (22,24) (22,32) (23,31) (24,27) (25,26) (26,31) (28,30)\nQ: Is there a path between node 17 and node 23?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "828"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,1) (0,3) (1,5) (1,3) (2,4) (3,5)\nQ: Is there a path between node 1 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "829"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,12) (0,1) (0,7) (0,16) (0,13) (0,9) (0,2) (0,10) (0,21) (0,19) (0,3) (0,20) (0,8) (0,23) (0,5) (0,4) (0,6) (0,22) (1,15) (1,12) (1,7) (1,16) (1,13) (1,9) (1,2) (1,10) (1,21) (1,19) (1,3) (1,20) (1,8) (1,23) (1,5) (1,4) (1,6) (1,22) (2,15) (2,12) (2,7) (2,16) (2,13) (2,9) (2,10) (2,21) (2,19) (2,3) (2,20) (2,8) (2,23) (2,5) (2,4) (2,6) (2,22) (3,15) (3,12) (3,7) (3,16) (3,13) (3,9) (3,10) (3,21) (3,19) (3,20) (3,8) (3,23) (3,5) (3,4) (3,6) (3,22) (4,15) (4,12) (4,7) (4,16) (4,13) (4,9) (4,10) (4,21) (4,19) (4,20) (4,8) (4,23) (4,5) (4,6) (4,22) (5,15) (5,12) (5,7) (5,16) (5,13) (5,9) (5,10) (5,21) (5,19) (5,20) (5,8) (5,23) (5,6) (5,22) (6,15) (6,12) (6,7) (6,16) (6,13) (6,9) (6,10) (6,21) (6,19) (6,20) (6,8) (6,23) (6,22) (7,15) (7,12) (7,16) (7,13) (7,9) (7,10) (7,21) (7,19) (7,20) (7,8) (7,23) (7,22) (8,15) (8,12) (8,16) (8,13) (8,9) (8,10) (8,21) (8,19) (8,20) (8,23) (8,22) (9,15) (9,12) (9,16) (9,13) (9,10) (9,21) (9,19) (9,20) (9,23) (9,22) (10,15) (10,12) (10,16) (10,13) (10,21) (10,19) (10,20) (10,23) (10,22) (11,17) (11,14) (11,18) (12,15) (12,16) (12,13) (12,21) (12,19) (12,20) (12,23) (12,22) (13,15) (13,16) (13,21) (13,19) (13,20) (13,23) (13,22) (14,17) (14,18) (15,16) (15,21) (15,19) (15,20) (15,23) (15,22) (16,21) (16,19) (16,20) (16,23) (16,22) (17,18) (19,21) (19,20) (19,23) (19,22) (20,21) (20,23) (20,22) (21,23) (21,22) (22,23)\nQ: Is there a path between node 20 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "830"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,11) (0,13) (0,3) (0,15) (0,4) (0,2) (1,7) (1,8) (2,14) (2,23) (2,21) (2,6) (2,10) (3,9) (3,17) (3,13) (3,5) (3,19) (3,4) (3,16) (3,10) (4,9) (4,22) (4,6) (5,11) (5,18) (5,23) (6,9) (6,14) (6,17) (6,20) (6,15) (6,21) (7,8) (9,17) (9,15) (9,21) (10,18) (10,12) (10,16) (11,17) (11,15) (11,22) (11,16) (12,15) (12,22) (13,23) (13,16) (14,17) (14,18) (14,20) (14,21) (14,22) (14,16) (15,20) (17,20) (17,19) (17,23) (18,19) (18,23) (19,20) (19,23) (21,23) (21,22)\nQ: Is there a path between node 12 and node 20?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "831"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,10) (0,1) (1,8) (1,3) (1,14) (3,5) (3,6) (3,9) (3,12) (4,9) (4,16) (6,7) (6,12) (7,14) (8,16) (8,14) (10,11) (10,14) (10,12) (11,14) (12,14)\nQ: Is there a path between node 8 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "832"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,25) (0,3) (1,25) (1,29) (2,14) (2,13) (2,20) (2,18) (2,31) (2,9) (2,27) (2,21) (2,12) (2,7) (2,33) (2,11) (2,24) (2,26) (2,30) (3,25) (4,23) (4,22) (4,34) (4,5) (5,23) (5,22) (5,34) (6,14) (6,13) (6,20) (6,18) (6,27) (6,21) (6,12) (6,7) (6,28) (6,24) (6,26) (6,30) (7,14) (7,13) (7,20) (7,31) (7,17) (7,9) (7,27) (7,21) (7,12) (7,10) (7,33) (7,28) (7,30) (8,14) (8,13) (8,31) (8,17) (8,9) (8,27) (8,12) (8,33) (8,11) (8,28) (8,26) (8,30) (9,14) (9,13) (9,20) (9,18) (9,27) (9,21) (9,12) (9,10) (9,33) (9,24) (9,26) (9,19) (9,30) (10,13) (10,20) (10,18) (10,31) (10,17) (10,27) (10,12) (10,33) (10,11) (10,28) (10,24) (11,14) (11,13) (11,20) (11,18) (11,31) (11,12) (11,33) (11,28) (11,24) (11,26) (11,30) (12,14) (12,13) (12,20) (12,18) (12,17) (12,27) (12,21) (12,33) (12,19) (13,14) (13,20) (13,18) (13,31) (13,17) (13,21) (13,28) (13,24) (13,26) (14,18) (14,31) (14,17) (14,27) (14,21) (14,33) (14,26) (15,32) (17,18) (17,31) (17,27) (17,33) (17,28) (17,24) (17,26) (17,19) (17,30) (18,20) (18,31) (18,33) (18,24) (18,26) (18,19) (18,30) (19,31) (19,27) (19,21) (19,33) (19,28) (19,26) (20,31) (20,27) (20,21) (20,33) (20,24) (20,26) (20,30) (21,27) (21,33) (21,28) (21,24) (21,30) (22,23) (22,34) (23,34) (24,33) (24,26) (25,29) (26,31) (26,33) (26,30) (27,31) (27,33) (27,28) (27,30) (28,31) (28,33) (28,30) (30,31) (30,33) (31,33)\nQ: Is there a path between node 25 and node 18?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "833"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,21) (0,7) (0,6) (0,3) (0,17) (0,20) (0,22) (0,16) (0,23) (0,25) (0,27) (1,5) (1,21) (1,4) (1,7) (1,15) (1,18) (1,2) (1,24) (1,20) (1,11) (1,16) (1,25) (1,27) (2,14) (2,5) (2,21) (2,4) (2,15) (2,24) (2,22) (2,11) (2,23) (2,25) (2,27) (3,14) (3,13) (3,21) (3,7) (3,15) (3,6) (3,17) (3,24) (3,22) (3,11) (3,16) (3,23) (4,14) (4,13) (4,5) (4,19) (4,7) (4,18) (4,17) (4,22) (4,11) (4,23) (4,25) (4,27) (5,13) (5,19) (5,15) (5,18) (5,24) (5,20) (5,22) (5,11) (5,23) (5,27) (6,14) (6,21) (6,19) (6,7) (6,15) (6,18) (6,17) (6,24) (6,20) (6,11) (6,16) (6,25) (6,27) (7,14) (7,13) (7,21) (7,19) (7,15) (7,18) (7,17) (7,20) (7,22) (7,11) (7,23) (7,27) (8,30) (8,28) (9,31) (9,10) (9,26) (9,29) (10,31) (10,26) (10,29) (11,13) (11,21) (11,19) (11,15) (11,24) (11,22) (11,25) (11,27) (12,28) (13,14) (13,21) (13,15) (13,18) (13,17) (13,24) (13,20) (13,16) (13,23) (13,25) (13,27) (14,21) (14,19) (14,24) (14,20) (14,22) (14,16) (14,23) (14,25) (15,21) (15,18) (15,17) (15,24) (15,20) (15,22) (15,16) (15,25) (15,27) (16,21) (16,18) (16,17) (16,24) (16,20) (16,22) (16,25) (17,21) (17,19) (17,18) (17,24) (17,20) (17,22) (17,23) (17,25) (17,27) (18,21) (18,24) (18,20) (18,25) (18,27) (19,21) (19,20) (19,22) (19,27) (20,21) (20,24) (20,22) (20,23) (20,27) (21,24) (21,22) (21,25) (21,27) (22,25) (23,25) (23,27) (25,27) (26,31) (26,29) (29,31)\nQ: Is there a path between node 29 and node 30?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "834"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (1,12) (1,19) (2,13) (3,20) (3,11) (4,7) (4,16) (4,18) (5,17) (5,7) (6,15) (6,20) (6,11) (7,20) (7,11) (8,12) (8,13) (8,19) (11,17) (11,15) (12,19) (16,17) (16,20) (17,20) (18,20)\nQ: Is there a path between node 22 and node 14?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "835"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,25) (0,3) (1,25) (1,29) (2,14) (2,13) (2,20) (2,18) (2,31) (2,9) (2,27) (2,21) (2,12) (2,7) (2,33) (2,11) (2,24) (2,26) (2,30) (3,25) (4,23) (4,22) (4,34) (4,5) (5,23) (5,22) (5,34) (6,14) (6,13) (6,20) (6,18) (6,27) (6,21) (6,12) (6,7) (6,28) (6,24) (6,26) (6,30) (7,14) (7,13) (7,20) (7,31) (7,17) (7,9) (7,27) (7,21) (7,12) (7,10) (7,33) (7,28) (7,30) (8,14) (8,13) (8,31) (8,17) (8,9) (8,27) (8,12) (8,33) (8,11) (8,28) (8,26) (8,30) (9,14) (9,13) (9,20) (9,18) (9,27) (9,21) (9,12) (9,10) (9,33) (9,24) (9,26) (9,19) (9,30) (10,13) (10,20) (10,18) (10,31) (10,17) (10,27) (10,12) (10,33) (10,11) (10,28) (10,24) (11,14) (11,13) (11,20) (11,18) (11,31) (11,12) (11,33) (11,28) (11,24) (11,26) (11,30) (12,14) (12,13) (12,20) (12,18) (12,17) (12,27) (12,21) (12,33) (12,19) (13,14) (13,20) (13,18) (13,31) (13,17) (13,21) (13,28) (13,24) (13,26) (14,18) (14,31) (14,17) (14,27) (14,21) (14,33) (14,26) (15,32) (17,18) (17,31) (17,27) (17,33) (17,28) (17,24) (17,26) (17,19) (17,30) (18,20) (18,31) (18,33) (18,24) (18,26) (18,19) (18,30) (19,31) (19,27) (19,21) (19,33) (19,28) (19,26) (20,31) (20,27) (20,21) (20,33) (20,24) (20,26) (20,30) (21,27) (21,33) (21,28) (21,24) (21,30) (22,23) (22,34) (23,34) (24,33) (24,26) (25,29) (26,31) (26,33) (26,30) (27,31) (27,33) (27,28) (27,30) (28,31) (28,33) (28,30) (30,31) (30,33) (31,33)\nQ: Is there a path between node 1 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "836"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,10) (0,17) (0,15) (0,4) (0,12) (0,24) (0,9) (0,3) (0,13) (0,23) (0,7) (0,19) (0,16) (0,6) (0,25) (0,8) (1,10) (1,17) (1,4) (1,12) (1,24) (1,3) (1,13) (1,23) (1,26) (1,22) (1,19) (1,6) (1,14) (1,25) (1,8) (1,20) (2,10) (2,17) (2,11) (2,4) (2,24) (2,9) (2,3) (2,13) (2,23) (2,26) (2,7) (2,22) (2,19) (2,6) (2,14) (2,25) (2,8) (3,10) (3,17) (3,11) (3,15) (3,4) (3,12) (3,24) (3,9) (3,13) (3,26) (3,7) (3,19) (3,16) (3,14) (3,25) (3,8) (3,20) (4,10) (4,17) (4,11) (4,15) (4,12) (4,24) (4,9) (4,7) (4,19) (4,16) (4,6) (4,25) (4,20) (5,18) (6,10) (6,17) (6,15) (6,12) (6,24) (6,9) (6,23) (6,7) (6,16) (6,25) (6,8) (7,10) (7,11) (7,15) (7,12) (7,13) (7,22) (7,19) (7,16) (7,25) (7,8) (7,20) (8,10) (8,17) (8,11) (8,15) (8,12) (8,24) (8,9) (8,23) (8,22) (8,19) (8,16) (8,14) (8,25) (8,20) (9,10) (9,17) (9,11) (9,12) (9,24) (9,13) (9,23) (9,26) (9,22) (9,19) (9,16) (9,20) (10,17) (10,11) (10,15) (10,12) (10,24) (10,13) (10,23) (10,26) (10,19) (10,14) (10,20) (11,15) (11,12) (11,24) (11,13) (11,23) (11,26) (11,19) (11,16) (11,14) (11,20) (12,15) (12,24) (12,23) (12,22) (12,19) (12,16) (12,14) (12,25) (12,20) (13,15) (13,24) (13,23) (13,19) (13,16) (13,14) (13,25) (13,20) (14,17) (14,15) (14,24) (14,23) (14,26) (14,22) (14,19) (14,16) (14,25) (14,20) (15,17) (15,24) (15,23) (15,26) (15,16) (15,20) (16,24) (16,23) (16,26) (16,19) (16,25) (16,20) (17,23) (17,20) (18,21) (19,23) (19,22) (19,25) (19,20) (20,24) (20,23) (20,22) (20,25) (22,26) (22,25) (23,24) (23,26) (23,25) (24,26) (24,25) (25,26)\nQ: Is there a path between node 21 and node 14?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "837"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,3) (0,5) (1,2) (1,8) (1,7) (2,8) (2,7) (3,11) (3,9) (3,13) (5,11) (5,12) (10,11) (11,12) (12,13)\nQ: Is there a path between node 3 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "838"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (3,8) (3,9) (4,5) (8,9)\nQ: Is there a path between node 4 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "839"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,11) (0,1) (0,3) (0,10) (0,4) (1,11) (1,3) (1,10) (1,4) (2,7) (3,11) (3,4) (4,5) (4,11) (5,11) (6,9) (6,8) (7,9) (7,8) (8,9) (10,11)\nQ: Is there a path between node 5 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "840"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,28) (0,1) (0,22) (0,20) (0,15) (0,18) (0,2) (0,5) (0,10) (0,8) (0,14) (0,6) (1,27) (1,12) (1,19) (1,28) (1,25) (1,29) (1,22) (1,4) (1,7) (1,15) (1,18) (1,3) (1,2) (1,24) (1,5) (1,11) (1,14) (1,13) (1,6) (2,12) (2,19) (2,28) (2,29) (2,4) (2,15) (2,16) (2,18) (2,3) (2,10) (2,13) (2,21) (2,6) (3,27) (3,19) (3,28) (3,20) (3,4) (3,7) (3,16) (3,18) (3,9) (3,24) (3,5) (3,11) (3,10) (3,8) (3,14) (3,23) (3,21) (3,6) (4,27) (4,12) (4,19) (4,28) (4,25) (4,20) (4,7) (4,15) (4,16) (4,5) (4,8) (4,14) (4,13) (4,21) (4,6) (5,27) (5,12) (5,19) (5,28) (5,25) (5,29) (5,22) (5,20) (5,7) (5,15) (5,16) (5,24) (5,11) (5,10) (5,8) (5,14) (5,23) (5,13) (5,21) (5,6) (6,27) (6,12) (6,28) (6,25) (6,29) (6,22) (6,20) (6,7) (6,16) (6,18) (6,9) (6,24) (6,8) (6,14) (6,21) (7,19) (7,25) (7,29) (7,22) (7,20) (7,15) (7,16) (7,24) (7,11) (7,10) (7,14) (7,23) (7,21) (8,27) (8,12) (8,19) (8,29) (8,22) (8,20) (8,15) (8,16) (8,9) (8,24) (8,11) (8,10) (8,14) (8,13) (9,12) (9,19) (9,25) (9,22) (9,20) (9,18) (9,24) (9,11) (9,10) (9,14) (9,23) (9,13) (9,21) (10,27) (10,12) (10,19) (10,28) (10,25) (10,29) (10,16) (10,18) (10,24) (10,14) (10,23) (10,13) (10,21) (11,27) (11,12) (11,25) (11,22) (11,20) (11,18) (11,24) (12,19) (12,28) (12,29) (12,22) (12,15) (12,16) (12,18) (12,14) (12,23) (12,13) (12,21) (13,27) (13,28) (13,25) (13,29) (13,22) (13,20) (13,15) (13,18) (13,24) (14,19) (14,28) (14,25) (14,29) (14,15) (14,16) (14,18) (14,24) (14,23) (15,27) (15,28) (15,25) (15,29) (15,20) (15,18) (15,23) (15,21) (16,27) (16,19) (16,28) (16,25) (16,29) (16,22) (16,20) (16,18) (16,24) (16,21) (18,19) (18,28) (18,29) (18,22) (18,20) (18,24) (18,23) (18,21) (19,27) (19,28) (19,25) (19,29) (19,22) (19,20) (19,24) (19,23) (19,21) (20,27) (20,28) (20,29) (20,22) (20,23) (20,21) (21,27) (21,28) (21,24) (21,23) (22,27) (22,28) (22,29) (22,23) (23,27) (23,28) (23,25) (23,29) (24,27) (24,28) (24,25) (24,29) (25,27) (25,29) (27,28) (27,29)\nQ: Is there a path between node 18 and node 26?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "841"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "842"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (1,2) (1,5) (5,6)\nQ: Is there a path between node 3 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "843"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,13) (0,12) (0,14) (0,8) (0,3) (0,6) (0,2) (0,9) (0,5) (1,10) (1,7) (1,11) (2,4) (2,13) (2,12) (2,14) (2,8) (2,3) (2,6) (2,9) (2,5) (3,4) (3,13) (3,12) (3,14) (3,8) (3,6) (3,9) (3,5) (4,13) (4,12) (4,14) (4,8) (4,6) (4,9) (4,5) (5,13) (5,12) (5,14) (5,8) (5,6) (5,9) (6,13) (6,12) (6,14) (6,8) (6,9) (7,10) (7,11) (8,13) (8,12) (8,14) (8,9) (9,13) (9,12) (9,14) (10,11) (12,13) (12,14) (13,14)\nQ: Is there a path between node 10 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "844"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,3) (0,5) (1,2) (1,8) (1,7) (2,8) (2,7) (3,11) (3,9) (3,13) (5,11) (5,12) (10,11) (11,12) (12,13)\nQ: Is there a path between node 0 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "845"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,1) (2,3) (4,6) (5,6) (5,7)\nQ: Is there a path between node 7 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "846"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,1) (0,12) (0,4) (1,13) (1,3) (1,6) (1,9) (2,15) (2,14) (2,11) (4,7) (5,16) (5,6) (5,9) (6,13) (6,8) (10,13) (10,12) (11,15) (11,14)\nQ: Is there a path between node 3 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "847"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (1,17) (2,9) (3,16) (5,18) (5,11) (5,21) (6,21) (6,15) (7,19) (7,21) (8,10) (8,12) (8,16) (10,16) (14,23) (15,21) (16,19) (17,20) (18,19) (20,23)\nQ: Is there a path between node 14 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "848"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,17) (0,10) (0,28) (0,30) (0,29) (0,3) (1,14) (1,2) (2,25) (2,20) (2,7) (2,32) (2,22) (3,24) (3,19) (3,23) (3,4) (3,12) (3,29) (4,26) (4,24) (4,23) (4,8) (4,13) (5,26) (5,19) (5,23) (5,8) (5,15) (5,21) (6,14) (7,32) (8,16) (8,12) (8,29) (9,26) (9,13) (9,18) (9,29) (9,31) (10,17) (10,11) (10,30) (10,23) (10,13) (11,16) (11,17) (11,19) (11,28) (11,23) (12,26) (12,24) (12,21) (13,26) (13,17) (13,19) (13,30) (13,31) (14,25) (14,22) (15,16) (15,17) (15,23) (15,18) (15,29) (16,26) (16,24) (16,18) (16,21) (17,24) (17,19) (17,28) (17,30) (17,23) (18,24) (18,21) (19,26) (19,24) (19,28) (19,23) (20,32) (22,32) (22,27) (24,26) (24,30) (26,29) (28,29)\nQ: Is there a path between node 25 and node 17?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "849"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,13) (0,6) (0,5) (0,15) (0,14) (0,1) (0,10) (0,8) (0,7) (0,2) (0,11) (0,3) (1,12) (1,13) (1,6) (1,5) (1,15) (1,14) (1,10) (1,8) (1,7) (1,2) (1,11) (1,3) (2,12) (2,13) (2,6) (2,5) (2,15) (2,14) (2,10) (2,8) (2,7) (2,11) (2,3) (3,12) (3,13) (3,6) (3,5) (3,15) (3,14) (3,10) (3,8) (3,7) (3,11) (4,9) (5,12) (5,13) (5,6) (5,15) (5,14) (5,10) (5,8) (5,7) (5,11) (6,12) (6,13) (6,15) (6,14) (6,10) (6,8) (6,7) (6,11) (7,12) (7,13) (7,15) (7,14) (7,10) (7,8) (7,11) (8,12) (8,13) (8,15) (8,14) (8,10) (8,11) (10,12) (10,13) (10,15) (10,14) (10,11) (11,12) (11,13) (11,15) (11,14) (12,13) (12,15) (12,14) (13,15) (13,14) (14,15)\nQ: Is there a path between node 8 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "850"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,8) (0,5) (0,4) (0,25) (0,22) (0,16) (0,24) (0,21) (2,15) (2,23) (2,26) (2,10) (2,3) (2,11) (2,6) (2,27) (3,15) (3,23) (3,14) (3,26) (3,10) (3,11) (3,27) (4,8) (4,13) (4,5) (4,20) (4,18) (4,7) (4,22) (4,16) (4,24) (5,8) (5,13) (5,20) (5,7) (5,22) (5,24) (5,21) (6,15) (6,23) (6,14) (6,26) (6,10) (6,11) (6,27) (7,12) (7,20) (7,25) (7,16) (7,21) (8,12) (8,20) (8,25) (8,16) (8,24) (10,15) (10,23) (10,14) (10,26) (10,19) (10,11) (10,27) (11,15) (11,23) (11,26) (11,27) (12,16) (12,24) (12,21) (13,20) (13,18) (13,25) (13,22) (13,16) (13,24) (13,21) (14,15) (14,26) (15,26) (15,27) (16,22) (16,24) (16,21) (18,25) (18,22) (18,21) (19,23) (19,26) (19,27) (20,25) (20,24) (21,25) (21,24) (22,25) (22,24) (23,26) (23,27) (24,25) (26,27)\nQ: Is there a path between node 19 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "851"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,17) (0,13) (0,12) (0,4) (0,1) (1,3) (1,17) (1,16) (1,14) (1,4) (2,5) (2,7) (2,9) (2,11) (2,8) (3,15) (3,13) (3,16) (3,12) (3,14) (3,6) (4,15) (4,13) (4,16) (4,12) (4,6) (5,9) (5,11) (5,10) (6,17) (6,13) (6,12) (7,11) (7,10) (7,8) (8,9) (8,11) (9,10) (10,11) (12,15) (12,17) (12,16) (12,14) (13,17) (13,16) (14,15) (14,17) (15,17) (15,16) (16,17)\nQ: Is there a path between node 1 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "852"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,4) (0,15) (0,19) (0,8) (0,17) (0,13) (0,3) (0,14) (0,5) (0,2) (0,16) (0,1) (0,10) (1,20) (1,4) (1,15) (1,19) (1,8) (1,17) (1,13) (1,3) (1,14) (1,5) (1,2) (1,16) (1,10) (2,20) (2,4) (2,15) (2,19) (2,8) (2,17) (2,13) (2,3) (2,14) (2,5) (2,16) (2,10) (3,20) (3,4) (3,15) (3,19) (3,8) (3,17) (3,13) (3,14) (3,5) (3,16) (3,10) (4,20) (4,15) (4,19) (4,8) (4,17) (4,13) (4,14) (4,5) (4,16) (4,10) (5,20) (5,15) (5,19) (5,8) (5,17) (5,13) (5,14) (5,16) (5,10) (6,12) (6,22) (6,9) (6,18) (6,21) (6,7) (6,11) (7,12) (7,22) (7,9) (7,18) (7,21) (7,11) (8,20) (8,15) (8,19) (8,17) (8,13) (8,14) (8,16) (8,10) (9,12) (9,22) (9,18) (9,21) (9,11) (10,20) (10,15) (10,19) (10,17) (10,13) (10,14) (10,16) (11,12) (11,22) (11,18) (11,21) (12,22) (12,18) (12,21) (13,20) (13,15) (13,19) (13,17) (13,14) (13,16) (14,20) (14,15) (14,19) (14,17) (14,16) (15,20) (15,19) (15,17) (15,16) (16,20) (16,19) (16,17) (17,20) (17,19) (18,22) (18,21) (19,20) (21,22)\nQ: Is there a path between node 16 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "853"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,8) (0,5) (0,4) (0,25) (0,22) (0,16) (0,24) (0,21) (2,15) (2,23) (2,26) (2,10) (2,3) (2,11) (2,6) (2,27) (3,15) (3,23) (3,14) (3,26) (3,10) (3,11) (3,27) (4,8) (4,13) (4,5) (4,20) (4,18) (4,7) (4,22) (4,16) (4,24) (5,8) (5,13) (5,20) (5,7) (5,22) (5,24) (5,21) (6,15) (6,23) (6,14) (6,26) (6,10) (6,11) (6,27) (7,12) (7,20) (7,25) (7,16) (7,21) (8,12) (8,20) (8,25) (8,16) (8,24) (10,15) (10,23) (10,14) (10,26) (10,19) (10,11) (10,27) (11,15) (11,23) (11,26) (11,27) (12,16) (12,24) (12,21) (13,20) (13,18) (13,25) (13,22) (13,16) (13,24) (13,21) (14,15) (14,26) (15,26) (15,27) (16,22) (16,24) (16,21) (18,25) (18,22) (18,21) (19,23) (19,26) (19,27) (20,25) (20,24) (21,25) (21,24) (22,25) (22,24) (23,26) (23,27) (24,25) (26,27)\nQ: Is there a path between node 9 and node 26?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "854"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,14) (1,21) (1,3) (1,15) (1,7) (3,12) (4,10) (5,10) (6,22) (7,21) (7,15) (9,12) (11,13) (11,21) (14,20) (15,17) (15,21) (16,18) (18,22)\nQ: Is there a path between node 11 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "855"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,5) (0,11) (0,8) (0,6) (0,1) (1,10) (1,3) (1,5) (1,9) (1,6) (1,2) (2,10) (2,3) (2,5) (2,9) (2,8) (2,7) (2,6) (2,13) (3,9) (3,11) (3,8) (3,7) (4,12) (5,10) (5,9) (5,8) (5,7) (5,6) (6,10) (6,9) (6,11) (6,8) (7,10) (7,11) (7,8) (7,13) (8,10) (8,11) (8,13) (9,10) (9,11) (9,13) (10,11) (10,13)\nQ: Is there a path between node 2 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "856"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,6) (0,11) (0,19) (0,20) (0,1) (0,15) (0,12) (0,7) (0,22) (0,5) (0,21) (0,3) (0,4) (0,18) (0,17) (1,14) (1,6) (1,11) (1,19) (1,20) (1,15) (1,12) (1,7) (1,22) (1,5) (1,21) (1,3) (1,4) (1,18) (1,17) (2,13) (2,10) (2,8) (2,16) (2,9) (3,14) (3,6) (3,11) (3,19) (3,20) (3,15) (3,12) (3,7) (3,22) (3,5) (3,21) (3,4) (3,18) (3,17) (4,14) (4,6) (4,11) (4,19) (4,20) (4,15) (4,12) (4,7) (4,22) (4,5) (4,21) (4,18) (4,17) (5,14) (5,6) (5,11) (5,19) (5,20) (5,15) (5,12) (5,7) (5,22) (5,21) (5,18) (5,17) (6,14) (6,11) (6,19) (6,20) (6,15) (6,12) (6,7) (6,22) (6,21) (6,18) (6,17) (7,14) (7,11) (7,19) (7,20) (7,15) (7,12) (7,22) (7,21) (7,18) (7,17) (8,13) (8,10) (8,16) (8,9) (9,13) (9,10) (9,16) (10,13) (10,16) (11,14) (11,19) (11,20) (11,15) (11,12) (11,22) (11,21) (11,18) (11,17) (12,14) (12,19) (12,20) (12,15) (12,22) (12,21) (12,18) (12,17) (13,16) (14,19) (14,20) (14,15) (14,22) (14,21) (14,18) (14,17) (15,19) (15,20) (15,22) (15,21) (15,18) (15,17) (17,19) (17,20) (17,22) (17,21) (17,18) (18,19) (18,20) (18,22) (18,21) (19,20) (19,22) (19,21) (20,22) (20,21) (21,22)\nQ: Is there a path between node 8 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "857"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,21) (1,17) (1,15) (1,2) (1,4) (1,18) (2,8) (2,13) (2,17) (2,15) (2,23) (2,22) (2,4) (2,18) (2,12) (4,21) (4,8) (4,13) (4,15) (4,23) (4,22) (4,18) (4,12) (5,21) (5,8) (5,13) (5,17) (5,15) (5,22) (5,18) (7,14) (7,16) (7,10) (7,11) (7,19) (8,21) (8,17) (8,23) (8,18) (9,14) (9,24) (10,14) (10,24) (10,19) (11,14) (11,16) (11,24) (12,21) (12,13) (12,17) (12,15) (12,23) (12,22) (12,18) (13,21) (13,17) (13,15) (13,23) (13,22) (14,24) (15,21) (15,17) (15,23) (15,22) (15,18) (16,19) (17,21) (17,18) (18,21) (18,23) (21,22) (22,23)\nQ: Is there a path between node 19 and node 23?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "858"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,10) (0,2) (2,15) (2,20) (2,23) (2,14) (2,17) (2,24) (2,18) (3,21) (4,27) (5,9) (5,22) (6,29) (6,8) (7,29) (7,25) (7,20) (7,17) (7,18) (7,8) (8,23) (8,24) (10,23) (10,18) (11,27) (12,13) (13,21) (14,25) (14,23) (14,17) (14,24) (15,29) (15,25) (15,23) (15,16) (16,29) (16,17) (17,25) (17,23) (17,24) (17,18) (18,29) (20,25) (22,26) (23,25) (24,29) (26,27)\nQ: Is there a path between node 9 and node 22?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "859"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (1,2) (1,5) (5,6)\nQ: Is there a path between node 1 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "860"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,4) (0,1) (0,5) (0,24) (0,3) (0,21) (0,19) (0,9) (0,15) (0,20) (0,27) (0,13) (1,24) (1,21) (1,31) (1,10) (1,7) (1,20) (1,27) (1,13) (2,6) (2,5) (2,24) (2,3) (2,21) (2,19) (2,9) (2,31) (2,15) (2,7) (2,27) (2,13) (3,6) (3,4) (3,5) (3,22) (3,24) (3,21) (3,19) (3,9) (3,31) (3,18) (3,7) (3,20) (4,5) (4,21) (4,19) (4,9) (4,31) (4,7) (4,20) (4,27) (4,13) (5,6) (5,22) (5,24) (5,21) (5,9) (5,31) (5,10) (5,15) (5,18) (5,20) (5,27) (5,13) (6,22) (6,21) (6,19) (6,9) (6,31) (6,10) (6,15) (6,18) (6,7) (6,27) (6,13) (7,22) (7,9) (7,10) (7,15) (7,18) (7,20) (7,27) (7,13) (8,16) (8,11) (8,28) (8,12) (8,25) (8,30) (8,14) (8,32) (8,29) (9,22) (9,24) (9,21) (9,19) (9,31) (9,10) (9,15) (9,18) (9,20) (10,22) (10,19) (10,31) (10,15) (10,20) (10,27) (10,13) (11,16) (11,28) (11,26) (11,23) (11,30) (11,14) (11,32) (11,17) (12,16) (12,28) (12,23) (12,30) (12,14) (12,33) (12,32) (12,17) (12,29) (13,22) (13,24) (13,21) (13,19) (13,15) (13,18) (13,20) (14,28) (14,26) (14,23) (14,25) (14,33) (14,32) (14,29) (15,22) (15,24) (15,21) (15,19) (15,20) (15,27) (16,26) (16,25) (16,30) (16,33) (16,32) (16,17) (16,29) (17,28) (17,26) (17,25) (17,30) (17,33) (17,32) (17,29) (18,24) (18,19) (18,31) (19,22) (19,24) (19,31) (19,20) (19,27) (20,21) (20,31) (20,27) (21,31) (23,28) (23,26) (23,25) (23,30) (24,31) (24,27) (25,26) (25,30) (25,33) (25,32) (25,29) (26,28) (26,33) (26,32) (28,30) (28,29) (29,30) (29,33) (29,32) (30,32)\nQ: Is there a path between node 28 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "861"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,19) (0,25) (0,2) (0,13) (0,1) (1,17) (1,24) (1,25) (1,11) (2,17) (2,25) (2,16) (2,13) (3,17) (4,23) (4,7) (4,14) (4,8) (5,18) (5,16) (6,18) (6,16) (6,21) (7,14) (7,15) (7,10) (8,23) (8,10) (9,14) (9,10) (10,23) (10,20) (11,17) (11,18) (11,25) (11,16) (11,13) (12,16) (13,17) (13,24) (13,25) (13,21) (14,15) (16,21) (17,19) (17,18) (17,25) (19,25) (19,21) (21,25)\nQ: Is there a path between node 4 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "862"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,9) (0,8) (0,19) (0,13) (0,11) (1,15) (1,6) (1,3) (1,12) (1,4) (1,2) (1,23) (1,5) (1,16) (1,22) (1,17) (1,18) (1,21) (1,24) (1,25) (2,15) (2,3) (2,4) (2,20) (2,23) (2,22) (2,27) (2,18) (2,21) (2,24) (3,15) (3,4) (3,26) (3,20) (3,23) (3,5) (3,16) (3,14) (3,22) (3,27) (3,18) (3,21) (3,24) (3,25) (4,15) (4,6) (4,12) (4,26) (4,20) (4,5) (4,22) (4,27) (4,17) (4,21) (4,25) (5,15) (5,6) (5,12) (5,20) (5,16) (5,14) (5,22) (5,27) (5,18) (5,21) (5,25) (6,15) (6,12) (6,27) (6,17) (6,21) (6,24) (6,25) (7,19) (7,13) (8,9) (8,19) (8,13) (9,19) (9,10) (10,19) (10,13) (10,11) (11,13) (12,15) (12,26) (12,20) (12,14) (12,22) (12,21) (12,24) (13,19) (14,15) (14,26) (14,20) (14,16) (14,22) (14,17) (14,21) (14,24) (14,25) (15,26) (15,20) (15,23) (15,16) (15,22) (15,17) (15,18) (15,24) (16,26) (16,27) (16,18) (16,25) (17,26) (17,23) (17,18) (17,21) (17,24) (17,25) (18,26) (18,20) (18,22) (18,27) (18,24) (18,25) (20,26) (20,23) (20,22) (20,27) (20,24) (20,25) (21,22) (21,27) (21,24) (21,25) (22,23) (22,27) (22,24) (22,25) (23,27) (23,25) (24,26) (24,27) (25,26) (25,27) (26,27)\nQ: Is there a path between node 20 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "863"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,23) (0,8) (1,6) (1,26) (1,11) (2,6) (2,11) (3,12) (3,19) (3,20) (4,13) (4,21) (4,17) (4,10) (4,6) (4,23) (4,8) (5,13) (5,7) (5,21) (5,17) (5,28) (5,6) (5,23) (5,8) (5,26) (5,24) (5,11) (6,13) (6,17) (6,10) (6,23) (6,24) (7,17) (7,28) (7,23) (8,21) (8,10) (9,15) (10,13) (10,21) (10,23) (10,11) (11,13) (11,17) (12,19) (12,14) (12,27) (12,15) (12,22) (13,17) (13,16) (14,22) (15,19) (16,17) (16,28) (16,24) (17,24) (18,19) (18,27) (19,27) (21,26) (21,24) (22,25) (23,28) (24,28) (25,27)\nQ: Is there a path between node 19 and node 22?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "864"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,3) (0,11) (0,18) (0,7) (0,8) (0,9) (0,1) (0,10) (0,15) (0,17) (0,13) (0,16) (0,19) (0,2) (0,6) (0,5) (0,14) (1,12) (1,3) (1,11) (1,18) (1,7) (1,8) (1,9) (1,10) (1,15) (1,17) (1,13) (1,16) (1,19) (1,2) (1,6) (1,5) (1,14) (2,12) (2,3) (2,11) (2,18) (2,7) (2,8) (2,9) (2,10) (2,15) (2,17) (2,13) (2,16) (2,19) (2,6) (2,5) (2,14) (3,12) (3,11) (3,18) (3,7) (3,8) (3,9) (3,10) (3,15) (3,17) (3,13) (3,16) (3,19) (3,6) (3,5) (3,14) (4,20) (4,21) (5,12) (5,11) (5,18) (5,7) (5,8) (5,9) (5,10) (5,15) (5,17) (5,13) (5,16) (5,19) (5,6) (5,14) (6,12) (6,11) (6,18) (6,7) (6,8) (6,9) (6,10) (6,15) (6,17) (6,13) (6,16) (6,19) (6,14) (7,12) (7,11) (7,18) (7,8) (7,9) (7,10) (7,15) (7,17) (7,13) (7,16) (7,19) (7,14) (8,12) (8,11) (8,18) (8,9) (8,10) (8,15) (8,17) (8,13) (8,16) (8,19) (8,14) (9,12) (9,11) (9,18) (9,10) (9,15) (9,17) (9,13) (9,16) (9,19) (9,14) (10,12) (10,11) (10,18) (10,15) (10,17) (10,13) (10,16) (10,19) (10,14) (11,12) (11,18) (11,15) (11,17) (11,13) (11,16) (11,19) (11,14) (12,18) (12,15) (12,17) (12,13) (12,16) (12,19) (12,14) (13,18) (13,15) (13,17) (13,16) (13,19) (13,14) (14,18) (14,15) (14,17) (14,16) (14,19) (15,18) (15,17) (15,16) (15,19) (16,18) (16,17) (16,19) (17,18) (17,19) (18,19) (20,21)\nQ: Is there a path between node 15 and node 20?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "865"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,2) (2,3)\nQ: Is there a path between node 3 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "866"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,5) (0,20) (0,7) (0,19) (0,1) (0,14) (0,12) (0,15) (0,18) (0,4) (1,10) (1,5) (1,7) (1,2) (1,14) (1,12) (1,3) (1,15) (1,16) (1,4) (2,10) (2,5) (2,20) (2,7) (2,19) (2,14) (2,12) (2,15) (2,16) (2,17) (2,18) (2,4) (3,5) (3,20) (3,7) (3,19) (3,14) (3,16) (3,17) (3,18) (4,10) (4,5) (4,20) (4,7) (4,19) (4,14) (4,12) (4,15) (4,16) (4,17) (5,20) (5,7) (5,19) (5,14) (5,12) (5,16) (5,17) (5,18) (6,11) (6,8) (7,10) (7,19) (7,14) (7,12) (7,15) (7,16) (7,17) (7,18) (8,11) (9,21) (9,13) (10,19) (10,14) (10,12) (10,16) (10,18) (12,20) (12,19) (12,14) (12,15) (12,16) (12,17) (14,20) (14,19) (14,15) (14,16) (14,17) (15,20) (15,19) (15,16) (15,17) (15,18) (16,20) (16,19) (16,17) (16,18) (17,20) (17,19) (17,18) (18,19) (19,20)\nQ: Is there a path between node 20 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "867"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,6) (0,21) (0,18) (1,24) (1,3) (3,24) (3,14) (4,6) (4,5) (4,23) (6,14) (6,21) (6,23) (7,11) (8,19) (8,13) (9,15) (9,19) (10,11) (10,12) (10,16) (10,17) (11,12) (11,16) (12,17) (13,15) (13,22) (14,23) (15,22) (16,17) (18,24) (18,21)\nQ: Is there a path between node 1 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "868"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,13) (0,11) (0,21) (0,8) (0,18) (0,3) (0,7) (0,15) (0,20) (0,17) (0,10) (0,22) (0,1) (0,9) (0,6) (0,19) (1,23) (1,14) (1,5) (1,13) (1,11) (1,12) (1,21) (1,8) (1,18) (1,3) (1,25) (1,7) (1,28) (1,15) (1,20) (1,17) (1,10) (1,22) (1,9) (1,6) (1,16) (1,19) (3,27) (3,14) (3,5) (3,13) (3,4) (3,21) (3,18) (3,25) (3,28) (3,15) (3,20) (3,17) (3,22) (3,6) (3,16) (3,19) (4,27) (4,23) (4,5) (4,13) (4,11) (4,12) (4,8) (4,28) (4,15) (4,20) (4,17) (4,10) (4,24) (4,6) (5,27) (5,23) (5,14) (5,13) (5,11) (5,12) (5,21) (5,8) (5,18) (5,25) (5,7) (5,15) (5,10) (5,22) (5,24) (5,9) (5,6) (5,16) (5,19) (6,27) (6,14) (6,11) (6,12) (6,18) (6,25) (6,7) (6,20) (6,17) (6,10) (6,22) (6,24) (6,9) (6,16) (6,19) (7,23) (7,14) (7,13) (7,12) (7,21) (7,8) (7,25) (7,28) (7,20) (7,10) (7,22) (7,16) (7,19) (8,27) (8,13) (8,18) (8,25) (8,15) (8,17) (8,10) (8,22) (8,24) (8,9) (8,16) (8,19) (9,27) (9,23) (9,11) (9,21) (9,25) (9,28) (9,15) (9,20) (9,17) (9,10) (9,22) (9,24) (9,16) (9,19) (10,27) (10,14) (10,11) (10,12) (10,25) (10,28) (10,15) (10,20) (10,17) (10,24) (10,16) (10,19) (11,23) (11,21) (11,18) (11,25) (11,28) (11,15) (11,17) (11,22) (11,24) (11,19) (12,27) (12,23) (12,13) (12,21) (12,18) (12,25) (12,28) (12,15) (12,17) (12,22) (12,24) (12,16) (13,27) (13,14) (13,21) (13,18) (13,28) (13,15) (13,17) (13,24) (13,16) (13,19) (14,27) (14,25) (14,28) (14,15) (14,17) (14,22) (14,24) (14,16) (15,23) (15,21) (15,18) (15,25) (15,20) (15,24) (16,27) (16,23) (16,17) (16,24) (16,19) (17,27) (17,23) (17,18) (17,25) (17,28) (17,20) (17,22) (17,24) (17,19) (18,23) (18,21) (18,25) (18,28) (18,20) (18,22) (18,24) (18,19) (19,27) (19,23) (19,21) (19,25) (19,24) (20,27) (20,23) (20,21) (20,25) (20,24) (21,23) (21,22) (23,27) (23,24) (25,27) (25,28) (27,28)\nQ: Is there a path between node 25 and node 26?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "869"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,2) (2,3)\nQ: Is there a path between node 2 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "870"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,11) (3,15) (3,8) (5,18) (5,7) (6,17) (6,7) (7,13) (7,8) (7,14) (8,18) (8,12) (9,11) (9,15) (9,13) (9,17) (10,18) (11,13) (11,17) (12,18) (12,17) (12,14) (13,17) (14,17) (17,18)\nQ: Is there a path between node 11 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "871"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,6) (2,7) (2,6) (2,4) (5,7) (6,8)\nQ: Is there a path between node 3 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "872"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,11) (0,13) (0,3) (0,15) (0,4) (0,2) (1,7) (1,8) (2,14) (2,23) (2,21) (2,6) (2,10) (3,9) (3,17) (3,13) (3,5) (3,19) (3,4) (3,16) (3,10) (4,9) (4,22) (4,6) (5,11) (5,18) (5,23) (6,9) (6,14) (6,17) (6,20) (6,15) (6,21) (7,8) (9,17) (9,15) (9,21) (10,18) (10,12) (10,16) (11,17) (11,15) (11,22) (11,16) (12,15) (12,22) (13,23) (13,16) (14,17) (14,18) (14,20) (14,21) (14,22) (14,16) (15,20) (17,20) (17,19) (17,23) (18,19) (18,23) (19,20) (19,23) (21,23) (21,22)\nQ: Is there a path between node 7 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "873"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (2,8) (2,4) (2,3) (3,8) (5,7) (6,7)\nQ: Is there a path between node 7 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "874"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,30) (0,6) (0,12) (1,15) (2,17) (2,4) (3,25) (3,30) (3,12) (4,18) (4,16) (4,20) (4,22) (4,28) (4,8) (4,17) (5,12) (5,11) (6,19) (7,9) (7,10) (8,22) (8,28) (8,21) (9,23) (10,12) (10,11) (11,30) (11,19) (11,12) (12,25) (12,19) (13,27) (13,26) (15,26) (16,18) (16,29) (16,20) (16,24) (16,22) (16,28) (16,17) (17,22) (17,28) (17,21) (18,29) (18,20) (18,24) (18,22) (19,30) (20,22) (20,28) (21,24) (24,28) (25,30)\nQ: Is there a path between node 21 and node 15?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "875"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,9) (0,2) (0,5) (0,10) (0,1) (1,4) (1,9) (1,2) (1,5) (1,10) (2,4) (2,9) (2,5) (2,10) (3,11) (3,8) (3,12) (3,7) (3,6) (4,9) (4,5) (4,10) (5,9) (5,10) (6,11) (6,8) (6,12) (6,7) (7,11) (7,8) (7,12) (8,11) (8,12) (9,10) (11,12)\nQ: Is there a path between node 10 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "876"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,11) (3,15) (3,8) (5,18) (5,7) (6,17) (6,7) (7,13) (7,8) (7,14) (8,18) (8,12) (9,11) (9,15) (9,13) (9,17) (10,18) (11,13) (11,17) (12,18) (12,17) (12,14) (13,17) (14,17) (17,18)\nQ: Is there a path between node 13 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "877"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,10) (0,15) (0,21) (0,1) (0,7) (0,29) (0,24) (0,16) (0,23) (0,17) (1,26) (1,10) (1,15) (1,7) (1,28) (1,29) (1,12) (1,24) (1,16) (1,3) (1,23) (2,14) (2,27) (2,34) (3,26) (3,32) (3,15) (3,21) (3,7) (3,28) (3,29) (3,12) (3,24) (3,23) (3,17) (4,9) (4,14) (4,27) (4,31) (5,19) (5,22) (5,13) (5,20) (5,25) (5,30) (5,8) (5,33) (6,9) (6,27) (6,34) (6,31) (7,26) (7,32) (7,10) (7,15) (7,21) (7,29) (7,12) (7,24) (7,16) (7,23) (7,17) (8,19) (8,22) (8,13) (8,20) (8,25) (8,18) (8,30) (8,33) (9,14) (9,34) (10,32) (10,15) (10,21) (10,29) (10,24) (10,23) (10,17) (11,19) (11,22) (11,13) (11,25) (11,18) (11,30) (12,26) (12,32) (12,15) (12,21) (12,24) (12,16) (12,23) (13,19) (13,20) (13,25) (13,18) (13,33) (14,27) (14,31) (15,26) (15,21) (15,28) (15,24) (15,16) (15,23) (15,17) (16,26) (16,32) (16,23) (16,17) (17,26) (17,32) (17,21) (17,28) (17,24) (18,19) (18,22) (18,20) (18,30) (19,22) (19,20) (19,25) (19,30) (20,25) (20,30) (20,33) (21,26) (21,32) (21,28) (21,29) (22,25) (22,30) (22,33) (23,32) (23,28) (23,29) (23,24) (24,32) (24,28) (25,30) (25,33) (26,32) (26,28) (27,31) (28,29) (30,33)\nQ: Is there a path between node 25 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "878"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,7) (0,8) (0,10) (0,3) (1,4) (1,11) (1,9) (1,6) (1,12) (1,2) (2,4) (2,11) (2,9) (2,6) (2,12) (3,5) (3,7) (3,8) (3,10) (4,11) (4,9) (4,6) (4,12) (5,7) (5,8) (5,10) (6,11) (6,9) (6,12) (7,8) (7,10) (8,10) (9,11) (9,12) (11,12)\nQ: Is there a path between node 11 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "879"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,16) (0,9) (0,3) (0,4) (0,8) (0,17) (1,6) (1,12) (1,13) (1,18) (1,2) (1,4) (1,8) (1,17) (2,6) (2,12) (2,15) (2,9) (2,13) (2,18) (2,4) (2,8) (2,17) (3,6) (3,16) (3,12) (3,9) (3,13) (3,18) (3,8) (3,17) (3,5) (4,6) (4,16) (4,12) (4,9) (4,18) (4,17) (4,5) (5,6) (5,12) (5,15) (5,9) (5,17) (6,12) (6,15) (6,9) (6,13) (6,18) (6,8) (7,10) (7,11) (7,19) (8,16) (8,15) (8,9) (8,18) (9,16) (9,12) (9,15) (9,13) (9,18) (9,17) (10,19) (11,14) (11,19) (12,16) (12,15) (12,13) (12,17) (13,18) (14,19) (15,17) (16,17) (17,18)\nQ: Is there a path between node 5 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "880"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,3) (0,13) (0,15) (0,7) (1,4) (1,6) (2,9) (2,18) (2,13) (3,12) (4,11) (6,8) (6,17) (7,16) (7,12) (7,13) (7,14) (8,11) (8,17) (8,20) (9,18) (9,21) (9,14) (9,15) (10,12) (12,16) (12,15) (13,18) (13,15) (14,16) (14,21) (15,16) (15,18) (16,18)\nQ: Is there a path between node 2 and node 17?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "881"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,6) (0,21) (0,18) (1,24) (1,3) (3,24) (3,14) (4,6) (4,5) (4,23) (6,14) (6,21) (6,23) (7,11) (8,19) (8,13) (9,15) (9,19) (10,11) (10,12) (10,16) (10,17) (11,12) (11,16) (12,17) (13,15) (13,22) (14,23) (15,22) (16,17) (18,24) (18,21)\nQ: Is there a path between node 0 and node 19?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "882"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,29) (0,1) (0,9) (0,20) (0,34) (0,7) (0,19) (0,22) (0,31) (1,11) (1,30) (1,6) (1,21) (1,14) (1,28) (1,19) (1,31) (1,4) (2,3) (2,11) (2,18) (2,21) (2,20) (2,14) (2,7) (2,17) (3,11) (3,33) (3,15) (3,30) (3,18) (3,21) (3,14) (3,5) (4,10) (4,26) (4,27) (4,21) (4,34) (5,9) (5,27) (5,30) (5,6) (5,24) (5,14) (5,34) (5,28) (5,17) (6,11) (6,25) (6,10) (6,26) (6,29) (6,15) (6,16) (6,14) (6,7) (6,12) (6,22) (7,10) (7,26) (7,27) (7,18) (7,24) (7,8) (7,31) (8,11) (8,33) (8,9) (8,30) (8,24) (8,20) (8,16) (8,22) (8,17) (9,10) (9,20) (9,16) (9,14) (10,25) (10,33) (10,30) (10,18) (10,24) (10,20) (10,31) (11,15) (11,12) (11,19) (11,17) (12,25) (12,29) (12,27) (12,30) (12,34) (12,28) (12,17) (14,25) (14,33) (14,26) (14,29) (14,30) (14,21) (14,17) (15,20) (15,17) (16,21) (16,28) (16,19) (16,22) (17,27) (17,30) (17,24) (17,19) (18,26) (18,21) (18,28) (19,33) (19,27) (19,34) (19,22) (20,25) (20,26) (20,27) (20,21) (20,28) (20,31) (21,22) (22,24) (22,31) (24,34) (24,28) (25,26) (25,29) (25,27) (26,33) (26,27) (26,30) (27,30) (27,28) (28,31) (29,30) (29,34) (29,31) (30,33) (30,34) (31,33) (31,34)\nQ: Is there a path between node 8 and node 19?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "883"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,11) (0,13) (0,3) (0,15) (0,4) (0,2) (1,7) (1,8) (2,14) (2,23) (2,21) (2,6) (2,10) (3,9) (3,17) (3,13) (3,5) (3,19) (3,4) (3,16) (3,10) (4,9) (4,22) (4,6) (5,11) (5,18) (5,23) (6,9) (6,14) (6,17) (6,20) (6,15) (6,21) (7,8) (9,17) (9,15) (9,21) (10,18) (10,12) (10,16) (11,17) (11,15) (11,22) (11,16) (12,15) (12,22) (13,23) (13,16) (14,17) (14,18) (14,20) (14,21) (14,22) (14,16) (15,20) (17,20) (17,19) (17,23) (18,19) (18,23) (19,20) (19,23) (21,23) (21,22)\nQ: Is there a path between node 3 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "884"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,28) (0,1) (0,22) (0,20) (0,15) (0,18) (0,2) (0,5) (0,10) (0,8) (0,14) (0,6) (1,27) (1,12) (1,19) (1,28) (1,25) (1,29) (1,22) (1,4) (1,7) (1,15) (1,18) (1,3) (1,2) (1,24) (1,5) (1,11) (1,14) (1,13) (1,6) (2,12) (2,19) (2,28) (2,29) (2,4) (2,15) (2,16) (2,18) (2,3) (2,10) (2,13) (2,21) (2,6) (3,27) (3,19) (3,28) (3,20) (3,4) (3,7) (3,16) (3,18) (3,9) (3,24) (3,5) (3,11) (3,10) (3,8) (3,14) (3,23) (3,21) (3,6) (4,27) (4,12) (4,19) (4,28) (4,25) (4,20) (4,7) (4,15) (4,16) (4,5) (4,8) (4,14) (4,13) (4,21) (4,6) (5,27) (5,12) (5,19) (5,28) (5,25) (5,29) (5,22) (5,20) (5,7) (5,15) (5,16) (5,24) (5,11) (5,10) (5,8) (5,14) (5,23) (5,13) (5,21) (5,6) (6,27) (6,12) (6,28) (6,25) (6,29) (6,22) (6,20) (6,7) (6,16) (6,18) (6,9) (6,24) (6,8) (6,14) (6,21) (7,19) (7,25) (7,29) (7,22) (7,20) (7,15) (7,16) (7,24) (7,11) (7,10) (7,14) (7,23) (7,21) (8,27) (8,12) (8,19) (8,29) (8,22) (8,20) (8,15) (8,16) (8,9) (8,24) (8,11) (8,10) (8,14) (8,13) (9,12) (9,19) (9,25) (9,22) (9,20) (9,18) (9,24) (9,11) (9,10) (9,14) (9,23) (9,13) (9,21) (10,27) (10,12) (10,19) (10,28) (10,25) (10,29) (10,16) (10,18) (10,24) (10,14) (10,23) (10,13) (10,21) (11,27) (11,12) (11,25) (11,22) (11,20) (11,18) (11,24) (12,19) (12,28) (12,29) (12,22) (12,15) (12,16) (12,18) (12,14) (12,23) (12,13) (12,21) (13,27) (13,28) (13,25) (13,29) (13,22) (13,20) (13,15) (13,18) (13,24) (14,19) (14,28) (14,25) (14,29) (14,15) (14,16) (14,18) (14,24) (14,23) (15,27) (15,28) (15,25) (15,29) (15,20) (15,18) (15,23) (15,21) (16,27) (16,19) (16,28) (16,25) (16,29) (16,22) (16,20) (16,18) (16,24) (16,21) (18,19) (18,28) (18,29) (18,22) (18,20) (18,24) (18,23) (18,21) (19,27) (19,28) (19,25) (19,29) (19,22) (19,20) (19,24) (19,23) (19,21) (20,27) (20,28) (20,29) (20,22) (20,23) (20,21) (21,27) (21,28) (21,24) (21,23) (22,27) (22,28) (22,29) (22,23) (23,27) (23,28) (23,25) (23,29) (24,27) (24,28) (24,25) (24,29) (25,27) (25,29) (27,28) (27,29)\nQ: Is there a path between node 29 and node 17?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "885"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (1,2)\nQ: Is there a path between node 3 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "886"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,3) (0,2) (0,1) (1,6) (1,3) (1,2) (2,6) (2,3) (3,6) (4,5)\nQ: Is there a path between node 6 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "887"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,6) (1,2) (3,7) (3,5)\nQ: Is there a path between node 5 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "888"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,8) (1,5) (2,3) (3,5) (3,11) (4,8) (5,9) (5,7) (5,10) (6,11)\nQ: Is there a path between node 0 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "889"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,2) (0,4) (0,5) (0,15) (0,7) (1,9) (1,13) (1,12) (1,3) (2,14) (2,10) (2,4) (2,8) (2,15) (2,7) (3,9) (3,13) (3,12) (3,11) (4,14) (4,6) (4,10) (4,8) (4,15) (5,6) (5,8) (5,7) (6,14) (6,8) (6,15) (7,14) (7,10) (7,8) (7,15) (8,14) (8,10) (8,15) (9,13) (9,12) (9,11) (10,14) (10,15) (11,13) (11,12) (12,13) (14,15)\nQ: Is there a path between node 3 and node 13?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "890"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,1) (0,3) (1,5) (1,3) (2,4) (3,5)\nQ: Is there a path between node 1 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "891"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (1,8) (1,4) (1,5) (1,7) (1,2) (1,9) (1,6) (2,8) (2,4) (2,5) (2,7) (2,9) (2,6) (4,8) (4,5) (4,7) (4,9) (4,6) (5,8) (5,7) (5,9) (5,6) (6,8) (6,7) (6,9) (7,8) (7,9) (8,9)\nQ: Is there a path between node 8 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "892"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,1) (2,3) (4,6) (5,6) (5,7)\nQ: Is there a path between node 5 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "893"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,18) (0,24) (0,5) (0,12) (0,26) (0,14) (0,16) (0,21) (0,9) (0,1) (0,28) (0,25) (1,3) (1,18) (1,24) (1,5) (1,12) (1,26) (1,14) (1,16) (1,21) (1,2) (1,23) (1,20) (1,28) (1,25) (2,3) (2,18) (2,10) (2,24) (2,5) (2,12) (2,26) (2,14) (2,16) (2,9) (2,23) (2,20) (2,28) (2,7) (2,25) (2,22) (2,13) (3,18) (3,24) (3,12) (3,26) (3,16) (3,9) (3,19) (3,7) (3,25) (3,22) (4,11) (4,27) (4,17) (4,15) (4,8) (5,18) (5,24) (5,12) (5,26) (5,14) (5,16) (5,21) (5,9) (5,23) (5,19) (5,20) (5,7) (5,13) (6,11) (6,27) (6,29) (6,15) (6,8) (7,18) (7,10) (7,12) (7,26) (7,14) (7,16) (7,21) (7,9) (7,20) (7,25) (7,22) (7,13) (8,11) (8,27) (8,29) (8,17) (8,15) (9,18) (9,10) (9,24) (9,16) (9,21) (9,19) (9,20) (9,28) (9,25) (9,13) (10,18) (10,24) (10,12) (10,26) (10,14) (10,16) (10,23) (10,20) (10,28) (10,25) (10,22) (10,13) (11,27) (11,29) (12,18) (12,24) (12,16) (12,21) (12,23) (12,20) (12,28) (12,22) (12,13) (13,18) (13,24) (13,26) (13,14) (13,16) (13,21) (13,23) (13,20) (13,28) (13,25) (13,22) (14,26) (14,16) (14,21) (14,23) (14,19) (14,20) (14,28) (14,25) (15,27) (15,17) (16,18) (16,24) (16,26) (16,20) (16,25) (16,22) (17,29) (18,24) (18,26) (18,23) (18,19) (18,20) (18,25) (18,22) (19,21) (19,23) (19,28) (19,25) (20,26) (20,23) (20,28) (20,25) (20,22) (21,26) (21,23) (21,28) (21,22) (22,26) (22,23) (22,25) (23,24) (23,26) (24,26) (24,28) (25,26)\nQ: Is there a path between node 13 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "894"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (0,13) (0,22) (1,12) (1,6) (2,20) (2,14) (2,11) (3,5) (3,23) (3,6) (5,17) (6,19) (7,23) (8,13) (8,15) (9,21) (9,18) (12,24) (12,17) (12,19) (13,21) (13,18) (13,25) (13,15) (13,16) (15,16) (16,21) (16,25) (17,23) (17,19) (19,26) (21,22) (22,25)\nQ: Is there a path between node 0 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "895"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,4) (0,16) (0,21) (0,1) (0,25) (0,14) (0,9) (0,5) (0,6) (0,12) (0,17) (0,24) (0,23) (1,29) (1,4) (1,27) (1,16) (1,21) (1,14) (1,9) (1,6) (1,24) (1,23) (2,26) (2,10) (2,22) (2,15) (2,28) (2,8) (2,30) (2,19) (3,26) (3,10) (3,11) (3,22) (3,15) (3,28) (3,8) (3,30) (3,19) (3,20) (4,29) (4,27) (4,16) (4,21) (4,14) (4,9) (4,5) (4,6) (4,12) (4,24) (5,29) (5,27) (5,21) (5,7) (5,14) (5,12) (5,17) (5,24) (5,23) (6,29) (6,27) (6,7) (6,25) (6,14) (6,9) (6,12) (6,24) (6,23) (7,25) (7,14) (7,9) (7,12) (7,17) (7,23) (8,26) (8,10) (8,11) (8,13) (8,30) (8,19) (9,29) (9,27) (9,16) (9,14) (9,12) (9,24) (9,23) (10,26) (10,13) (10,15) (10,28) (10,19) (10,20) (11,26) (11,13) (11,15) (11,28) (11,30) (11,19) (11,20) (12,29) (12,27) (12,16) (12,21) (12,25) (12,17) (12,24) (12,23) (13,26) (13,28) (13,30) (14,29) (14,16) (14,21) (14,25) (14,17) (14,24) (14,23) (15,26) (15,28) (15,30) (15,20) (16,27) (16,21) (16,17) (16,24) (16,23) (17,29) (17,27) (17,21) (17,25) (17,24) (19,26) (19,22) (19,30) (19,20) (20,26) (20,22) (20,28) (21,29) (21,27) (21,25) (21,24) (21,23) (22,26) (22,28) (22,30) (23,29) (23,27) (23,25) (24,29) (24,27) (24,25) (25,29) (26,28) (28,30)\nQ: Is there a path between node 25 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "896"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,21) (0,14) (0,1) (0,22) (0,16) (0,19) (0,5) (0,10) (0,20) (0,11) (0,24) (0,13) (1,21) (1,9) (1,3) (1,14) (1,22) (1,10) (1,20) (1,12) (1,11) (1,24) (1,13) (1,23) (2,8) (2,4) (2,18) (2,15) (3,9) (3,14) (3,16) (3,19) (3,7) (3,6) (3,5) (3,10) (3,11) (4,8) (4,17) (4,18) (4,15) (5,9) (5,14) (5,22) (5,7) (5,6) (5,10) (5,20) (5,12) (5,11) (5,13) (5,23) (6,21) (6,9) (6,22) (6,19) (6,7) (6,20) (6,12) (6,11) (6,13) (6,23) (7,21) (7,9) (7,14) (7,16) (7,19) (7,10) (7,20) (7,12) (7,11) (7,24) (7,13) (7,23) (8,17) (8,18) (8,15) (9,21) (9,16) (9,10) (9,20) (9,12) (9,11) (9,24) (9,13) (9,23) (10,22) (10,19) (10,12) (10,11) (10,13) (10,23) (11,21) (11,22) (11,19) (11,20) (11,12) (11,24) (11,13) (11,23) (12,21) (12,14) (12,22) (12,20) (12,24) (12,13) (12,23) (13,21) (13,14) (13,22) (13,16) (13,20) (13,23) (14,21) (14,16) (14,20) (14,24) (14,23) (15,18) (16,21) (16,22) (16,19) (16,20) (16,24) (16,23) (17,18) (19,21) (19,20) (19,24) (19,23) (20,21) (20,24) (20,23) (21,24) (21,23) (22,23) (23,24)\nQ: Is there a path between node 24 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "897"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,2) (0,8) (0,4) (0,7) (0,3) (0,1) (1,5) (1,2) (1,8) (1,4) (1,7) (1,3) (2,5) (2,8) (2,4) (2,7) (2,3) (3,5) (3,8) (3,4) (3,7) (4,5) (4,8) (4,7) (5,8) (5,7) (6,9) (7,8)\nQ: Is there a path between node 6 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "898"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,15) (1,3) (1,20) (2,11) (3,12) (3,6) (3,16) (3,20) (5,14) (5,7) (6,20) (6,21) (7,13) (7,18) (8,14) (8,13) (9,12) (9,16) (9,21) (10,21) (11,17) (12,16) (14,18) (15,16) (15,21) (16,20) (20,21)\nQ: Is there a path between node 5 and node 13?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "899"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,13) (1,6) (1,8) (1,3) (1,4) (2,5) (2,9) (3,12) (3,9) (3,13) (4,6) (4,10) (5,6) (5,9) (6,12) (6,8) (8,9) (9,10) (12,13)\nQ: Is there a path between node 10 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "900"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,11) (0,22) (0,30) (0,25) (0,19) (0,12) (0,13) (0,10) (0,29) (1,17) (1,4) (1,18) (1,7) (1,27) (1,2) (1,3) (1,9) (1,23) (1,28) (2,4) (2,21) (2,26) (2,7) (2,27) (2,9) (2,23) (2,28) (3,17) (3,4) (3,21) (3,26) (3,18) (3,7) (3,27) (3,14) (3,9) (3,23) (3,28) (3,24) (4,17) (4,21) (4,26) (4,18) (4,14) (4,9) (4,28) (4,24) (5,11) (5,22) (5,20) (5,25) (5,29) (6,8) (7,21) (7,26) (7,18) (7,27) (7,23) (7,28) (7,24) (9,21) (9,26) (9,18) (9,27) (9,14) (9,23) (9,28) (9,24) (10,11) (10,22) (10,20) (10,30) (10,25) (10,16) (10,19) (10,15) (10,13) (10,29) (11,22) (11,20) (11,30) (11,25) (11,16) (11,19) (11,12) (11,15) (11,13) (11,29) (12,22) (12,20) (12,30) (12,16) (12,15) (12,13) (13,22) (13,20) (13,30) (13,25) (13,16) (13,19) (13,15) (13,29) (14,26) (14,18) (14,23) (14,28) (14,24) (15,22) (15,30) (15,16) (15,19) (15,29) (16,22) (16,30) (16,25) (16,19) (16,29) (17,26) (17,18) (17,27) (17,23) (17,28) (18,21) (18,26) (18,27) (18,24) (19,20) (19,30) (19,25) (19,29) (20,22) (20,25) (20,29) (21,26) (21,27) (21,28) (21,24) (22,30) (22,29) (23,26) (23,27) (23,28) (23,24) (24,27) (24,28) (25,29) (26,27) (27,28) (29,30)\nQ: Is there a path between node 23 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "901"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,3) (0,2) (0,9) (0,8) (1,6) (1,4) (2,7) (2,10) (2,3) (2,8) (2,5) (3,10) (3,9) (3,8) (4,6) (5,7) (5,10) (5,9) (7,8) (8,9)\nQ: Is there a path between node 3 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "902"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,4) (0,1) (1,2) (1,5) (1,4) (2,5) (2,4) (4,5)\nQ: Is there a path between node 2 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "903"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,2) (0,8) (0,4) (0,7) (0,3) (0,1) (1,5) (1,2) (1,8) (1,4) (1,7) (1,3) (2,5) (2,8) (2,4) (2,7) (2,3) (3,5) (3,8) (3,4) (3,7) (4,5) (4,8) (4,7) (5,8) (5,7) (6,9) (7,8)\nQ: Is there a path between node 4 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "904"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,2) (0,4) (0,5) (0,15) (0,7) (1,9) (1,13) (1,12) (1,3) (2,14) (2,10) (2,4) (2,8) (2,15) (2,7) (3,9) (3,13) (3,12) (3,11) (4,14) (4,6) (4,10) (4,8) (4,15) (5,6) (5,8) (5,7) (6,14) (6,8) (6,15) (7,14) (7,10) (7,8) (7,15) (8,14) (8,10) (8,15) (9,13) (9,12) (9,11) (10,14) (10,15) (11,13) (11,12) (12,13) (14,15)\nQ: Is there a path between node 4 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "905"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,4) (1,23) (1,7) (1,18) (1,24) (1,32) (1,31) (1,21) (1,27) (1,11) (1,6) (1,29) (1,17) (1,20) (2,23) (2,7) (2,18) (2,33) (2,24) (2,31) (2,21) (2,8) (2,27) (2,11) (2,29) (2,17) (2,26) (3,9) (3,22) (3,13) (3,5) (3,30) (3,28) (3,16) (3,14) (3,15) (4,19) (4,10) (5,9) (5,22) (5,13) (5,28) (5,16) (5,14) (6,18) (6,32) (6,25) (6,21) (6,8) (6,11) (6,17) (6,20) (6,26) (7,18) (7,33) (7,24) (7,32) (7,25) (7,31) (7,21) (7,17) (7,20) (7,26) (8,18) (8,33) (8,32) (8,25) (8,31) (8,27) (8,11) (8,29) (8,20) (8,26) (9,22) (9,13) (9,30) (9,28) (9,14) (9,15) (10,19) (10,12) (11,18) (11,33) (11,24) (11,25) (11,31) (11,27) (11,29) (11,26) (12,19) (13,28) (13,15) (14,30) (14,28) (14,16) (14,15) (15,22) (15,30) (15,16) (16,22) (17,23) (17,18) (17,33) (17,25) (17,31) (17,21) (17,27) (17,29) (17,20) (17,26) (18,23) (18,32) (18,25) (18,21) (18,29) (18,20) (18,26) (20,23) (20,33) (20,32) (20,25) (20,31) (20,21) (20,27) (20,29) (20,26) (21,23) (21,33) (21,24) (21,25) (21,29) (23,33) (23,24) (23,25) (23,31) (23,27) (23,29) (23,26) (24,33) (24,32) (24,25) (24,27) (24,29) (24,26) (25,32) (25,31) (25,27) (25,29) (25,26) (26,33) (26,31) (26,27) (27,31) (27,29) (28,30) (31,32) (32,33)\nQ: Is there a path between node 24 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "906"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,1) (0,15) (0,6) (0,9) (0,4) (0,16) (0,19) (1,20) (1,15) (1,6) (1,9) (1,4) (1,16) (1,19) (2,14) (2,10) (2,3) (2,11) (2,7) (2,18) (2,5) (2,12) (2,17) (2,8) (3,14) (3,10) (3,11) (3,7) (3,18) (3,5) (3,12) (3,17) (3,8) (4,20) (4,15) (4,6) (4,9) (4,16) (4,19) (5,14) (5,10) (5,11) (5,7) (5,18) (5,12) (5,17) (5,8) (6,20) (6,15) (6,9) (6,16) (6,19) (7,14) (7,10) (7,11) (7,18) (7,12) (7,17) (7,8) (8,14) (8,10) (8,11) (8,18) (8,12) (8,17) (9,20) (9,15) (9,16) (9,19) (10,14) (10,11) (10,18) (10,12) (10,17) (11,14) (11,18) (11,12) (11,17) (12,14) (12,18) (12,17) (14,18) (14,17) (15,20) (15,16) (15,19) (16,20) (16,19) (17,18) (19,20)\nQ: Is there a path between node 16 and node 20?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "907"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,24) (0,1) (0,6) (0,14) (1,10) (2,25) (2,5) (2,20) (2,18) (3,22) (3,6) (3,19) (3,23) (4,9) (4,18) (5,15) (5,25) (5,17) (5,20) (6,11) (6,24) (6,14) (6,7) (6,21) (7,24) (8,25) (8,17) (8,20) (8,18) (9,25) (10,24) (10,22) (10,21) (11,22) (11,19) (11,23) (12,15) (12,16) (12,17) (13,19) (13,14) (14,22) (14,19) (15,16) (15,18) (16,17) (17,20) (18,25) (19,24) (19,22) (20,25) (21,23) (22,24) (22,23)\nQ: Is there a path between node 24 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "908"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,17) (0,1) (0,4) (0,15) (0,2) (0,13) (0,10) (0,6) (0,18) (0,11) (0,12) (0,5) (1,19) (1,17) (1,4) (1,15) (1,2) (1,13) (1,10) (1,6) (1,18) (1,11) (1,12) (1,5) (2,19) (2,17) (2,4) (2,15) (2,13) (2,10) (2,6) (2,18) (2,11) (2,12) (2,5) (3,20) (3,16) (3,14) (3,8) (4,19) (4,17) (4,15) (4,13) (4,10) (4,6) (4,18) (4,11) (4,12) (4,5) (5,19) (5,17) (5,15) (5,13) (5,10) (5,6) (5,18) (5,11) (5,12) (6,19) (6,17) (6,15) (6,13) (6,10) (6,18) (6,11) (6,12) (7,9) (8,20) (8,16) (8,14) (10,19) (10,17) (10,15) (10,13) (10,18) (10,11) (10,12) (11,19) (11,17) (11,15) (11,13) (11,18) (11,12) (12,19) (12,17) (12,15) (12,13) (12,18) (13,19) (13,17) (13,15) (13,18) (14,20) (14,16) (15,19) (15,17) (15,18) (16,20) (17,19) (17,18) (18,19)\nQ: Is there a path between node 8 and node 18?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "909"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,6) (0,2) (0,5) (1,7) (1,16) (1,14) (1,17) (1,3) (1,9) (1,13) (1,10) (2,11) (2,6) (2,5) (3,7) (3,16) (3,14) (3,17) (3,9) (3,13) (3,10) (4,8) (4,15) (4,12) (5,11) (5,6) (6,11) (7,16) (7,14) (7,17) (7,9) (7,13) (7,10) (8,15) (8,12) (9,16) (9,14) (9,17) (9,13) (9,10) (10,16) (10,14) (10,17) (10,13) (12,15) (13,16) (13,14) (13,17) (14,16) (14,17) (16,17)\nQ: Is there a path between node 11 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "910"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,12) (0,2) (0,3) (1,13) (1,22) (1,7) (1,11) (1,19) (1,6) (1,8) (2,14) (2,20) (2,3) (3,14) (3,20) (4,21) (4,18) (4,5) (4,17) (4,9) (4,15) (4,10) (5,21) (5,17) (5,9) (5,15) (5,10) (6,16) (6,13) (6,22) (6,7) (6,11) (6,19) (6,8) (7,16) (7,13) (7,22) (7,8) (8,16) (8,13) (8,11) (8,19) (9,18) (9,17) (9,15) (9,10) (10,21) (10,18) (11,16) (11,13) (11,22) (11,19) (12,14) (12,20) (13,16) (13,19) (14,20) (15,21) (15,18) (15,17) (16,22) (17,21) (17,18) (19,22)\nQ: Is there a path between node 6 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "911"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,15) (0,18) (0,27) (0,9) (0,13) (0,25) (0,3) (1,8) (1,5) (1,26) (1,12) (1,2) (1,16) (1,14) (2,8) (2,26) (2,12) (2,16) (2,14) (3,7) (3,4) (3,15) (3,18) (3,27) (3,13) (4,7) (4,15) (4,18) (4,27) (4,13) (5,8) (5,12) (5,11) (5,16) (5,14) (5,20) (6,17) (6,21) (6,29) (6,28) (7,15) (7,18) (7,27) (7,9) (7,13) (8,26) (8,23) (8,16) (8,14) (9,15) (10,29) (10,24) (11,12) (11,16) (11,14) (11,20) (12,22) (12,23) (12,14) (12,20) (13,18) (13,27) (14,26) (14,22) (14,23) (14,20) (15,18) (15,27) (15,25) (16,26) (16,22) (16,23) (16,20) (17,21) (17,19) (17,24) (17,28) (19,21) (19,29) (19,24) (19,28) (20,26) (20,22) (20,23) (21,29) (21,24) (22,26) (22,23) (24,29) (24,28) (25,27)\nQ: Is there a path between node 4 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "912"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,8) (0,18) (0,6) (0,1) (0,12) (0,3) (0,7) (0,14) (0,10) (0,19) (0,16) (0,13) (1,17) (1,8) (1,18) (1,2) (1,19) (2,8) (2,6) (2,20) (2,14) (3,17) (3,18) (3,6) (3,14) (3,10) (3,19) (4,17) (4,18) (4,6) (4,19) (4,13) (5,15) (6,17) (6,8) (6,18) (6,13) (7,17) (7,14) (7,10) (8,20) (9,15) (9,11) (10,17) (10,18) (11,15) (12,17) (12,18) (12,14) (12,19) (13,17) (13,18) (13,20) (14,17) (14,18) (14,20) (18,20) (19,20)\nQ: Is there a path between node 13 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "913"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,10) (0,17) (0,5) (0,13) (0,15) (0,16) (0,3) (0,7) (0,11) (0,1) (0,4) (0,14) (1,12) (1,10) (1,17) (1,5) (1,13) (1,15) (1,16) (1,3) (1,7) (1,11) (1,4) (1,14) (2,8) (2,6) (3,12) (3,10) (3,17) (3,5) (3,13) (3,15) (3,16) (3,7) (3,11) (3,4) (3,14) (4,12) (4,10) (4,17) (4,5) (4,13) (4,15) (4,16) (4,7) (4,11) (4,14) (5,12) (5,10) (5,17) (5,13) (5,15) (5,16) (5,7) (5,11) (5,14) (6,8) (7,12) (7,10) (7,17) (7,13) (7,15) (7,16) (7,11) (7,14) (10,12) (10,17) (10,13) (10,15) (10,16) (10,11) (10,14) (11,12) (11,17) (11,13) (11,15) (11,16) (11,14) (12,17) (12,13) (12,15) (12,16) (12,14) (13,17) (13,15) (13,16) (13,14) (14,17) (14,15) (14,16) (15,17) (15,16) (16,17)\nQ: Is there a path between node 1 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "914"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,22) (0,12) (0,24) (0,18) (0,19) (0,30) (0,1) (0,21) (0,9) (0,5) (0,6) (0,7) (0,2) (1,22) (1,24) (1,18) (1,19) (1,30) (1,21) (1,9) (1,5) (1,6) (1,11) (1,7) (1,31) (1,2) (2,12) (2,24) (2,18) (2,19) (2,21) (2,5) (2,6) (2,11) (2,7) (2,31) (3,26) (3,16) (3,4) (3,28) (3,13) (3,20) (4,26) (4,16) (4,8) (4,28) (5,12) (5,24) (5,30) (5,21) (5,9) (5,11) (5,7) (5,31) (6,22) (6,12) (6,24) (6,30) (6,21) (6,9) (6,11) (6,7) (7,12) (7,18) (7,30) (7,9) (7,11) (7,31) (8,26) (8,16) (8,28) (9,22) (9,12) (9,24) (9,18) (9,19) (9,30) (9,11) (9,31) (10,25) (10,14) (10,29) (10,32) (10,15) (10,23) (11,22) (11,12) (11,24) (11,18) (11,30) (11,21) (12,24) (12,30) (12,21) (12,31) (13,26) (13,28) (14,27) (14,17) (14,29) (14,32) (14,15) (15,25) (15,27) (15,17) (15,29) (15,32) (15,23) (16,26) (17,29) (18,22) (18,24) (18,19) (18,21) (19,22) (19,30) (19,21) (20,26) (21,22) (21,24) (21,31) (22,24) (23,25) (23,27) (23,32) (24,30) (24,31) (25,27) (25,29) (25,32) (26,28) (27,29) (27,32) (30,31)\nQ: Is there a path between node 5 and node 22?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "915"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,6) (2,7) (2,6) (2,4) (5,7) (6,8)\nQ: Is there a path between node 3 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "916"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,13) (2,25) (2,28) (2,21) (2,5) (2,23) (3,22) (3,8) (3,6) (3,19) (3,21) (3,31) (3,15) (5,20) (5,16) (5,21) (5,23) (6,18) (6,17) (6,23) (7,10) (8,21) (9,24) (12,22) (12,18) (13,30) (13,27) (14,26) (15,16) (15,19) (15,31) (16,22) (16,20) (16,19) (17,20) (17,21) (17,31) (18,22) (18,25) (18,20) (18,21) (18,23) (19,25) (19,28) (20,28) (20,21) (21,25) (22,25) (22,28) (23,28) (27,29) (29,30) (30,32)\nQ: Is there a path between node 16 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "917"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (1,27) (1,24) (1,21) (1,3) (2,10) (2,22) (2,6) (2,18) (2,25) (2,12) (3,19) (3,27) (3,24) (4,10) (4,6) (4,18) (4,25) (5,28) (5,16) (6,10) (6,13) (6,25) (6,12) (6,9) (7,28) (8,10) (8,14) (8,18) (8,29) (8,25) (8,23) (9,13) (9,14) (10,29) (10,25) (12,22) (12,18) (12,17) (13,29) (13,26) (14,20) (14,17) (15,19) (17,25) (18,20) (18,25) (20,29) (20,26) (20,23) (21,27) (21,24) (23,26) (23,25) (24,27) (26,29)\nQ: Is there a path between node 3 and node 20?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "918"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,15) (0,6) (0,17) (0,4) (0,12) (0,16) (0,9) (1,14) (1,23) (1,18) (1,19) (1,3) (1,21) (2,14) (2,5) (2,11) (2,23) (2,22) (2,8) (2,18) (2,19) (2,3) (2,20) (3,14) (3,5) (3,23) (3,22) (3,8) (3,18) (3,19) (3,20) (3,21) (4,7) (4,15) (4,6) (4,17) (4,13) (4,10) (4,16) (5,14) (5,8) (5,18) (5,19) (5,21) (6,13) (6,10) (6,16) (6,9) (7,15) (7,13) (7,9) (8,14) (8,11) (8,23) (8,22) (8,18) (8,19) (8,20) (8,21) (9,15) (9,13) (9,12) (9,16) (10,15) (10,17) (10,13) (10,12) (11,14) (11,23) (11,22) (11,18) (11,19) (12,17) (12,16) (13,17) (13,16) (14,23) (14,19) (15,17) (16,17) (18,23) (18,22) (18,19) (18,21) (19,23) (19,22) (19,20) (20,23) (20,21) (21,23) (22,23)\nQ: Is there a path between node 18 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "919"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,7) (0,8) (0,10) (0,3) (1,4) (1,11) (1,9) (1,6) (1,12) (1,2) (2,4) (2,11) (2,9) (2,6) (2,12) (3,5) (3,7) (3,8) (3,10) (4,11) (4,9) (4,6) (4,12) (5,7) (5,8) (5,10) (6,11) (6,9) (6,12) (7,8) (7,10) (8,10) (9,11) (9,12) (11,12)\nQ: Is there a path between node 9 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "920"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,10) (0,15) (0,21) (0,1) (0,7) (0,29) (0,24) (0,16) (0,23) (0,17) (1,26) (1,10) (1,15) (1,7) (1,28) (1,29) (1,12) (1,24) (1,16) (1,3) (1,23) (2,14) (2,27) (2,34) (3,26) (3,32) (3,15) (3,21) (3,7) (3,28) (3,29) (3,12) (3,24) (3,23) (3,17) (4,9) (4,14) (4,27) (4,31) (5,19) (5,22) (5,13) (5,20) (5,25) (5,30) (5,8) (5,33) (6,9) (6,27) (6,34) (6,31) (7,26) (7,32) (7,10) (7,15) (7,21) (7,29) (7,12) (7,24) (7,16) (7,23) (7,17) (8,19) (8,22) (8,13) (8,20) (8,25) (8,18) (8,30) (8,33) (9,14) (9,34) (10,32) (10,15) (10,21) (10,29) (10,24) (10,23) (10,17) (11,19) (11,22) (11,13) (11,25) (11,18) (11,30) (12,26) (12,32) (12,15) (12,21) (12,24) (12,16) (12,23) (13,19) (13,20) (13,25) (13,18) (13,33) (14,27) (14,31) (15,26) (15,21) (15,28) (15,24) (15,16) (15,23) (15,17) (16,26) (16,32) (16,23) (16,17) (17,26) (17,32) (17,21) (17,28) (17,24) (18,19) (18,22) (18,20) (18,30) (19,22) (19,20) (19,25) (19,30) (20,25) (20,30) (20,33) (21,26) (21,32) (21,28) (21,29) (22,25) (22,30) (22,33) (23,32) (23,28) (23,29) (23,24) (24,32) (24,28) (25,30) (25,33) (26,32) (26,28) (27,31) (28,29) (30,33)\nQ: Is there a path between node 14 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "921"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,3) (0,5) (1,2) (1,10) (1,3) (1,5) (2,6) (2,10) (3,17) (3,14) (3,6) (3,9) (4,14) (4,7) (4,9) (5,17) (5,14) (5,6) (5,10) (5,7) (6,14) (6,16) (6,7) (9,17) (9,16) (9,10) (10,14) (11,15) (12,13) (14,17) (14,16) (14,15) (15,17)\nQ: Is there a path between node 2 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "922"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,13) (0,6) (0,5) (0,15) (0,14) (0,1) (0,10) (0,8) (0,7) (0,2) (0,11) (0,3) (1,12) (1,13) (1,6) (1,5) (1,15) (1,14) (1,10) (1,8) (1,7) (1,2) (1,11) (1,3) (2,12) (2,13) (2,6) (2,5) (2,15) (2,14) (2,10) (2,8) (2,7) (2,11) (2,3) (3,12) (3,13) (3,6) (3,5) (3,15) (3,14) (3,10) (3,8) (3,7) (3,11) (4,9) (5,12) (5,13) (5,6) (5,15) (5,14) (5,10) (5,8) (5,7) (5,11) (6,12) (6,13) (6,15) (6,14) (6,10) (6,8) (6,7) (6,11) (7,12) (7,13) (7,15) (7,14) (7,10) (7,8) (7,11) (8,12) (8,13) (8,15) (8,14) (8,10) (8,11) (10,12) (10,13) (10,15) (10,14) (10,11) (11,12) (11,13) (11,15) (11,14) (12,13) (12,15) (12,14) (13,15) (13,14) (14,15)\nQ: Is there a path between node 9 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "923"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,13) (2,25) (2,28) (2,21) (2,5) (2,23) (3,22) (3,8) (3,6) (3,19) (3,21) (3,31) (3,15) (5,20) (5,16) (5,21) (5,23) (6,18) (6,17) (6,23) (7,10) (8,21) (9,24) (12,22) (12,18) (13,30) (13,27) (14,26) (15,16) (15,19) (15,31) (16,22) (16,20) (16,19) (17,20) (17,21) (17,31) (18,22) (18,25) (18,20) (18,21) (18,23) (19,25) (19,28) (20,28) (20,21) (21,25) (22,25) (22,28) (23,28) (27,29) (29,30) (30,32)\nQ: Is there a path between node 19 and node 25?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "924"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,5) (3,5)\nQ: Is there a path between node 3 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "925"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (1,5) (1,18) (1,7) (1,22) (1,11) (1,20) (1,4) (1,23) (2,14) (2,10) (2,21) (2,15) (2,16) (2,3) (3,14) (3,10) (3,15) (3,16) (3,6) (3,19) (4,18) (4,7) (4,22) (4,11) (4,20) (4,23) (5,13) (5,7) (5,22) (5,11) (5,20) (5,23) (6,10) (6,21) (6,15) (6,16) (6,9) (6,8) (6,19) (7,13) (7,22) (7,20) (7,23) (8,10) (8,9) (8,19) (9,21) (9,15) (9,19) (10,21) (10,16) (10,19) (11,18) (11,13) (11,22) (11,23) (12,17) (13,22) (13,20) (14,15) (14,16) (14,19) (15,16) (15,19) (16,21) (16,19) (18,20) (18,23) (19,21) (20,22) (20,23) (22,23)\nQ: Is there a path between node 15 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "926"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,4) (0,3) (0,6) (0,2) (0,8) (0,5) (0,11) (1,4) (1,3) (1,6) (1,2) (1,8) (1,5) (1,11) (2,4) (2,3) (2,6) (2,8) (2,5) (2,11) (3,4) (3,6) (3,8) (3,5) (3,11) (4,6) (4,8) (4,5) (4,11) (5,6) (5,8) (5,11) (6,8) (6,11) (7,9) (7,10) (8,11) (9,10)\nQ: Is there a path between node 11 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "927"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,24) (0,1) (0,6) (0,14) (1,10) (2,25) (2,5) (2,20) (2,18) (3,22) (3,6) (3,19) (3,23) (4,9) (4,18) (5,15) (5,25) (5,17) (5,20) (6,11) (6,24) (6,14) (6,7) (6,21) (7,24) (8,25) (8,17) (8,20) (8,18) (9,25) (10,24) (10,22) (10,21) (11,22) (11,19) (11,23) (12,15) (12,16) (12,17) (13,19) (13,14) (14,22) (14,19) (15,16) (15,18) (16,17) (17,20) (18,25) (19,24) (19,22) (20,25) (21,23) (22,24) (22,23)\nQ: Is there a path between node 9 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "928"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,3) (0,2) (0,9) (0,8) (1,6) (1,4) (2,7) (2,10) (2,3) (2,8) (2,5) (3,10) (3,9) (3,8) (4,6) (5,7) (5,10) (5,9) (7,8) (8,9)\nQ: Is there a path between node 0 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "929"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,23) (0,8) (1,6) (1,26) (1,11) (2,6) (2,11) (3,12) (3,19) (3,20) (4,13) (4,21) (4,17) (4,10) (4,6) (4,23) (4,8) (5,13) (5,7) (5,21) (5,17) (5,28) (5,6) (5,23) (5,8) (5,26) (5,24) (5,11) (6,13) (6,17) (6,10) (6,23) (6,24) (7,17) (7,28) (7,23) (8,21) (8,10) (9,15) (10,13) (10,21) (10,23) (10,11) (11,13) (11,17) (12,19) (12,14) (12,27) (12,15) (12,22) (13,17) (13,16) (14,22) (15,19) (16,17) (16,28) (16,24) (17,24) (18,19) (18,27) (19,27) (21,26) (21,24) (22,25) (23,28) (24,28) (25,27)\nQ: Is there a path between node 12 and node 27?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "930"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,18) (0,17) (0,10) (1,7) (1,24) (1,27) (2,4) (2,8) (2,13) (2,19) (2,27) (3,16) (3,28) (3,9) (4,18) (4,6) (4,10) (4,11) (4,27) (6,20) (6,8) (6,7) (6,27) (7,8) (7,18) (7,17) (7,23) (7,24) (7,10) (7,13) (7,19) (7,11) (7,14) (8,17) (8,22) (8,24) (8,10) (8,11) (10,18) (10,17) (10,12) (10,11) (10,27) (11,17) (11,12) (12,20) (12,18) (12,17) (12,14) (13,20) (13,18) (13,24) (13,27) (13,26) (14,18) (15,28) (15,25) (16,25) (17,20) (17,18) (17,26) (18,22) (18,23) (18,19) (18,27) (19,23) (19,27) (19,26) (20,24) (22,23) (22,24) (22,26) (26,27)\nQ: Is there a path between node 22 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "931"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,12) (0,1) (0,7) (0,16) (0,13) (0,9) (0,2) (0,10) (0,21) (0,19) (0,3) (0,20) (0,8) (0,23) (0,5) (0,4) (0,6) (0,22) (1,15) (1,12) (1,7) (1,16) (1,13) (1,9) (1,2) (1,10) (1,21) (1,19) (1,3) (1,20) (1,8) (1,23) (1,5) (1,4) (1,6) (1,22) (2,15) (2,12) (2,7) (2,16) (2,13) (2,9) (2,10) (2,21) (2,19) (2,3) (2,20) (2,8) (2,23) (2,5) (2,4) (2,6) (2,22) (3,15) (3,12) (3,7) (3,16) (3,13) (3,9) (3,10) (3,21) (3,19) (3,20) (3,8) (3,23) (3,5) (3,4) (3,6) (3,22) (4,15) (4,12) (4,7) (4,16) (4,13) (4,9) (4,10) (4,21) (4,19) (4,20) (4,8) (4,23) (4,5) (4,6) (4,22) (5,15) (5,12) (5,7) (5,16) (5,13) (5,9) (5,10) (5,21) (5,19) (5,20) (5,8) (5,23) (5,6) (5,22) (6,15) (6,12) (6,7) (6,16) (6,13) (6,9) (6,10) (6,21) (6,19) (6,20) (6,8) (6,23) (6,22) (7,15) (7,12) (7,16) (7,13) (7,9) (7,10) (7,21) (7,19) (7,20) (7,8) (7,23) (7,22) (8,15) (8,12) (8,16) (8,13) (8,9) (8,10) (8,21) (8,19) (8,20) (8,23) (8,22) (9,15) (9,12) (9,16) (9,13) (9,10) (9,21) (9,19) (9,20) (9,23) (9,22) (10,15) (10,12) (10,16) (10,13) (10,21) (10,19) (10,20) (10,23) (10,22) (11,17) (11,14) (11,18) (12,15) (12,16) (12,13) (12,21) (12,19) (12,20) (12,23) (12,22) (13,15) (13,16) (13,21) (13,19) (13,20) (13,23) (13,22) (14,17) (14,18) (15,16) (15,21) (15,19) (15,20) (15,23) (15,22) (16,21) (16,19) (16,20) (16,23) (16,22) (17,18) (19,21) (19,20) (19,23) (19,22) (20,21) (20,23) (20,22) (21,23) (21,22) (22,23)\nQ: Is there a path between node 11 and node 19?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "932"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,15) (0,6) (0,17) (0,4) (0,12) (0,16) (0,9) (1,14) (1,23) (1,18) (1,19) (1,3) (1,21) (2,14) (2,5) (2,11) (2,23) (2,22) (2,8) (2,18) (2,19) (2,3) (2,20) (3,14) (3,5) (3,23) (3,22) (3,8) (3,18) (3,19) (3,20) (3,21) (4,7) (4,15) (4,6) (4,17) (4,13) (4,10) (4,16) (5,14) (5,8) (5,18) (5,19) (5,21) (6,13) (6,10) (6,16) (6,9) (7,15) (7,13) (7,9) (8,14) (8,11) (8,23) (8,22) (8,18) (8,19) (8,20) (8,21) (9,15) (9,13) (9,12) (9,16) (10,15) (10,17) (10,13) (10,12) (11,14) (11,23) (11,22) (11,18) (11,19) (12,17) (12,16) (13,17) (13,16) (14,23) (14,19) (15,17) (16,17) (18,23) (18,22) (18,19) (18,21) (19,23) (19,22) (19,20) (20,23) (20,21) (21,23) (22,23)\nQ: Is there a path between node 17 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "933"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,30) (0,27) (0,33) (0,11) (0,5) (0,12) (0,20) (0,7) (0,28) (0,17) (0,6) (0,4) (0,32) (0,13) (0,3) (0,22) (0,31) (1,25) (1,29) (1,30) (1,27) (1,33) (1,2) (1,5) (1,12) (1,20) (1,28) (1,18) (1,16) (1,24) (1,6) (1,13) (1,3) (1,22) (1,31) (2,25) (2,23) (2,29) (2,30) (2,27) (2,33) (2,11) (2,5) (2,12) (2,7) (2,18) (2,16) (2,17) (2,24) (2,13) (2,22) (2,15) (3,25) (3,23) (3,29) (3,30) (3,12) (3,7) (3,18) (3,16) (3,24) (3,4) (3,13) (3,22) (3,31) (4,23) (4,29) (4,27) (4,33) (4,11) (4,5) (4,7) (4,18) (4,24) (4,32) (4,15) (4,31) (5,25) (5,23) (5,30) (5,27) (5,33) (5,11) (5,12) (5,20) (5,7) (5,28) (5,24) (5,6) (5,32) (5,13) (5,22) (5,15) (5,31) (6,25) (6,23) (6,30) (6,27) (6,33) (6,12) (6,20) (6,7) (6,18) (6,24) (6,32) (6,13) (7,25) (7,30) (7,27) (7,33) (7,20) (7,28) (7,18) (7,24) (7,32) (7,13) (7,22) (7,15) (7,31) (8,14) (8,26) (8,19) (9,14) (9,26) (9,19) (9,21) (9,10) (10,14) (10,26) (10,19) (11,23) (11,29) (11,30) (11,27) (11,33) (11,20) (11,18) (11,16) (11,17) (11,32) (11,13) (11,22) (11,15) (11,31) (12,25) (12,23) (12,29) (12,27) (12,33) (12,28) (12,16) (12,24) (12,13) (12,22) (12,15) (12,31) (13,25) (13,23) (13,29) (13,27) (13,33) (13,20) (13,28) (13,18) (13,16) (13,17) (13,24) (13,32) (13,15) (13,31) (14,26) (15,25) (15,23) (15,29) (15,30) (15,33) (15,16) (15,17) (15,24) (15,22) (15,31) (16,25) (16,23) (16,29) (16,30) (16,27) (16,28) (16,17) (16,24) (16,32) (16,22) (17,25) (17,23) (17,29) (17,33) (17,20) (17,18) (17,24) (17,31) (18,25) (18,29) (18,30) (18,33) (18,28) (18,24) (18,31) (20,25) (20,23) (20,30) (20,24) (20,32) (20,22) (20,31) (21,26) (22,25) (22,29) (22,30) (22,28) (22,24) (23,25) (23,29) (23,27) (23,28) (23,24) (23,32) (24,25) (24,29) (24,27) (24,33) (24,28) (24,31) (25,29) (25,30) (25,27) (25,28) (25,32) (25,31) (27,29) (27,30) (27,33) (27,28) (28,29) (28,30) (28,33) (28,32) (28,31) (29,30) (29,33) (29,32) (29,31) (30,33) (30,32) (30,31) (31,33) (31,32) (32,33)\nQ: Is there a path between node 16 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "934"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,13) (0,11) (0,21) (0,8) (0,18) (0,3) (0,7) (0,15) (0,20) (0,17) (0,10) (0,22) (0,1) (0,9) (0,6) (0,19) (1,23) (1,14) (1,5) (1,13) (1,11) (1,12) (1,21) (1,8) (1,18) (1,3) (1,25) (1,7) (1,28) (1,15) (1,20) (1,17) (1,10) (1,22) (1,9) (1,6) (1,16) (1,19) (3,27) (3,14) (3,5) (3,13) (3,4) (3,21) (3,18) (3,25) (3,28) (3,15) (3,20) (3,17) (3,22) (3,6) (3,16) (3,19) (4,27) (4,23) (4,5) (4,13) (4,11) (4,12) (4,8) (4,28) (4,15) (4,20) (4,17) (4,10) (4,24) (4,6) (5,27) (5,23) (5,14) (5,13) (5,11) (5,12) (5,21) (5,8) (5,18) (5,25) (5,7) (5,15) (5,10) (5,22) (5,24) (5,9) (5,6) (5,16) (5,19) (6,27) (6,14) (6,11) (6,12) (6,18) (6,25) (6,7) (6,20) (6,17) (6,10) (6,22) (6,24) (6,9) (6,16) (6,19) (7,23) (7,14) (7,13) (7,12) (7,21) (7,8) (7,25) (7,28) (7,20) (7,10) (7,22) (7,16) (7,19) (8,27) (8,13) (8,18) (8,25) (8,15) (8,17) (8,10) (8,22) (8,24) (8,9) (8,16) (8,19) (9,27) (9,23) (9,11) (9,21) (9,25) (9,28) (9,15) (9,20) (9,17) (9,10) (9,22) (9,24) (9,16) (9,19) (10,27) (10,14) (10,11) (10,12) (10,25) (10,28) (10,15) (10,20) (10,17) (10,24) (10,16) (10,19) (11,23) (11,21) (11,18) (11,25) (11,28) (11,15) (11,17) (11,22) (11,24) (11,19) (12,27) (12,23) (12,13) (12,21) (12,18) (12,25) (12,28) (12,15) (12,17) (12,22) (12,24) (12,16) (13,27) (13,14) (13,21) (13,18) (13,28) (13,15) (13,17) (13,24) (13,16) (13,19) (14,27) (14,25) (14,28) (14,15) (14,17) (14,22) (14,24) (14,16) (15,23) (15,21) (15,18) (15,25) (15,20) (15,24) (16,27) (16,23) (16,17) (16,24) (16,19) (17,27) (17,23) (17,18) (17,25) (17,28) (17,20) (17,22) (17,24) (17,19) (18,23) (18,21) (18,25) (18,28) (18,20) (18,22) (18,24) (18,19) (19,27) (19,23) (19,21) (19,25) (19,24) (20,27) (20,23) (20,21) (20,25) (20,24) (21,23) (21,22) (23,27) (23,24) (25,27) (25,28) (27,28)\nQ: Is there a path between node 23 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "935"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,11) (0,6) (1,5) (1,8) (1,10) (1,15) (1,17) (1,13) (1,16) (2,5) (2,4) (2,8) (2,10) (2,14) (2,17) (2,13) (2,16) (3,9) (3,6) (3,12) (4,8) (4,15) (4,14) (4,17) (4,13) (5,8) (5,15) (5,17) (6,7) (6,9) (7,11) (7,9) (8,15) (8,17) (8,13) (8,16) (9,11) (10,15) (10,14) (10,17) (11,12) (13,15) (13,14) (13,16) (14,15) (14,17) (14,16) (15,17) (15,16) (16,17)\nQ: Is there a path between node 17 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "936"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,9) (1,10) (1,3) (2,6) (2,4) (2,7) (3,6) (3,10) (3,9) (3,12) (4,8) (5,9) (5,12) (6,9) (6,12) (6,7) (7,10) (7,9) (7,14) (8,10) (8,9) (8,14) (12,14)\nQ: Is there a path between node 4 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "937"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (0,13) (0,22) (1,12) (1,6) (2,20) (2,14) (2,11) (3,5) (3,23) (3,6) (5,17) (6,19) (7,23) (8,13) (8,15) (9,21) (9,18) (12,24) (12,17) (12,19) (13,21) (13,18) (13,25) (13,15) (13,16) (15,16) (16,21) (16,25) (17,23) (17,19) (19,26) (21,22) (22,25)\nQ: Is there a path between node 4 and node 19?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "938"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,7) (0,8) (0,10) (0,3) (1,4) (1,11) (1,9) (1,6) (1,12) (1,2) (2,4) (2,11) (2,9) (2,6) (2,12) (3,5) (3,7) (3,8) (3,10) (4,11) (4,9) (4,6) (4,12) (5,7) (5,8) (5,10) (6,11) (6,9) (6,12) (7,8) (7,10) (8,10) (9,11) (9,12) (11,12)\nQ: Is there a path between node 4 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "939"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,4) (0,1) (0,11) (0,9) (0,12) (1,2) (1,4) (1,11) (1,9) (1,13) (1,8) (1,12) (2,6) (2,3) (2,4) (2,11) (2,9) (2,13) (2,8) (3,6) (3,9) (3,13) (3,8) (3,12) (4,6) (4,11) (4,9) (4,13) (4,8) (4,12) (5,7) (5,10) (6,11) (6,9) (6,8) (6,12) (8,9) (8,12) (9,11) (9,12) (11,13) (12,13)\nQ: Is there a path between node 4 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "940"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (0,4) (1,32) (1,22) (1,34) (1,7) (1,5) (1,28) (1,11) (1,13) (1,30) (1,31) (1,26) (2,12) (2,3) (2,24) (2,15) (2,18) (2,8) (2,20) (2,25) (2,19) (2,17) (2,16) (3,10) (3,24) (3,15) (3,18) (3,8) (3,20) (3,14) (3,19) (3,21) (4,23) (4,6) (5,32) (5,22) (5,7) (5,33) (5,11) (5,13) (5,27) (5,31) (5,26) (6,23) (7,22) (7,34) (7,28) (7,13) (7,27) (7,30) (7,26) (7,29) (8,10) (8,24) (8,15) (8,18) (8,20) (8,14) (8,17) (8,21) (8,16) (9,32) (9,22) (9,34) (9,28) (9,13) (9,27) (9,31) (9,26) (9,29) (10,12) (10,24) (10,15) (10,18) (10,20) (10,25) (10,17) (11,32) (11,22) (11,34) (11,28) (11,13) (11,27) (11,30) (11,31) (11,26) (12,24) (12,25) (12,14) (12,17) (12,21) (12,16) (13,34) (13,33) (13,27) (13,30) (13,31) (13,29) (14,15) (14,18) (14,20) (14,25) (14,19) (14,17) (14,21) (14,16) (15,24) (15,18) (15,20) (15,17) (15,21) (16,24) (16,20) (16,19) (16,17) (17,24) (17,20) (17,21) (18,20) (18,25) (18,19) (20,24) (20,25) (20,21) (21,25) (22,32) (22,28) (22,27) (22,30) (22,31) (22,26) (24,25) (26,34) (26,33) (26,31) (27,34) (27,33) (27,28) (27,30) (27,31) (27,29) (28,32) (28,33) (28,30) (28,31) (28,29) (29,32) (29,33) (30,32) (31,32) (31,34) (32,34) (32,33) (33,34)\nQ: Is there a path between node 29 and node 22?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "941"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (1,24) (1,13) (1,7) (2,24) (2,15) (2,18) (2,8) (2,13) (2,7) (3,23) (3,6) (5,20) (5,14) (6,11) (6,23) (7,12) (7,10) (7,21) (7,8) (7,13) (8,10) (8,15) (8,18) (8,22) (8,13) (9,21) (9,13) (10,12) (10,15) (10,13) (12,24) (13,24) (13,22) (14,20) (15,24) (17,24) (19,20) (21,24)\nQ: Is there a path between node 21 and node 13?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "942"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,21) (0,7) (0,6) (0,3) (0,17) (0,20) (0,22) (0,16) (0,23) (0,25) (0,27) (1,5) (1,21) (1,4) (1,7) (1,15) (1,18) (1,2) (1,24) (1,20) (1,11) (1,16) (1,25) (1,27) (2,14) (2,5) (2,21) (2,4) (2,15) (2,24) (2,22) (2,11) (2,23) (2,25) (2,27) (3,14) (3,13) (3,21) (3,7) (3,15) (3,6) (3,17) (3,24) (3,22) (3,11) (3,16) (3,23) (4,14) (4,13) (4,5) (4,19) (4,7) (4,18) (4,17) (4,22) (4,11) (4,23) (4,25) (4,27) (5,13) (5,19) (5,15) (5,18) (5,24) (5,20) (5,22) (5,11) (5,23) (5,27) (6,14) (6,21) (6,19) (6,7) (6,15) (6,18) (6,17) (6,24) (6,20) (6,11) (6,16) (6,25) (6,27) (7,14) (7,13) (7,21) (7,19) (7,15) (7,18) (7,17) (7,20) (7,22) (7,11) (7,23) (7,27) (8,30) (8,28) (9,31) (9,10) (9,26) (9,29) (10,31) (10,26) (10,29) (11,13) (11,21) (11,19) (11,15) (11,24) (11,22) (11,25) (11,27) (12,28) (13,14) (13,21) (13,15) (13,18) (13,17) (13,24) (13,20) (13,16) (13,23) (13,25) (13,27) (14,21) (14,19) (14,24) (14,20) (14,22) (14,16) (14,23) (14,25) (15,21) (15,18) (15,17) (15,24) (15,20) (15,22) (15,16) (15,25) (15,27) (16,21) (16,18) (16,17) (16,24) (16,20) (16,22) (16,25) (17,21) (17,19) (17,18) (17,24) (17,20) (17,22) (17,23) (17,25) (17,27) (18,21) (18,24) (18,20) (18,25) (18,27) (19,21) (19,20) (19,22) (19,27) (20,21) (20,24) (20,22) (20,23) (20,27) (21,24) (21,22) (21,25) (21,27) (22,25) (23,25) (23,27) (25,27) (26,31) (26,29) (29,31)\nQ: Is there a path between node 19 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "943"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (0,1) (0,19) (0,15) (0,20) (0,9) (0,21) (0,3) (0,22) (0,32) (0,24) (0,14) (0,11) (0,17) (0,5) (0,34) (0,4) (0,26) (0,10) (0,8) (1,27) (1,23) (1,30) (1,6) (1,19) (1,20) (1,2) (1,9) (1,21) (1,3) (1,22) (1,24) (1,14) (1,11) (1,17) (1,5) (1,4) (1,26) (1,8) (2,27) (2,30) (2,6) (2,19) (2,20) (2,9) (2,21) (2,3) (2,22) (2,32) (2,7) (2,11) (2,17) (2,5) (2,34) (2,4) (2,26) (2,12) (2,10) (3,27) (3,23) (3,30) (3,6) (3,19) (3,15) (3,20) (3,9) (3,22) (3,24) (3,14) (3,34) (3,4) (3,12) (3,10) (3,8) (3,28) (4,27) (4,23) (4,30) (4,19) (4,15) (4,20) (4,9) (4,21) (4,32) (4,24) (4,14) (4,7) (4,11) (4,17) (4,5) (4,26) (4,12) (4,8) (4,28) (5,30) (5,19) (5,9) (5,21) (5,24) (5,7) (5,11) (5,17) (5,34) (5,12) (6,27) (6,23) (6,30) (6,19) (6,20) (6,9) (6,21) (6,22) (6,32) (6,24) (6,14) (6,7) (6,11) (6,17) (6,34) (6,26) (6,8) (6,28) (7,23) (7,30) (7,19) (7,15) (7,20) (7,21) (7,32) (7,24) (7,11) (7,17) (7,34) (7,12) (7,10) (7,8) (7,28) (8,23) (8,15) (8,20) (8,24) (8,14) (8,11) (8,17) (8,34) (8,26) (8,12) (8,10) (8,28) (9,30) (9,19) (9,15) (9,20) (9,22) (9,32) (9,24) (9,11) (9,34) (9,12) (9,10) (9,28) (10,27) (10,23) (10,30) (10,19) (10,21) (10,32) (10,24) (10,26) (10,12) (11,27) (11,30) (11,19) (11,20) (11,21) (11,22) (11,32) (11,24) (11,14) (11,17) (11,34) (11,12) (12,27) (12,30) (12,19) (12,20) (12,22) (12,32) (12,24) (12,14) (12,17) (12,34) (12,28) (14,27) (14,23) (14,30) (14,19) (14,15) (14,21) (14,22) (14,32) (14,17) (14,34) (14,28) (15,19) (15,20) (15,21) (15,22) (15,32) (15,24) (15,34) (15,26) (15,28) (16,33) (16,29) (16,18) (16,31) (17,27) (17,23) (17,30) (17,19) (17,20) (17,21) (17,22) (17,32) (17,24) (17,34) (17,28) (18,33) (18,31) (18,25) (19,27) (19,23) (19,30) (19,20) (19,22) (19,32) (19,34) (19,26) (19,28) (20,23) (20,30) (20,21) (20,22) (20,32) (20,24) (20,34) (20,26) (21,27) (21,23) (21,30) (21,22) (21,32) (21,24) (21,34) (21,26) (21,28) (22,27) (22,23) (22,24) (22,34) (22,26) (22,28) (23,32) (23,26) (23,28) (24,27) (24,32) (24,34) (24,26) (25,33) (26,30) (26,32) (26,34) (27,30) (27,32) (27,28) (28,30) (28,32) (28,34) (29,33) (29,31) (31,33) (32,34)\nQ: Is there a path between node 16 and node 24?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "944"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,12) (0,5) (0,6) (0,4) (0,8) (0,2) (0,9) (0,1) (0,7) (1,12) (1,5) (1,6) (1,4) (1,8) (1,2) (1,9) (1,10) (1,7) (2,8) (2,10) (2,7) (4,11) (4,12) (4,5) (4,6) (4,8) (4,9) (4,7) (5,11) (5,6) (5,8) (5,10) (5,7) (6,11) (6,12) (6,8) (6,9) (7,11) (7,12) (7,9) (7,10) (8,12) (8,9) (8,10) (9,11) (9,12) (9,10) (10,11) (10,12) (11,12)\nQ: Is there a path between node 0 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "945"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,10) (0,12) (0,20) (0,14) (0,8) (0,3) (0,6) (0,5) (0,15) (0,19) (0,7) (0,9) (0,22) (0,2) (0,21) (0,18) (1,4) (1,10) (1,12) (1,20) (1,8) (1,5) (1,15) (1,16) (1,19) (1,7) (1,9) (1,22) (1,2) (1,18) (2,4) (2,10) (2,12) (2,14) (2,3) (2,5) (2,15) (2,19) (2,7) (2,22) (2,21) (2,18) (3,4) (3,12) (3,20) (3,14) (3,6) (3,5) (3,15) (3,16) (3,19) (3,7) (3,9) (3,22) (3,21) (3,18) (4,10) (4,12) (4,8) (4,6) (4,5) (4,15) (4,16) (4,19) (4,7) (4,9) (4,21) (4,18) (5,12) (5,14) (5,8) (5,6) (5,15) (5,16) (5,19) (5,7) (5,9) (5,22) (5,18) (6,10) (6,12) (6,20) (6,14) (6,16) (6,19) (6,7) (6,9) (6,22) (6,21) (6,18) (7,10) (7,12) (7,14) (7,8) (7,16) (7,9) (7,22) (7,21) (7,18) (8,10) (8,12) (8,14) (8,15) (8,16) (8,19) (8,9) (8,21) (9,12) (9,20) (9,15) (9,16) (9,22) (9,21) (9,18) (10,12) (10,20) (10,14) (10,15) (10,16) (10,18) (12,16) (12,19) (13,17) (14,20) (14,16) (15,16) (15,22) (15,21) (16,20) (16,21) (16,18) (18,22) (18,21) (19,20) (19,22) (19,21) (21,22)\nQ: Is there a path between node 10 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "946"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,2) (2,3)\nQ: Is there a path between node 4 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "947"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,9) (0,4) (0,14) (0,6) (0,10) (0,12) (0,2) (1,13) (1,11) (1,3) (1,5) (1,7) (1,16) (1,8) (1,17) (2,15) (2,9) (2,4) (2,14) (2,6) (2,10) (2,12) (3,13) (3,11) (3,5) (3,7) (3,16) (3,8) (3,17) (4,15) (4,9) (4,14) (4,6) (4,10) (4,12) (5,13) (5,11) (5,7) (5,16) (5,8) (5,17) (6,15) (6,9) (6,14) (6,10) (6,12) (7,13) (7,11) (7,16) (7,8) (7,17) (8,13) (8,11) (8,16) (8,17) (9,15) (9,14) (9,10) (9,12) (10,15) (10,14) (10,12) (11,13) (11,16) (11,17) (12,15) (12,14) (13,16) (13,17) (14,15) (16,17)\nQ: Is there a path between node 12 and node 17?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "948"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,34) (0,1) (0,10) (0,12) (1,12) (2,24) (3,31) (3,30) (3,25) (4,19) (4,6) (5,8) (7,26) (10,20) (10,28) (10,17) (10,18) (12,20) (12,32) (12,17) (13,14) (13,15) (13,21) (13,26) (13,23) (14,15) (14,21) (15,26) (15,23) (16,21) (16,30) (17,20) (17,27) (17,32) (18,27) (18,34) (19,33) (20,27) (21,31) (21,22) (22,26) (22,31) (23,31) (26,31) (28,34) (30,31)\nQ: Is there a path between node 12 and node 28?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "949"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,20) (0,13) (0,24) (0,4) (1,21) (1,3) (1,11) (1,10) (1,23) (1,8) (1,2) (1,22) (1,19) (1,18) (2,21) (2,3) (2,11) (2,10) (2,23) (2,8) (2,22) (2,19) (2,18) (3,21) (3,11) (3,10) (3,23) (3,8) (3,22) (3,19) (3,18) (4,14) (4,20) (4,13) (4,24) (5,7) (5,9) (5,12) (5,16) (5,15) (5,17) (5,6) (6,7) (6,9) (6,12) (6,16) (6,15) (6,17) (7,9) (7,12) (7,16) (7,15) (7,17) (8,21) (8,11) (8,10) (8,23) (8,22) (8,19) (8,18) (9,12) (9,16) (9,15) (9,17) (10,21) (10,11) (10,23) (10,22) (10,19) (10,18) (11,21) (11,23) (11,22) (11,19) (11,18) (12,16) (12,15) (12,17) (13,14) (13,20) (13,24) (14,20) (14,24) (15,16) (15,17) (16,17) (18,21) (18,23) (18,22) (18,19) (19,21) (19,23) (19,22) (20,24) (21,23) (21,22) (22,23)\nQ: Is there a path between node 20 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "950"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,10) (0,12) (0,20) (0,14) (0,8) (0,3) (0,6) (0,5) (0,15) (0,19) (0,7) (0,9) (0,22) (0,2) (0,21) (0,18) (1,4) (1,10) (1,12) (1,20) (1,8) (1,5) (1,15) (1,16) (1,19) (1,7) (1,9) (1,22) (1,2) (1,18) (2,4) (2,10) (2,12) (2,14) (2,3) (2,5) (2,15) (2,19) (2,7) (2,22) (2,21) (2,18) (3,4) (3,12) (3,20) (3,14) (3,6) (3,5) (3,15) (3,16) (3,19) (3,7) (3,9) (3,22) (3,21) (3,18) (4,10) (4,12) (4,8) (4,6) (4,5) (4,15) (4,16) (4,19) (4,7) (4,9) (4,21) (4,18) (5,12) (5,14) (5,8) (5,6) (5,15) (5,16) (5,19) (5,7) (5,9) (5,22) (5,18) (6,10) (6,12) (6,20) (6,14) (6,16) (6,19) (6,7) (6,9) (6,22) (6,21) (6,18) (7,10) (7,12) (7,14) (7,8) (7,16) (7,9) (7,22) (7,21) (7,18) (8,10) (8,12) (8,14) (8,15) (8,16) (8,19) (8,9) (8,21) (9,12) (9,20) (9,15) (9,16) (9,22) (9,21) (9,18) (10,12) (10,20) (10,14) (10,15) (10,16) (10,18) (12,16) (12,19) (13,17) (14,20) (14,16) (15,16) (15,22) (15,21) (16,20) (16,21) (16,18) (18,22) (18,21) (19,20) (19,22) (19,21) (21,22)\nQ: Is there a path between node 17 and node 19?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "951"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (1,15) (1,16) (2,18) (2,17) (2,7) (3,14) (3,7) (5,11) (6,13) (7,17) (8,15) (8,13) (9,17) (10,17) (13,15) (13,16) (16,19)\nQ: Is there a path between node 10 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "952"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (0,13) (0,3) (0,14) (0,15) (0,19) (0,7) (0,9) (0,10) (1,5) (1,18) (1,12) (1,13) (1,14) (1,6) (1,17) (1,16) (1,9) (1,10) (1,11) (2,18) (2,12) (2,13) (2,6) (2,15) (2,19) (2,7) (2,17) (2,16) (2,9) (2,10) (2,11) (3,18) (3,12) (3,13) (3,14) (3,6) (3,19) (3,17) (3,9) (3,10) (3,11) (5,18) (5,12) (5,13) (5,14) (5,6) (5,15) (5,19) (5,7) (5,16) (5,11) (6,18) (6,12) (6,7) (6,17) (6,16) (6,9) (6,10) (7,18) (7,12) (7,13) (7,15) (7,19) (7,17) (7,16) (7,10) (7,11) (9,18) (9,13) (9,15) (9,19) (9,16) (9,10) (10,18) (10,13) (10,14) (10,19) (10,17) (10,11) (11,12) (11,13) (11,14) (11,15) (11,19) (11,17) (11,16) (12,14) (12,19) (12,17) (12,16) (13,18) (13,15) (13,19) (13,17) (14,18) (14,15) (14,19) (14,17) (14,16) (15,18) (15,19) (15,16) (16,18) (17,18) (17,19) (18,19)\nQ: Is there a path between node 8 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "953"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,6) (0,4) (1,3) (1,7) (1,2) (2,3) (3,9) (4,6) (5,9) (6,8) (7,9)\nQ: Is there a path between node 3 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "954"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,8) (0,10) (0,12) (0,13) (1,10) (2,5) (2,16) (3,13) (4,16) (5,7) (5,14) (6,7) (7,16) (7,14) (9,13) (10,15) (11,12) (12,15)\nQ: Is there a path between node 13 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "955"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (2,3) (2,5) (3,5) (4,6)\nQ: Is there a path between node 1 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "956"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,3) (0,11) (0,18) (0,7) (0,8) (0,9) (0,1) (0,10) (0,15) (0,17) (0,13) (0,16) (0,19) (0,2) (0,6) (0,5) (0,14) (1,12) (1,3) (1,11) (1,18) (1,7) (1,8) (1,9) (1,10) (1,15) (1,17) (1,13) (1,16) (1,19) (1,2) (1,6) (1,5) (1,14) (2,12) (2,3) (2,11) (2,18) (2,7) (2,8) (2,9) (2,10) (2,15) (2,17) (2,13) (2,16) (2,19) (2,6) (2,5) (2,14) (3,12) (3,11) (3,18) (3,7) (3,8) (3,9) (3,10) (3,15) (3,17) (3,13) (3,16) (3,19) (3,6) (3,5) (3,14) (4,20) (4,21) (5,12) (5,11) (5,18) (5,7) (5,8) (5,9) (5,10) (5,15) (5,17) (5,13) (5,16) (5,19) (5,6) (5,14) (6,12) (6,11) (6,18) (6,7) (6,8) (6,9) (6,10) (6,15) (6,17) (6,13) (6,16) (6,19) (6,14) (7,12) (7,11) (7,18) (7,8) (7,9) (7,10) (7,15) (7,17) (7,13) (7,16) (7,19) (7,14) (8,12) (8,11) (8,18) (8,9) (8,10) (8,15) (8,17) (8,13) (8,16) (8,19) (8,14) (9,12) (9,11) (9,18) (9,10) (9,15) (9,17) (9,13) (9,16) (9,19) (9,14) (10,12) (10,11) (10,18) (10,15) (10,17) (10,13) (10,16) (10,19) (10,14) (11,12) (11,18) (11,15) (11,17) (11,13) (11,16) (11,19) (11,14) (12,18) (12,15) (12,17) (12,13) (12,16) (12,19) (12,14) (13,18) (13,15) (13,17) (13,16) (13,19) (13,14) (14,18) (14,15) (14,17) (14,16) (14,19) (15,18) (15,17) (15,16) (15,19) (16,18) (16,17) (16,19) (17,18) (17,19) (18,19) (20,21)\nQ: Is there a path between node 2 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "957"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (1,14) (1,3) (1,9) (1,10) (1,4) (1,7) (1,6) (1,13) (1,12) (1,11) (2,15) (3,14) (3,8) (3,9) (3,10) (3,4) (3,12) (3,11) (4,8) (4,9) (4,10) (4,7) (4,5) (4,11) (5,9) (5,7) (5,13) (5,12) (5,11) (6,14) (6,8) (6,7) (6,13) (6,11) (7,8) (7,9) (7,10) (7,11) (8,14) (8,10) (8,12) (8,11) (9,14) (9,10) (9,13) (9,12) (10,14) (10,13) (10,12) (11,14) (11,13) (11,12) (12,14)\nQ: Is there a path between node 10 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "958"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,7) (0,13) (0,24) (0,19) (0,5) (0,10) (0,4) (0,2) (0,21) (0,17) (0,23) (0,9) (0,20) (0,15) (0,22) (1,3) (1,18) (1,6) (1,14) (1,8) (1,11) (2,12) (2,7) (2,13) (2,24) (2,19) (2,5) (2,10) (2,4) (2,21) (2,17) (2,23) (2,9) (2,20) (2,15) (2,22) (3,18) (3,6) (3,14) (3,8) (3,11) (4,12) (4,7) (4,13) (4,24) (4,19) (4,5) (4,10) (4,21) (4,17) (4,23) (4,9) (4,20) (4,15) (4,22) (5,12) (5,7) (5,13) (5,24) (5,19) (5,10) (5,21) (5,17) (5,23) (5,9) (5,20) (5,15) (5,22) (6,18) (6,14) (6,8) (6,11) (7,12) (7,13) (7,24) (7,19) (7,10) (7,21) (7,17) (7,23) (7,9) (7,20) (7,15) (7,22) (8,18) (8,14) (8,11) (9,12) (9,13) (9,24) (9,19) (9,10) (9,21) (9,17) (9,23) (9,20) (9,15) (9,22) (10,12) (10,13) (10,24) (10,19) (10,21) (10,17) (10,23) (10,20) (10,15) (10,22) (11,18) (11,14) (12,13) (12,24) (12,19) (12,21) (12,17) (12,23) (12,20) (12,15) (12,22) (13,24) (13,19) (13,21) (13,17) (13,23) (13,20) (13,15) (13,22) (14,18) (15,24) (15,19) (15,21) (15,17) (15,23) (15,20) (15,22) (17,24) (17,19) (17,21) (17,23) (17,20) (17,22) (19,24) (19,21) (19,23) (19,20) (19,22) (20,24) (20,21) (20,23) (20,22) (21,24) (21,23) (21,22) (22,24) (22,23) (23,24)\nQ: Is there a path between node 14 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "959"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,13) (1,6) (1,8) (1,3) (1,4) (2,5) (2,9) (3,12) (3,9) (3,13) (4,6) (4,10) (5,6) (5,9) (6,12) (6,8) (8,9) (9,10) (12,13)\nQ: Is there a path between node 10 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "960"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,10) (0,15) (0,21) (0,1) (0,7) (0,29) (0,24) (0,16) (0,23) (0,17) (1,26) (1,10) (1,15) (1,7) (1,28) (1,29) (1,12) (1,24) (1,16) (1,3) (1,23) (2,14) (2,27) (2,34) (3,26) (3,32) (3,15) (3,21) (3,7) (3,28) (3,29) (3,12) (3,24) (3,23) (3,17) (4,9) (4,14) (4,27) (4,31) (5,19) (5,22) (5,13) (5,20) (5,25) (5,30) (5,8) (5,33) (6,9) (6,27) (6,34) (6,31) (7,26) (7,32) (7,10) (7,15) (7,21) (7,29) (7,12) (7,24) (7,16) (7,23) (7,17) (8,19) (8,22) (8,13) (8,20) (8,25) (8,18) (8,30) (8,33) (9,14) (9,34) (10,32) (10,15) (10,21) (10,29) (10,24) (10,23) (10,17) (11,19) (11,22) (11,13) (11,25) (11,18) (11,30) (12,26) (12,32) (12,15) (12,21) (12,24) (12,16) (12,23) (13,19) (13,20) (13,25) (13,18) (13,33) (14,27) (14,31) (15,26) (15,21) (15,28) (15,24) (15,16) (15,23) (15,17) (16,26) (16,32) (16,23) (16,17) (17,26) (17,32) (17,21) (17,28) (17,24) (18,19) (18,22) (18,20) (18,30) (19,22) (19,20) (19,25) (19,30) (20,25) (20,30) (20,33) (21,26) (21,32) (21,28) (21,29) (22,25) (22,30) (22,33) (23,32) (23,28) (23,29) (23,24) (24,32) (24,28) (25,30) (25,33) (26,32) (26,28) (27,31) (28,29) (30,33)\nQ: Is there a path between node 5 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "961"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,25) (0,3) (1,25) (1,29) (2,14) (2,13) (2,20) (2,18) (2,31) (2,9) (2,27) (2,21) (2,12) (2,7) (2,33) (2,11) (2,24) (2,26) (2,30) (3,25) (4,23) (4,22) (4,34) (4,5) (5,23) (5,22) (5,34) (6,14) (6,13) (6,20) (6,18) (6,27) (6,21) (6,12) (6,7) (6,28) (6,24) (6,26) (6,30) (7,14) (7,13) (7,20) (7,31) (7,17) (7,9) (7,27) (7,21) (7,12) (7,10) (7,33) (7,28) (7,30) (8,14) (8,13) (8,31) (8,17) (8,9) (8,27) (8,12) (8,33) (8,11) (8,28) (8,26) (8,30) (9,14) (9,13) (9,20) (9,18) (9,27) (9,21) (9,12) (9,10) (9,33) (9,24) (9,26) (9,19) (9,30) (10,13) (10,20) (10,18) (10,31) (10,17) (10,27) (10,12) (10,33) (10,11) (10,28) (10,24) (11,14) (11,13) (11,20) (11,18) (11,31) (11,12) (11,33) (11,28) (11,24) (11,26) (11,30) (12,14) (12,13) (12,20) (12,18) (12,17) (12,27) (12,21) (12,33) (12,19) (13,14) (13,20) (13,18) (13,31) (13,17) (13,21) (13,28) (13,24) (13,26) (14,18) (14,31) (14,17) (14,27) (14,21) (14,33) (14,26) (15,32) (17,18) (17,31) (17,27) (17,33) (17,28) (17,24) (17,26) (17,19) (17,30) (18,20) (18,31) (18,33) (18,24) (18,26) (18,19) (18,30) (19,31) (19,27) (19,21) (19,33) (19,28) (19,26) (20,31) (20,27) (20,21) (20,33) (20,24) (20,26) (20,30) (21,27) (21,33) (21,28) (21,24) (21,30) (22,23) (22,34) (23,34) (24,33) (24,26) (25,29) (26,31) (26,33) (26,30) (27,31) (27,33) (27,28) (27,30) (28,31) (28,33) (28,30) (30,31) (30,33) (31,33)\nQ: Is there a path between node 33 and node 12?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "962"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,9) (0,4) (0,14) (0,6) (0,10) (0,12) (0,2) (1,13) (1,11) (1,3) (1,5) (1,7) (1,16) (1,8) (1,17) (2,15) (2,9) (2,4) (2,14) (2,6) (2,10) (2,12) (3,13) (3,11) (3,5) (3,7) (3,16) (3,8) (3,17) (4,15) (4,9) (4,14) (4,6) (4,10) (4,12) (5,13) (5,11) (5,7) (5,16) (5,8) (5,17) (6,15) (6,9) (6,14) (6,10) (6,12) (7,13) (7,11) (7,16) (7,8) (7,17) (8,13) (8,11) (8,16) (8,17) (9,15) (9,14) (9,10) (9,12) (10,15) (10,14) (10,12) (11,13) (11,16) (11,17) (12,15) (12,14) (13,16) (13,17) (14,15) (16,17)\nQ: Is there a path between node 5 and node 14?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "963"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,6) (0,3) (0,18) (0,1) (0,15) (0,12) (0,14) (0,9) (0,16) (0,8) (0,2) (0,11) (0,19) (1,7) (1,6) (1,3) (1,18) (1,15) (1,9) (1,8) (1,2) (1,20) (2,7) (2,3) (2,18) (2,15) (2,12) (2,14) (2,9) (2,16) (2,8) (2,11) (2,19) (2,20) (3,18) (3,15) (3,12) (3,9) (3,16) (3,8) (3,19) (3,20) (4,13) (4,17) (5,17) (6,7) (6,18) (6,15) (6,14) (6,9) (6,16) (6,11) (6,19) (6,20) (7,15) (7,12) (7,14) (7,9) (7,16) (8,18) (8,12) (8,14) (8,9) (8,16) (8,11) (8,19) (8,20) (9,18) (9,15) (9,12) (9,11) (9,19) (9,20) (10,13) (11,18) (11,12) (11,14) (11,16) (11,19) (11,20) (12,18) (12,15) (12,14) (12,19) (12,20) (13,17) (14,19) (16,18) (16,19) (18,20)\nQ: Is there a path between node 11 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "964"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (1,18) (1,8) (1,4) (2,15) (2,18) (2,11) (2,23) (2,4) (3,12) (3,5) (4,23) (4,25) (5,12) (5,17) (6,22) (6,13) (7,18) (7,23) (7,8) (9,17) (10,19) (10,17) (11,15) (12,24) (14,20) (14,22) (15,18) (16,20) (16,22) (20,22) (21,22) (23,25)\nQ: Is there a path between node 21 and node 13?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "965"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,13) (0,11) (0,21) (0,8) (0,18) (0,3) (0,7) (0,15) (0,20) (0,17) (0,10) (0,22) (0,1) (0,9) (0,6) (0,19) (1,23) (1,14) (1,5) (1,13) (1,11) (1,12) (1,21) (1,8) (1,18) (1,3) (1,25) (1,7) (1,28) (1,15) (1,20) (1,17) (1,10) (1,22) (1,9) (1,6) (1,16) (1,19) (3,27) (3,14) (3,5) (3,13) (3,4) (3,21) (3,18) (3,25) (3,28) (3,15) (3,20) (3,17) (3,22) (3,6) (3,16) (3,19) (4,27) (4,23) (4,5) (4,13) (4,11) (4,12) (4,8) (4,28) (4,15) (4,20) (4,17) (4,10) (4,24) (4,6) (5,27) (5,23) (5,14) (5,13) (5,11) (5,12) (5,21) (5,8) (5,18) (5,25) (5,7) (5,15) (5,10) (5,22) (5,24) (5,9) (5,6) (5,16) (5,19) (6,27) (6,14) (6,11) (6,12) (6,18) (6,25) (6,7) (6,20) (6,17) (6,10) (6,22) (6,24) (6,9) (6,16) (6,19) (7,23) (7,14) (7,13) (7,12) (7,21) (7,8) (7,25) (7,28) (7,20) (7,10) (7,22) (7,16) (7,19) (8,27) (8,13) (8,18) (8,25) (8,15) (8,17) (8,10) (8,22) (8,24) (8,9) (8,16) (8,19) (9,27) (9,23) (9,11) (9,21) (9,25) (9,28) (9,15) (9,20) (9,17) (9,10) (9,22) (9,24) (9,16) (9,19) (10,27) (10,14) (10,11) (10,12) (10,25) (10,28) (10,15) (10,20) (10,17) (10,24) (10,16) (10,19) (11,23) (11,21) (11,18) (11,25) (11,28) (11,15) (11,17) (11,22) (11,24) (11,19) (12,27) (12,23) (12,13) (12,21) (12,18) (12,25) (12,28) (12,15) (12,17) (12,22) (12,24) (12,16) (13,27) (13,14) (13,21) (13,18) (13,28) (13,15) (13,17) (13,24) (13,16) (13,19) (14,27) (14,25) (14,28) (14,15) (14,17) (14,22) (14,24) (14,16) (15,23) (15,21) (15,18) (15,25) (15,20) (15,24) (16,27) (16,23) (16,17) (16,24) (16,19) (17,27) (17,23) (17,18) (17,25) (17,28) (17,20) (17,22) (17,24) (17,19) (18,23) (18,21) (18,25) (18,28) (18,20) (18,22) (18,24) (18,19) (19,27) (19,23) (19,21) (19,25) (19,24) (20,27) (20,23) (20,21) (20,25) (20,24) (21,23) (21,22) (23,27) (23,24) (25,27) (25,28) (27,28)\nQ: Is there a path between node 26 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "966"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,13) (0,17) (0,10) (0,5) (0,4) (0,16) (0,19) (0,20) (0,7) (0,8) (0,15) (0,1) (0,18) (0,9) (0,12) (1,13) (1,17) (1,10) (1,5) (1,4) (1,16) (1,19) (1,20) (1,7) (1,8) (1,15) (1,18) (1,9) (1,12) (2,11) (2,21) (2,3) (2,14) (3,11) (3,21) (3,14) (4,13) (4,17) (4,10) (4,5) (4,16) (4,19) (4,20) (4,7) (4,8) (4,15) (4,18) (4,9) (4,12) (5,13) (5,17) (5,10) (5,16) (5,19) (5,20) (5,7) (5,8) (5,15) (5,18) (5,9) (5,12) (7,13) (7,17) (7,10) (7,16) (7,19) (7,20) (7,8) (7,15) (7,18) (7,9) (7,12) (8,13) (8,17) (8,10) (8,16) (8,19) (8,20) (8,15) (8,18) (8,9) (8,12) (9,13) (9,17) (9,10) (9,16) (9,19) (9,20) (9,15) (9,18) (9,12) (10,13) (10,17) (10,16) (10,19) (10,20) (10,15) (10,18) (10,12) (11,21) (11,14) (12,13) (12,17) (12,16) (12,19) (12,20) (12,15) (12,18) (13,17) (13,16) (13,19) (13,20) (13,15) (13,18) (14,21) (15,17) (15,16) (15,19) (15,20) (15,18) (16,17) (16,19) (16,20) (16,18) (17,19) (17,20) (17,18) (18,19) (18,20) (19,20)\nQ: Is there a path between node 3 and node 20?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "967"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,11) (0,5) (0,9) (0,6) (1,2) (1,7) (1,3) (1,10) (1,8) (2,7) (2,3) (2,10) (2,8) (3,7) (3,10) (3,8) (4,11) (4,5) (4,9) (4,6) (5,11) (5,9) (5,6) (6,11) (6,9) (7,10) (7,8) (8,10) (9,11)\nQ: Is there a path between node 0 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "968"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,13) (0,1) (0,9) (0,5) (0,7) (0,3) (0,10) (0,23) (0,26) (0,27) (0,8) (0,14) (0,22) (0,20) (0,15) (0,4) (0,2) (1,25) (1,11) (1,21) (1,13) (1,9) (1,3) (1,10) (1,23) (1,26) (1,27) (1,14) (1,20) (1,15) (1,2) (1,28) (2,25) (2,11) (2,16) (2,21) (2,6) (2,13) (2,9) (2,7) (2,23) (2,26) (2,8) (2,20) (2,15) (3,25) (3,6) (3,13) (3,9) (3,10) (3,27) (3,20) (3,15) (3,4) (3,28) (4,11) (4,16) (4,6) (4,13) (4,10) (4,23) (4,26) (4,27) (4,8) (4,14) (4,22) (4,15) (4,28) (5,25) (5,16) (5,21) (5,6) (5,13) (5,9) (5,7) (5,26) (5,8) (5,22) (5,15) (5,28) (6,11) (6,16) (6,21) (6,13) (6,9) (6,7) (6,10) (6,27) (6,22) (6,20) (6,15) (7,25) (7,16) (7,21) (7,9) (7,10) (7,27) (7,8) (7,14) (7,22) (7,20) (7,15) (7,28) (8,25) (8,13) (8,23) (8,26) (8,27) (8,14) (8,20) (8,28) (9,25) (9,11) (9,16) (9,21) (9,10) (9,23) (9,26) (9,27) (9,22) (9,20) (9,28) (10,11) (10,16) (10,21) (10,13) (10,23) (10,26) (10,27) (10,14) (10,22) (10,20) (10,15) (10,28) (11,25) (11,16) (11,21) (11,13) (11,23) (11,26) (11,27) (11,14) (11,22) (11,20) (12,24) (12,19) (13,25) (13,16) (13,14) (13,22) (13,15) (13,28) (14,25) (14,21) (14,23) (14,26) (14,20) (14,15) (15,16) (15,21) (15,26) (15,27) (15,22) (15,28) (16,21) (16,23) (16,26) (16,27) (16,28) (17,18) (20,25) (20,23) (20,26) (20,27) (20,22) (20,28) (21,25) (21,23) (21,26) (21,22) (22,25) (22,23) (22,27) (23,25) (23,26) (23,27) (23,28) (25,26) (25,27) (26,27) (27,28)\nQ: Is there a path between node 24 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "969"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,5) (0,7) (0,2) (0,8) (0,4) (0,9) (0,1) (0,12) (0,3) (0,11) (0,13) (1,10) (1,5) (1,7) (1,2) (1,8) (1,4) (1,9) (1,12) (1,3) (1,11) (1,13) (2,10) (2,5) (2,7) (2,8) (2,4) (2,9) (2,12) (2,3) (2,11) (2,13) (3,10) (3,5) (3,7) (3,8) (3,4) (3,9) (3,12) (3,11) (3,13) (4,10) (4,5) (4,7) (4,8) (4,9) (4,12) (4,11) (4,13) (5,10) (5,7) (5,8) (5,9) (5,12) (5,11) (5,13) (7,10) (7,8) (7,9) (7,12) (7,11) (7,13) (8,10) (8,9) (8,12) (8,11) (8,13) (9,10) (9,12) (9,11) (9,13) (10,12) (10,11) (10,13) (11,12) (11,13) (12,13)\nQ: Is there a path between node 6 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "970"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,25) (0,3) (1,25) (1,29) (2,14) (2,13) (2,20) (2,18) (2,31) (2,9) (2,27) (2,21) (2,12) (2,7) (2,33) (2,11) (2,24) (2,26) (2,30) (3,25) (4,23) (4,22) (4,34) (4,5) (5,23) (5,22) (5,34) (6,14) (6,13) (6,20) (6,18) (6,27) (6,21) (6,12) (6,7) (6,28) (6,24) (6,26) (6,30) (7,14) (7,13) (7,20) (7,31) (7,17) (7,9) (7,27) (7,21) (7,12) (7,10) (7,33) (7,28) (7,30) (8,14) (8,13) (8,31) (8,17) (8,9) (8,27) (8,12) (8,33) (8,11) (8,28) (8,26) (8,30) (9,14) (9,13) (9,20) (9,18) (9,27) (9,21) (9,12) (9,10) (9,33) (9,24) (9,26) (9,19) (9,30) (10,13) (10,20) (10,18) (10,31) (10,17) (10,27) (10,12) (10,33) (10,11) (10,28) (10,24) (11,14) (11,13) (11,20) (11,18) (11,31) (11,12) (11,33) (11,28) (11,24) (11,26) (11,30) (12,14) (12,13) (12,20) (12,18) (12,17) (12,27) (12,21) (12,33) (12,19) (13,14) (13,20) (13,18) (13,31) (13,17) (13,21) (13,28) (13,24) (13,26) (14,18) (14,31) (14,17) (14,27) (14,21) (14,33) (14,26) (15,32) (17,18) (17,31) (17,27) (17,33) (17,28) (17,24) (17,26) (17,19) (17,30) (18,20) (18,31) (18,33) (18,24) (18,26) (18,19) (18,30) (19,31) (19,27) (19,21) (19,33) (19,28) (19,26) (20,31) (20,27) (20,21) (20,33) (20,24) (20,26) (20,30) (21,27) (21,33) (21,28) (21,24) (21,30) (22,23) (22,34) (23,34) (24,33) (24,26) (25,29) (26,31) (26,33) (26,30) (27,31) (27,33) (27,28) (27,30) (28,31) (28,33) (28,30) (30,31) (30,33) (31,33)\nQ: Is there a path between node 17 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "971"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,21) (0,11) (0,15) (0,4) (0,22) (0,5) (0,3) (0,6) (0,20) (0,13) (0,18) (0,9) (0,1) (0,12) (0,24) (0,16) (0,8) (0,23) (0,2) (1,21) (1,11) (1,15) (1,4) (1,22) (1,5) (1,3) (1,6) (1,20) (1,13) (1,18) (1,9) (1,12) (1,24) (1,16) (1,8) (1,23) (1,2) (2,21) (2,11) (2,15) (2,4) (2,22) (2,5) (2,3) (2,6) (2,20) (2,13) (2,18) (2,9) (2,12) (2,24) (2,16) (2,8) (2,23) (3,21) (3,11) (3,15) (3,4) (3,22) (3,5) (3,6) (3,20) (3,13) (3,18) (3,9) (3,12) (3,24) (3,16) (3,8) (3,23) (4,21) (4,11) (4,15) (4,22) (4,5) (4,6) (4,20) (4,13) (4,18) (4,9) (4,12) (4,24) (4,16) (4,8) (4,23) (5,21) (5,11) (5,15) (5,22) (5,6) (5,20) (5,13) (5,18) (5,9) (5,12) (5,24) (5,16) (5,8) (5,23) (6,21) (6,11) (6,15) (6,22) (6,20) (6,13) (6,18) (6,9) (6,12) (6,24) (6,16) (6,8) (6,23) (7,10) (7,14) (7,17) (7,19) (8,21) (8,11) (8,15) (8,22) (8,20) (8,13) (8,18) (8,9) (8,12) (8,24) (8,16) (8,23) (9,21) (9,11) (9,15) (9,22) (9,20) (9,13) (9,18) (9,12) (9,24) (9,16) (9,23) (10,14) (10,17) (10,19) (11,21) (11,15) (11,22) (11,20) (11,13) (11,18) (11,12) (11,24) (11,16) (11,23) (12,21) (12,15) (12,22) (12,20) (12,13) (12,18) (12,24) (12,16) (12,23) (13,21) (13,15) (13,22) (13,20) (13,18) (13,24) (13,16) (13,23) (14,17) (14,19) (15,21) (15,22) (15,20) (15,18) (15,24) (15,16) (15,23) (16,21) (16,22) (16,20) (16,18) (16,24) (16,23) (17,19) (18,21) (18,22) (18,20) (18,24) (18,23) (20,21) (20,22) (20,24) (20,23) (21,22) (21,24) (21,23) (22,24) (22,23) (23,24)\nQ: Is there a path between node 14 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "972"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,3) (0,2) (1,5) (1,3) (2,5) (2,3) (3,5)\nQ: Is there a path between node 4 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "973"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,20) (0,13) (0,24) (0,4) (1,21) (1,3) (1,11) (1,10) (1,23) (1,8) (1,2) (1,22) (1,19) (1,18) (2,21) (2,3) (2,11) (2,10) (2,23) (2,8) (2,22) (2,19) (2,18) (3,21) (3,11) (3,10) (3,23) (3,8) (3,22) (3,19) (3,18) (4,14) (4,20) (4,13) (4,24) (5,7) (5,9) (5,12) (5,16) (5,15) (5,17) (5,6) (6,7) (6,9) (6,12) (6,16) (6,15) (6,17) (7,9) (7,12) (7,16) (7,15) (7,17) (8,21) (8,11) (8,10) (8,23) (8,22) (8,19) (8,18) (9,12) (9,16) (9,15) (9,17) (10,21) (10,11) (10,23) (10,22) (10,19) (10,18) (11,21) (11,23) (11,22) (11,19) (11,18) (12,16) (12,15) (12,17) (13,14) (13,20) (13,24) (14,20) (14,24) (15,16) (15,17) (16,17) (18,21) (18,23) (18,22) (18,19) (19,21) (19,23) (19,22) (20,24) (21,23) (21,22) (22,23)\nQ: Is there a path between node 6 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "974"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,31) (1,4) (1,27) (1,25) (2,31) (2,24) (2,13) (2,10) (3,30) (3,32) (3,27) (3,15) (4,30) (4,6) (4,28) (4,8) (5,22) (6,27) (7,20) (7,11) (7,12) (8,15) (9,14) (10,17) (10,23) (10,13) (11,14) (12,18) (13,23) (14,22) (15,30) (15,27) (15,25) (15,16) (15,28) (17,23) (17,21) (18,22) (18,33) (20,22) (21,31) (23,24) (25,30) (25,27) (25,28) (26,31) (27,30) (27,32) (28,32)\nQ: Is there a path between node 6 and node 28?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "975"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,6) (0,1) (0,7) (0,4) (1,5) (1,6) (1,7) (1,4) (2,3) (4,5) (4,6) (4,7) (5,6) (5,7) (6,7)\nQ: Is there a path between node 5 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "976"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,10) (0,13) (0,12) (0,9) (0,18) (0,24) (0,5) (0,20) (0,21) (0,7) (0,3) (0,23) (1,2) (1,13) (1,16) (1,12) (1,18) (1,24) (1,20) (1,4) (1,7) (1,3) (1,19) (1,23) (2,13) (2,16) (2,12) (2,9) (2,11) (2,18) (2,24) (2,5) (2,20) (2,4) (2,21) (2,7) (2,3) (2,23) (3,13) (3,16) (3,12) (3,9) (3,11) (3,24) (3,5) (3,20) (3,21) (3,7) (3,19) (3,23) (4,10) (4,16) (4,12) (4,11) (4,18) (4,24) (4,5) (4,20) (4,21) (4,7) (4,19) (4,23) (5,13) (5,12) (5,11) (5,18) (5,24) (5,20) (5,21) (5,7) (5,23) (6,15) (6,25) (6,22) (6,8) (7,13) (7,12) (7,9) (7,11) (7,18) (7,20) (7,21) (7,19) (8,17) (8,15) (8,22) (8,14) (9,10) (9,13) (9,16) (9,11) (9,18) (9,21) (9,19) (9,23) (10,13) (10,12) (10,11) (10,24) (10,20) (10,21) (10,19) (10,23) (11,13) (11,16) (11,24) (11,20) (11,21) (11,19) (11,23) (12,13) (12,16) (12,18) (12,24) (12,20) (12,21) (12,19) (12,23) (13,16) (13,24) (13,21) (13,23) (14,17) (14,15) (14,22) (15,17) (15,25) (15,22) (16,18) (16,24) (16,21) (16,23) (17,25) (17,22) (18,20) (18,21) (18,19) (18,23) (19,20) (19,23) (20,24) (20,21) (21,23) (22,25) (23,24)\nQ: Is there a path between node 13 and node 22?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "977"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (2,3) (2,5) (3,5) (4,6)\nQ: Is there a path between node 5 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "978"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,15) (0,6) (0,17) (0,4) (0,12) (0,16) (0,9) (1,14) (1,23) (1,18) (1,19) (1,3) (1,21) (2,14) (2,5) (2,11) (2,23) (2,22) (2,8) (2,18) (2,19) (2,3) (2,20) (3,14) (3,5) (3,23) (3,22) (3,8) (3,18) (3,19) (3,20) (3,21) (4,7) (4,15) (4,6) (4,17) (4,13) (4,10) (4,16) (5,14) (5,8) (5,18) (5,19) (5,21) (6,13) (6,10) (6,16) (6,9) (7,15) (7,13) (7,9) (8,14) (8,11) (8,23) (8,22) (8,18) (8,19) (8,20) (8,21) (9,15) (9,13) (9,12) (9,16) (10,15) (10,17) (10,13) (10,12) (11,14) (11,23) (11,22) (11,18) (11,19) (12,17) (12,16) (13,17) (13,16) (14,23) (14,19) (15,17) (16,17) (18,23) (18,22) (18,19) (18,21) (19,23) (19,22) (19,20) (20,23) (20,21) (21,23) (22,23)\nQ: Is there a path between node 20 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "979"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,7) (0,2) (0,8) (1,6) (2,3) (3,6) (3,7) (4,6) (4,5) (5,8) (7,8)\nQ: Is there a path between node 9 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "980"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,10) (0,15) (0,21) (0,1) (0,7) (0,29) (0,24) (0,16) (0,23) (0,17) (1,26) (1,10) (1,15) (1,7) (1,28) (1,29) (1,12) (1,24) (1,16) (1,3) (1,23) (2,14) (2,27) (2,34) (3,26) (3,32) (3,15) (3,21) (3,7) (3,28) (3,29) (3,12) (3,24) (3,23) (3,17) (4,9) (4,14) (4,27) (4,31) (5,19) (5,22) (5,13) (5,20) (5,25) (5,30) (5,8) (5,33) (6,9) (6,27) (6,34) (6,31) (7,26) (7,32) (7,10) (7,15) (7,21) (7,29) (7,12) (7,24) (7,16) (7,23) (7,17) (8,19) (8,22) (8,13) (8,20) (8,25) (8,18) (8,30) (8,33) (9,14) (9,34) (10,32) (10,15) (10,21) (10,29) (10,24) (10,23) (10,17) (11,19) (11,22) (11,13) (11,25) (11,18) (11,30) (12,26) (12,32) (12,15) (12,21) (12,24) (12,16) (12,23) (13,19) (13,20) (13,25) (13,18) (13,33) (14,27) (14,31) (15,26) (15,21) (15,28) (15,24) (15,16) (15,23) (15,17) (16,26) (16,32) (16,23) (16,17) (17,26) (17,32) (17,21) (17,28) (17,24) (18,19) (18,22) (18,20) (18,30) (19,22) (19,20) (19,25) (19,30) (20,25) (20,30) (20,33) (21,26) (21,32) (21,28) (21,29) (22,25) (22,30) (22,33) (23,32) (23,28) (23,29) (23,24) (24,32) (24,28) (25,30) (25,33) (26,32) (26,28) (27,31) (28,29) (30,33)\nQ: Is there a path between node 31 and node 34?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "981"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,14) (0,5) (0,9) (0,8) (0,6) (0,21) (1,4) (1,15) (1,18) (1,11) (1,10) (1,12) (2,20) (2,14) (2,5) (2,9) (2,22) (2,6) (2,16) (3,9) (3,23) (3,22) (3,6) (3,21) (4,15) (4,11) (4,19) (4,13) (5,20) (5,14) (5,9) (5,8) (5,6) (5,21) (6,20) (6,14) (6,9) (6,23) (6,8) (6,16) (7,18) (7,11) (7,10) (7,12) (7,19) (7,13) (8,20) (8,14) (8,23) (8,21) (9,20) (9,23) (9,22) (9,21) (10,15) (10,18) (10,11) (10,12) (10,19) (10,13) (11,15) (11,13) (12,18) (12,19) (13,18) (13,19) (14,23) (14,22) (14,21) (15,19) (16,23) (16,22) (20,21) (22,23)\nQ: Is there a path between node 10 and node 18?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "982"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,7) (0,6) (0,8) (0,4) (0,1) (1,2) (1,7) (1,6) (1,8) (1,4) (2,7) (2,6) (2,8) (2,4) (3,5) (4,7) (4,6) (4,8) (6,7) (6,8) (7,8)\nQ: Is there a path between node 1 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "983"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,5) (3,5)\nQ: Is there a path between node 1 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "984"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (1,24) (1,13) (1,7) (2,24) (2,15) (2,18) (2,8) (2,13) (2,7) (3,23) (3,6) (5,20) (5,14) (6,11) (6,23) (7,12) (7,10) (7,21) (7,8) (7,13) (8,10) (8,15) (8,18) (8,22) (8,13) (9,21) (9,13) (10,12) (10,15) (10,13) (12,24) (13,24) (13,22) (14,20) (15,24) (17,24) (19,20) (21,24)\nQ: Is there a path between node 24 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "985"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,5) (0,11) (0,8) (0,6) (0,1) (1,10) (1,3) (1,5) (1,9) (1,6) (1,2) (2,10) (2,3) (2,5) (2,9) (2,8) (2,7) (2,6) (2,13) (3,9) (3,11) (3,8) (3,7) (4,12) (5,10) (5,9) (5,8) (5,7) (5,6) (6,10) (6,9) (6,11) (6,8) (7,10) (7,11) (7,8) (7,13) (8,10) (8,11) (8,13) (9,10) (9,11) (9,13) (10,11) (10,13)\nQ: Is there a path between node 12 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "986"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,1) (0,13) (0,15) (0,16) (0,9) (0,14) (0,3) (0,12) (0,17) (0,2) (0,18) (1,11) (1,13) (1,15) (1,16) (1,9) (1,8) (1,14) (1,3) (1,4) (1,17) (1,18) (2,11) (2,13) (2,15) (2,9) (2,8) (2,14) (2,3) (2,12) (2,17) (2,18) (3,11) (3,13) (3,15) (3,16) (3,9) (3,8) (3,14) (3,12) (3,17) (3,18) (4,13) (4,15) (4,16) (4,8) (4,14) (4,12) (4,18) (5,6) (5,7) (5,10) (6,7) (6,10) (7,10) (8,11) (8,15) (8,16) (8,18) (9,11) (9,13) (9,15) (9,16) (9,14) (9,12) (9,17) (9,18) (11,13) (11,16) (11,17) (11,18) (12,15) (12,16) (12,17) (12,18) (13,15) (13,18) (14,15) (14,17) (15,16) (16,17) (16,18) (17,18)\nQ: Is there a path between node 13 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "987"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,10) (0,2) (2,15) (2,20) (2,23) (2,14) (2,17) (2,24) (2,18) (3,21) (4,27) (5,9) (5,22) (6,29) (6,8) (7,29) (7,25) (7,20) (7,17) (7,18) (7,8) (8,23) (8,24) (10,23) (10,18) (11,27) (12,13) (13,21) (14,25) (14,23) (14,17) (14,24) (15,29) (15,25) (15,23) (15,16) (16,29) (16,17) (17,25) (17,23) (17,24) (17,18) (18,29) (20,25) (22,26) (23,25) (24,29) (26,27)\nQ: Is there a path between node 7 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "988"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,1) (0,15) (0,6) (0,9) (0,4) (0,16) (0,19) (1,20) (1,15) (1,6) (1,9) (1,4) (1,16) (1,19) (2,14) (2,10) (2,3) (2,11) (2,7) (2,18) (2,5) (2,12) (2,17) (2,8) (3,14) (3,10) (3,11) (3,7) (3,18) (3,5) (3,12) (3,17) (3,8) (4,20) (4,15) (4,6) (4,9) (4,16) (4,19) (5,14) (5,10) (5,11) (5,7) (5,18) (5,12) (5,17) (5,8) (6,20) (6,15) (6,9) (6,16) (6,19) (7,14) (7,10) (7,11) (7,18) (7,12) (7,17) (7,8) (8,14) (8,10) (8,11) (8,18) (8,12) (8,17) (9,20) (9,15) (9,16) (9,19) (10,14) (10,11) (10,18) (10,12) (10,17) (11,14) (11,18) (11,12) (11,17) (12,14) (12,18) (12,17) (14,18) (14,17) (15,20) (15,16) (15,19) (16,20) (16,19) (17,18) (19,20)\nQ: Is there a path between node 4 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "989"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,4) (0,15) (0,19) (0,8) (0,17) (0,13) (0,3) (0,14) (0,5) (0,2) (0,16) (0,1) (0,10) (1,20) (1,4) (1,15) (1,19) (1,8) (1,17) (1,13) (1,3) (1,14) (1,5) (1,2) (1,16) (1,10) (2,20) (2,4) (2,15) (2,19) (2,8) (2,17) (2,13) (2,3) (2,14) (2,5) (2,16) (2,10) (3,20) (3,4) (3,15) (3,19) (3,8) (3,17) (3,13) (3,14) (3,5) (3,16) (3,10) (4,20) (4,15) (4,19) (4,8) (4,17) (4,13) (4,14) (4,5) (4,16) (4,10) (5,20) (5,15) (5,19) (5,8) (5,17) (5,13) (5,14) (5,16) (5,10) (6,12) (6,22) (6,9) (6,18) (6,21) (6,7) (6,11) (7,12) (7,22) (7,9) (7,18) (7,21) (7,11) (8,20) (8,15) (8,19) (8,17) (8,13) (8,14) (8,16) (8,10) (9,12) (9,22) (9,18) (9,21) (9,11) (10,20) (10,15) (10,19) (10,17) (10,13) (10,14) (10,16) (11,12) (11,22) (11,18) (11,21) (12,22) (12,18) (12,21) (13,20) (13,15) (13,19) (13,17) (13,14) (13,16) (14,20) (14,15) (14,19) (14,17) (14,16) (15,20) (15,19) (15,17) (15,16) (16,20) (16,19) (16,17) (17,20) (17,19) (18,22) (18,21) (19,20) (21,22)\nQ: Is there a path between node 2 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "990"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,9) (0,14) (0,18) (0,3) (0,1) (0,17) (0,4) (0,8) (0,7) (0,15) (0,11) (0,10) (0,13) (1,5) (1,9) (1,14) (1,18) (1,3) (1,17) (1,4) (1,8) (1,7) (1,15) (1,11) (1,10) (1,13) (3,5) (3,9) (3,14) (3,18) (3,17) (3,4) (3,8) (3,7) (3,15) (3,11) (3,10) (3,13) (4,5) (4,9) (4,14) (4,18) (4,17) (4,8) (4,7) (4,15) (4,11) (4,10) (4,13) (5,9) (5,14) (5,18) (5,17) (5,8) (5,7) (5,15) (5,11) (5,10) (5,13) (6,12) (6,16) (7,9) (7,14) (7,18) (7,17) (7,8) (7,15) (7,11) (7,10) (7,13) (8,9) (8,14) (8,18) (8,17) (8,15) (8,11) (8,10) (8,13) (9,14) (9,18) (9,17) (9,15) (9,11) (9,10) (9,13) (10,14) (10,18) (10,17) (10,15) (10,11) (10,13) (11,14) (11,18) (11,17) (11,15) (11,13) (12,16) (13,14) (13,18) (13,17) (13,15) (14,18) (14,17) (14,15) (15,18) (15,17) (17,18)\nQ: Is there a path between node 9 and node 18?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "991"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,17) (0,24) (1,11) (1,9) (1,3) (2,19) (2,29) (2,27) (3,7) (3,20) (4,23) (4,25) (5,17) (6,22) (7,29) (7,27) (7,9) (8,16) (8,30) (8,26) (8,18) (8,31) (9,11) (9,27) (10,13) (10,12) (11,19) (11,27) (12,26) (12,18) (14,28) (15,27) (16,30) (17,23) (18,26) (19,28) (20,29) (21,22) (23,24) (24,25) (27,28) (30,31)\nQ: Is there a path between node 20 and node 28?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "992"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,13) (0,19) (0,11) (0,16) (0,20) (0,8) (0,5) (0,3) (0,2) (0,7) (0,6) (0,17) (0,14) (0,12) (0,1) (0,18) (0,10) (0,23) (0,9) (1,4) (1,13) (1,19) (1,11) (1,16) (1,20) (1,8) (1,5) (1,3) (1,2) (1,7) (1,6) (1,17) (1,14) (1,12) (1,18) (1,10) (1,23) (1,9) (2,4) (2,13) (2,19) (2,11) (2,16) (2,20) (2,8) (2,5) (2,3) (2,7) (2,6) (2,17) (2,14) (2,12) (2,18) (2,10) (2,23) (2,9) (3,4) (3,13) (3,19) (3,11) (3,16) (3,20) (3,8) (3,5) (3,7) (3,6) (3,17) (3,14) (3,12) (3,18) (3,10) (3,23) (3,9) (4,13) (4,19) (4,11) (4,16) (4,20) (4,8) (4,5) (4,7) (4,6) (4,17) (4,14) (4,12) (4,18) (4,10) (4,23) (4,9) (5,13) (5,19) (5,11) (5,16) (5,20) (5,8) (5,7) (5,6) (5,17) (5,14) (5,12) (5,18) (5,10) (5,23) (5,9) (6,13) (6,19) (6,11) (6,16) (6,20) (6,8) (6,7) (6,17) (6,14) (6,12) (6,18) (6,10) (6,23) (6,9) (7,13) (7,19) (7,11) (7,16) (7,20) (7,8) (7,17) (7,14) (7,12) (7,18) (7,10) (7,23) (7,9) (8,13) (8,19) (8,11) (8,16) (8,20) (8,17) (8,14) (8,12) (8,18) (8,10) (8,23) (8,9) (9,13) (9,19) (9,11) (9,16) (9,20) (9,17) (9,14) (9,12) (9,18) (9,10) (9,23) (10,13) (10,19) (10,11) (10,16) (10,20) (10,17) (10,14) (10,12) (10,18) (10,23) (11,13) (11,19) (11,16) (11,20) (11,17) (11,14) (11,12) (11,18) (11,23) (12,13) (12,19) (12,16) (12,20) (12,17) (12,14) (12,18) (12,23) (13,19) (13,16) (13,20) (13,17) (13,14) (13,18) (13,23) (14,19) (14,16) (14,20) (14,17) (14,18) (14,23) (15,21) (15,22) (16,19) (16,20) (16,17) (16,18) (16,23) (17,19) (17,20) (17,18) (17,23) (18,19) (18,20) (18,23) (19,20) (19,23) (20,23) (21,22)\nQ: Is there a path between node 18 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "993"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,17) (0,10) (0,28) (0,30) (0,29) (0,3) (1,14) (1,2) (2,25) (2,20) (2,7) (2,32) (2,22) (3,24) (3,19) (3,23) (3,4) (3,12) (3,29) (4,26) (4,24) (4,23) (4,8) (4,13) (5,26) (5,19) (5,23) (5,8) (5,15) (5,21) (6,14) (7,32) (8,16) (8,12) (8,29) (9,26) (9,13) (9,18) (9,29) (9,31) (10,17) (10,11) (10,30) (10,23) (10,13) (11,16) (11,17) (11,19) (11,28) (11,23) (12,26) (12,24) (12,21) (13,26) (13,17) (13,19) (13,30) (13,31) (14,25) (14,22) (15,16) (15,17) (15,23) (15,18) (15,29) (16,26) (16,24) (16,18) (16,21) (17,24) (17,19) (17,28) (17,30) (17,23) (18,24) (18,21) (19,26) (19,24) (19,28) (19,23) (20,32) (22,32) (22,27) (24,26) (24,30) (26,29) (28,29)\nQ: Is there a path between node 8 and node 18?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "994"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,10) (0,13) (0,12) (0,9) (0,18) (0,24) (0,5) (0,20) (0,21) (0,7) (0,3) (0,23) (1,2) (1,13) (1,16) (1,12) (1,18) (1,24) (1,20) (1,4) (1,7) (1,3) (1,19) (1,23) (2,13) (2,16) (2,12) (2,9) (2,11) (2,18) (2,24) (2,5) (2,20) (2,4) (2,21) (2,7) (2,3) (2,23) (3,13) (3,16) (3,12) (3,9) (3,11) (3,24) (3,5) (3,20) (3,21) (3,7) (3,19) (3,23) (4,10) (4,16) (4,12) (4,11) (4,18) (4,24) (4,5) (4,20) (4,21) (4,7) (4,19) (4,23) (5,13) (5,12) (5,11) (5,18) (5,24) (5,20) (5,21) (5,7) (5,23) (6,15) (6,25) (6,22) (6,8) (7,13) (7,12) (7,9) (7,11) (7,18) (7,20) (7,21) (7,19) (8,17) (8,15) (8,22) (8,14) (9,10) (9,13) (9,16) (9,11) (9,18) (9,21) (9,19) (9,23) (10,13) (10,12) (10,11) (10,24) (10,20) (10,21) (10,19) (10,23) (11,13) (11,16) (11,24) (11,20) (11,21) (11,19) (11,23) (12,13) (12,16) (12,18) (12,24) (12,20) (12,21) (12,19) (12,23) (13,16) (13,24) (13,21) (13,23) (14,17) (14,15) (14,22) (15,17) (15,25) (15,22) (16,18) (16,24) (16,21) (16,23) (17,25) (17,22) (18,20) (18,21) (18,19) (18,23) (19,20) (19,23) (20,24) (20,21) (21,23) (22,25) (23,24)\nQ: Is there a path between node 10 and node 23?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "995"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,5) (0,1) (0,9) (0,3) (0,4) (1,6) (1,5) (1,9) (1,3) (1,4) (2,7) (2,8) (2,10) (3,6) (3,5) (3,9) (3,4) (4,6) (4,5) (4,9) (5,6) (5,9) (6,9) (7,8) (7,10) (8,10)\nQ: Is there a path between node 0 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "996"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,21) (0,8) (0,11) (0,16) (0,13) (0,10) (0,20) (0,6) (0,4) (1,14) (1,17) (1,18) (1,5) (1,19) (1,2) (2,22) (2,14) (2,5) (3,8) (3,11) (3,10) (3,12) (3,6) (4,11) (4,13) (4,20) (4,12) (5,22) (5,14) (5,17) (5,18) (5,9) (5,19) (6,8) (6,11) (6,16) (6,13) (6,10) (6,20) (6,12) (7,15) (8,11) (8,13) (8,10) (8,20) (8,12) (9,22) (9,14) (9,17) (9,18) (9,19) (10,21) (10,13) (11,16) (11,13) (11,20) (11,12) (12,21) (12,16) (12,13) (12,20) (13,21) (13,16) (13,20) (14,22) (14,18) (16,21) (16,20) (17,22) (17,18) (17,19) (18,19) (20,21)\nQ: Is there a path between node 0 and node 21?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "997"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (3,8) (3,9) (4,5) (8,9)\nQ: Is there a path between node 9 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "998"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,9) (0,13) (0,3) (0,1) (0,2) (0,7) (0,8) (0,11) (1,14) (1,13) (1,8) (1,10) (1,11) (1,5) (2,9) (2,13) (2,3) (2,7) (2,8) (2,10) (3,14) (3,9) (3,13) (3,8) (3,11) (3,5) (4,6) (4,12) (5,14) (5,9) (5,7) (5,8) (5,10) (5,11) (6,12) (7,14) (7,13) (7,8) (7,10) (8,14) (8,9) (8,10) (9,14) (9,13) (10,14) (10,13) (11,14) (13,14)\nQ: Is there a path between node 11 and node 13?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "999"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,6) (0,11) (0,19) (0,20) (0,1) (0,15) (0,12) (0,7) (0,22) (0,5) (0,21) (0,3) (0,4) (0,18) (0,17) (1,14) (1,6) (1,11) (1,19) (1,20) (1,15) (1,12) (1,7) (1,22) (1,5) (1,21) (1,3) (1,4) (1,18) (1,17) (2,13) (2,10) (2,8) (2,16) (2,9) (3,14) (3,6) (3,11) (3,19) (3,20) (3,15) (3,12) (3,7) (3,22) (3,5) (3,21) (3,4) (3,18) (3,17) (4,14) (4,6) (4,11) (4,19) (4,20) (4,15) (4,12) (4,7) (4,22) (4,5) (4,21) (4,18) (4,17) (5,14) (5,6) (5,11) (5,19) (5,20) (5,15) (5,12) (5,7) (5,22) (5,21) (5,18) (5,17) (6,14) (6,11) (6,19) (6,20) (6,15) (6,12) (6,7) (6,22) (6,21) (6,18) (6,17) (7,14) (7,11) (7,19) (7,20) (7,15) (7,12) (7,22) (7,21) (7,18) (7,17) (8,13) (8,10) (8,16) (8,9) (9,13) (9,10) (9,16) (10,13) (10,16) (11,14) (11,19) (11,20) (11,15) (11,12) (11,22) (11,21) (11,18) (11,17) (12,14) (12,19) (12,20) (12,15) (12,22) (12,21) (12,18) (12,17) (13,16) (14,19) (14,20) (14,15) (14,22) (14,21) (14,18) (14,17) (15,19) (15,20) (15,22) (15,21) (15,18) (15,17) (17,19) (17,20) (17,22) (17,21) (17,18) (18,19) (18,20) (18,22) (18,21) (19,20) (19,22) (19,21) (20,22) (20,21) (21,22)\nQ: Is there a path between node 18 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1000"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,22) (0,6) (0,11) (0,10) (0,4) (0,5) (0,9) (0,1) (0,13) (0,21) (0,20) (0,12) (1,22) (1,11) (1,10) (1,5) (1,16) (1,9) (1,13) (1,21) (1,20) (2,8) (2,19) (2,3) (2,18) (2,24) (3,19) (3,17) (3,24) (3,23) (4,22) (4,6) (4,16) (4,9) (4,21) (4,20) (5,22) (5,6) (5,14) (5,11) (5,16) (5,15) (5,9) (5,13) (5,21) (5,20) (6,22) (6,11) (6,10) (6,16) (6,13) (6,21) (6,12) (7,8) (7,17) (7,18) (7,24) (7,23) (8,17) (8,24) (9,14) (9,11) (9,10) (9,16) (9,15) (9,21) (9,20) (9,12) (10,22) (10,14) (10,11) (10,16) (10,15) (10,21) (10,20) (11,22) (11,16) (11,15) (11,20) (12,22) (12,14) (12,15) (12,13) (12,21) (12,20) (13,14) (13,16) (13,15) (13,21) (13,20) (14,22) (14,16) (14,15) (14,21) (15,16) (15,21) (16,22) (16,21) (16,20) (17,19) (17,18) (17,24) (17,23) (18,23) (19,24) (23,24)\nQ: Is there a path between node 2 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1001"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,6) (1,2) (3,7) (3,5)\nQ: Is there a path between node 2 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1002"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,3) (0,12) (0,6) (0,11) (1,16) (1,3) (1,12) (1,6) (1,11) (1,14) (1,10) (2,15) (2,7) (2,13) (2,5) (2,9) (2,4) (2,18) (3,17) (3,12) (3,11) (3,14) (4,15) (4,7) (4,5) (4,9) (4,8) (5,15) (5,13) (5,9) (5,8) (5,18) (6,16) (6,17) (6,12) (6,14) (6,10) (7,15) (7,13) (7,9) (7,18) (8,15) (8,9) (8,18) (9,13) (9,18) (10,16) (10,17) (10,12) (10,11) (11,16) (11,17) (11,12) (12,16) (12,17) (12,14) (13,15) (13,18) (14,16) (14,17) (15,18) (16,17)\nQ: Is there a path between node 12 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1003"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,18) (1,12) (1,15) (1,7) (2,17) (2,3) (3,17) (4,12) (5,17) (5,19) (6,18) (6,10) (6,9) (6,12) (6,16) (7,18) (7,9) (7,13) (7,8) (8,14) (9,18) (9,14) (9,12) (9,13) (10,12) (10,15) (11,17) (12,16) (14,18)\nQ: Is there a path between node 9 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1004"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,10) (0,19) (0,16) (0,7) (0,8) (0,4) (0,3) (0,11) (0,1) (0,18) (0,9) (0,5) (0,2) (0,13) (1,17) (1,10) (1,19) (1,16) (1,7) (1,8) (1,4) (1,3) (1,11) (1,18) (1,9) (1,5) (1,2) (1,13) (2,17) (2,10) (2,19) (2,16) (2,7) (2,8) (2,4) (2,3) (2,11) (2,18) (2,9) (2,5) (2,13) (3,17) (3,10) (3,19) (3,16) (3,7) (3,8) (3,4) (3,11) (3,18) (3,9) (3,5) (3,13) (4,17) (4,10) (4,19) (4,16) (4,7) (4,8) (4,11) (4,18) (4,9) (4,5) (4,13) (5,17) (5,10) (5,19) (5,16) (5,7) (5,8) (5,11) (5,18) (5,9) (5,13) (6,15) (7,17) (7,10) (7,19) (7,16) (7,8) (7,11) (7,18) (7,9) (7,13) (8,17) (8,10) (8,19) (8,16) (8,11) (8,18) (8,9) (8,13) (9,17) (9,10) (9,19) (9,16) (9,11) (9,18) (9,13) (10,17) (10,19) (10,16) (10,11) (10,18) (10,13) (11,17) (11,19) (11,16) (11,18) (11,13) (12,14) (13,17) (13,19) (13,16) (13,18) (16,17) (16,19) (16,18) (17,19) (17,18) (18,19)\nQ: Is there a path between node 16 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1005"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,1) (0,13) (0,15) (0,16) (0,9) (0,14) (0,3) (0,12) (0,17) (0,2) (0,18) (1,11) (1,13) (1,15) (1,16) (1,9) (1,8) (1,14) (1,3) (1,4) (1,17) (1,18) (2,11) (2,13) (2,15) (2,9) (2,8) (2,14) (2,3) (2,12) (2,17) (2,18) (3,11) (3,13) (3,15) (3,16) (3,9) (3,8) (3,14) (3,12) (3,17) (3,18) (4,13) (4,15) (4,16) (4,8) (4,14) (4,12) (4,18) (5,6) (5,7) (5,10) (6,7) (6,10) (7,10) (8,11) (8,15) (8,16) (8,18) (9,11) (9,13) (9,15) (9,16) (9,14) (9,12) (9,17) (9,18) (11,13) (11,16) (11,17) (11,18) (12,15) (12,16) (12,17) (12,18) (13,15) (13,18) (14,15) (14,17) (15,16) (16,17) (16,18) (17,18)\nQ: Is there a path between node 10 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1006"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,11) (0,6) (1,5) (1,8) (1,10) (1,15) (1,17) (1,13) (1,16) (2,5) (2,4) (2,8) (2,10) (2,14) (2,17) (2,13) (2,16) (3,9) (3,6) (3,12) (4,8) (4,15) (4,14) (4,17) (4,13) (5,8) (5,15) (5,17) (6,7) (6,9) (7,11) (7,9) (8,15) (8,17) (8,13) (8,16) (9,11) (10,15) (10,14) (10,17) (11,12) (13,15) (13,14) (13,16) (14,15) (14,17) (14,16) (15,17) (15,16) (16,17)\nQ: Is there a path between node 17 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1007"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,27) (0,13) (0,10) (0,15) (0,2) (0,17) (1,5) (1,22) (1,8) (1,19) (1,26) (1,24) (1,18) (1,16) (1,14) (1,12) (1,4) (1,9) (2,7) (2,27) (2,13) (2,3) (2,6) (2,10) (2,11) (2,17) (3,7) (3,27) (3,20) (3,6) (3,10) (3,15) (3,21) (3,17) (4,5) (4,8) (4,19) (4,26) (4,25) (4,18) (4,14) (4,12) (5,8) (5,26) (5,18) (5,16) (5,14) (5,12) (6,7) (6,13) (6,10) (6,21) (7,20) (7,13) (7,10) (7,15) (7,11) (8,19) (8,26) (8,18) (8,16) (8,14) (8,9) (9,22) (9,19) (9,26) (9,25) (9,16) (9,14) (9,12) (10,13) (10,21) (10,17) (11,27) (11,13) (11,15) (11,21) (11,17) (12,22) (12,19) (12,26) (12,24) (12,25) (12,16) (12,14) (13,27) (13,15) (14,22) (14,19) (14,26) (15,27) (15,20) (15,21) (15,17) (16,22) (16,19) (16,24) (16,25) (16,18) (17,27) (17,20) (17,21) (18,22) (18,19) (18,26) (18,24) (19,26) (19,25) (20,27) (20,21) (21,27) (22,26) (22,24) (24,26)\nQ: Is there a path between node 14 and node 20?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1008"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,2) (0,8) (0,4) (0,7) (0,3) (0,1) (1,5) (1,2) (1,8) (1,4) (1,7) (1,3) (2,5) (2,8) (2,4) (2,7) (2,3) (3,5) (3,8) (3,4) (3,7) (4,5) (4,8) (4,7) (5,8) (5,7) (6,9) (7,8)\nQ: Is there a path between node 8 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1009"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (2,8) (2,4) (2,3) (3,8) (5,7) (6,7)\nQ: Is there a path between node 0 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1010"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,4) (1,2) (3,4)\nQ: Is there a path between node 1 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1011"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,12) (1,25) (1,2) (1,10) (1,12) (1,3) (2,8) (2,22) (2,25) (2,26) (2,19) (2,11) (2,12) (2,7) (2,21) (3,25) (3,26) (3,10) (3,27) (3,21) (5,24) (5,6) (6,23) (6,9) (7,22) (7,25) (7,11) (8,20) (8,22) (8,25) (8,26) (8,27) (9,24) (10,14) (10,25) (10,13) (10,27) (10,21) (11,22) (11,12) (11,17) (11,21) (12,19) (12,18) (12,17) (12,27) (12,21) (13,17) (13,21) (14,17) (14,21) (15,23) (15,24) (16,22) (17,22) (17,25) (17,19) (18,20) (18,26) (18,21) (19,22) (19,26) (19,27) (20,27) (22,25) (25,26)\nQ: Is there a path between node 26 and node 22?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1012"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,13) (0,1) (0,9) (0,5) (0,7) (0,3) (0,10) (0,23) (0,26) (0,27) (0,8) (0,14) (0,22) (0,20) (0,15) (0,4) (0,2) (1,25) (1,11) (1,21) (1,13) (1,9) (1,3) (1,10) (1,23) (1,26) (1,27) (1,14) (1,20) (1,15) (1,2) (1,28) (2,25) (2,11) (2,16) (2,21) (2,6) (2,13) (2,9) (2,7) (2,23) (2,26) (2,8) (2,20) (2,15) (3,25) (3,6) (3,13) (3,9) (3,10) (3,27) (3,20) (3,15) (3,4) (3,28) (4,11) (4,16) (4,6) (4,13) (4,10) (4,23) (4,26) (4,27) (4,8) (4,14) (4,22) (4,15) (4,28) (5,25) (5,16) (5,21) (5,6) (5,13) (5,9) (5,7) (5,26) (5,8) (5,22) (5,15) (5,28) (6,11) (6,16) (6,21) (6,13) (6,9) (6,7) (6,10) (6,27) (6,22) (6,20) (6,15) (7,25) (7,16) (7,21) (7,9) (7,10) (7,27) (7,8) (7,14) (7,22) (7,20) (7,15) (7,28) (8,25) (8,13) (8,23) (8,26) (8,27) (8,14) (8,20) (8,28) (9,25) (9,11) (9,16) (9,21) (9,10) (9,23) (9,26) (9,27) (9,22) (9,20) (9,28) (10,11) (10,16) (10,21) (10,13) (10,23) (10,26) (10,27) (10,14) (10,22) (10,20) (10,15) (10,28) (11,25) (11,16) (11,21) (11,13) (11,23) (11,26) (11,27) (11,14) (11,22) (11,20) (12,24) (12,19) (13,25) (13,16) (13,14) (13,22) (13,15) (13,28) (14,25) (14,21) (14,23) (14,26) (14,20) (14,15) (15,16) (15,21) (15,26) (15,27) (15,22) (15,28) (16,21) (16,23) (16,26) (16,27) (16,28) (17,18) (20,25) (20,23) (20,26) (20,27) (20,22) (20,28) (21,25) (21,23) (21,26) (21,22) (22,25) (22,23) (22,27) (23,25) (23,26) (23,27) (23,28) (25,26) (25,27) (26,27) (27,28)\nQ: Is there a path between node 3 and node 16?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1013"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,6) (1,2) (3,7) (3,5)\nQ: Is there a path between node 6 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1014"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (0,11) (0,8) (0,17) (0,13) (0,6) (0,3) (0,15) (0,7) (1,14) (1,19) (1,9) (1,21) (1,12) (1,22) (1,4) (1,18) (1,5) (1,10) (1,20) (2,16) (3,23) (3,11) (3,8) (3,17) (3,13) (3,6) (3,15) (3,7) (4,14) (4,19) (4,9) (4,21) (4,12) (4,22) (4,18) (4,5) (4,10) (4,20) (5,14) (5,19) (5,9) (5,21) (5,12) (5,22) (5,18) (5,10) (5,20) (6,23) (6,11) (6,8) (6,17) (6,13) (6,15) (6,7) (7,23) (7,11) (7,8) (7,17) (7,13) (7,15) (8,23) (8,11) (8,17) (8,13) (8,15) (9,14) (9,19) (9,21) (9,12) (9,22) (9,18) (9,10) (9,20) (10,14) (10,19) (10,21) (10,12) (10,22) (10,18) (10,20) (11,23) (11,17) (11,13) (11,15) (12,14) (12,19) (12,21) (12,22) (12,18) (12,20) (13,23) (13,17) (13,15) (14,19) (14,21) (14,22) (14,18) (14,20) (15,23) (15,17) (17,23) (18,19) (18,21) (18,22) (18,20) (19,21) (19,22) (19,20) (20,21) (20,22) (21,22)\nQ: Is there a path between node 22 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1015"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,18) (1,12) (1,15) (1,7) (2,17) (2,3) (3,17) (4,12) (5,17) (5,19) (6,18) (6,10) (6,9) (6,12) (6,16) (7,18) (7,9) (7,13) (7,8) (8,14) (9,18) (9,14) (9,12) (9,13) (10,12) (10,15) (11,17) (12,16) (14,18)\nQ: Is there a path between node 12 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1016"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (1,2)\nQ: Is there a path between node 2 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1017"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,6) (0,21) (0,18) (1,24) (1,3) (3,24) (3,14) (4,6) (4,5) (4,23) (6,14) (6,21) (6,23) (7,11) (8,19) (8,13) (9,15) (9,19) (10,11) (10,12) (10,16) (10,17) (11,12) (11,16) (12,17) (13,15) (13,22) (14,23) (15,22) (16,17) (18,24) (18,21)\nQ: Is there a path between node 12 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1018"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,19) (1,11) (2,4) (2,13) (3,17) (3,10) (3,11) (5,8) (5,13) (6,10) (6,12) (7,18) (7,9) (10,17) (10,12) (11,12) (12,17) (13,16) (13,15) (14,18)\nQ: Is there a path between node 12 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1019"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,11) (0,13) (0,3) (0,15) (0,4) (0,2) (1,7) (1,8) (2,14) (2,23) (2,21) (2,6) (2,10) (3,9) (3,17) (3,13) (3,5) (3,19) (3,4) (3,16) (3,10) (4,9) (4,22) (4,6) (5,11) (5,18) (5,23) (6,9) (6,14) (6,17) (6,20) (6,15) (6,21) (7,8) (9,17) (9,15) (9,21) (10,18) (10,12) (10,16) (11,17) (11,15) (11,22) (11,16) (12,15) (12,22) (13,23) (13,16) (14,17) (14,18) (14,20) (14,21) (14,22) (14,16) (15,20) (17,20) (17,19) (17,23) (18,19) (18,23) (19,20) (19,23) (21,23) (21,22)\nQ: Is there a path between node 20 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1020"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,3) (0,14) (1,8) (1,6) (1,14) (2,6) (2,12) (2,18) (3,8) (3,6) (3,12) (3,18) (4,12) (4,9) (4,14) (5,15) (5,16) (5,7) (6,8) (6,12) (6,14) (7,10) (9,11) (9,18) (15,17) (15,16)\nQ: Is there a path between node 15 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1021"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,10) (0,26) (0,13) (0,23) (0,14) (0,27) (0,30) (0,31) (0,28) (0,2) (0,8) (0,12) (0,9) (0,24) (0,5) (1,19) (1,15) (1,6) (1,11) (1,29) (1,17) (1,21) (1,4) (1,25) (1,7) (2,3) (2,14) (2,31) (2,28) (2,18) (2,8) (2,12) (2,9) (2,24) (2,5) (3,10) (3,13) (3,23) (3,27) (3,30) (3,31) (3,28) (3,18) (3,8) (3,12) (3,9) (3,24) (3,5) (4,20) (4,19) (4,15) (4,11) (4,29) (4,16) (4,22) (4,7) (5,10) (5,13) (5,23) (5,14) (5,27) (5,31) (5,18) (5,8) (5,12) (5,9) (6,20) (6,15) (6,11) (6,29) (6,17) (6,21) (6,16) (6,25) (6,7) (7,20) (7,15) (7,11) (7,29) (7,17) (7,21) (7,25) (8,10) (8,26) (8,13) (8,23) (8,14) (8,27) (8,30) (8,12) (8,24) (9,10) (9,26) (9,13) (9,14) (9,27) (9,30) (9,31) (9,18) (9,24) (10,26) (10,13) (10,23) (10,14) (10,27) (10,30) (10,31) (10,18) (11,20) (11,19) (11,15) (11,29) (11,17) (11,21) (11,16) (11,25) (11,22) (12,13) (12,23) (12,14) (12,27) (12,28) (13,26) (13,23) (13,14) (13,27) (13,31) (13,28) (14,23) (14,30) (14,28) (14,18) (14,24) (15,19) (15,29) (15,21) (15,16) (15,22) (16,20) (16,19) (16,29) (16,17) (16,21) (16,25) (17,20) (17,19) (17,29) (17,21) (17,25) (17,22) (18,26) (18,27) (18,30) (18,31) (18,28) (19,29) (19,21) (19,25) (19,22) (20,29) (20,22) (21,29) (21,25) (21,22) (22,25) (23,26) (23,27) (23,30) (23,31) (23,24) (24,27) (24,30) (24,31) (25,29) (26,27) (26,30) (26,28) (27,30) (27,31) (28,30) (28,31) (30,31)\nQ: Is there a path between node 24 and node 29?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1022"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,4) (0,1) (0,11) (0,9) (0,12) (1,2) (1,4) (1,11) (1,9) (1,13) (1,8) (1,12) (2,6) (2,3) (2,4) (2,11) (2,9) (2,13) (2,8) (3,6) (3,9) (3,13) (3,8) (3,12) (4,6) (4,11) (4,9) (4,13) (4,8) (4,12) (5,7) (5,10) (6,11) (6,9) (6,8) (6,12) (8,9) (8,12) (9,11) (9,12) (11,13) (12,13)\nQ: Is there a path between node 8 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1023"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,2) (0,8) (0,4) (0,7) (0,3) (0,1) (1,5) (1,2) (1,8) (1,4) (1,7) (1,3) (2,5) (2,8) (2,4) (2,7) (2,3) (3,5) (3,8) (3,4) (3,7) (4,5) (4,8) (4,7) (5,8) (5,7) (6,9) (7,8)\nQ: Is there a path between node 0 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1024"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,1) (0,6) (0,2) (0,3) (0,7) (0,5) (1,8) (1,6) (1,2) (1,3) (1,7) (1,5) (2,8) (2,6) (2,3) (2,7) (2,5) (3,8) (3,6) (3,7) (3,5) (5,8) (5,6) (5,7) (6,8) (6,7) (7,8)\nQ: Is there a path between node 1 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1025"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,10) (2,9) (2,5) (3,12) (3,14) (3,4) (3,8) (3,18) (4,19) (4,16) (4,11) (5,20) (5,12) (5,14) (5,11) (6,18) (6,16) (7,15) (8,20) (8,12) (8,18) (8,16) (9,20) (9,14) (9,19) (9,11) (11,13) (11,12) (11,18) (11,16) (12,18) (13,19) (13,18) (14,19) (16,20) (18,19)\nQ: Is there a path between node 4 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1026"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,6) (3,4) (4,5) (5,10) (6,8) (8,9)\nQ: Is there a path between node 4 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1027"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,22) (0,15) (0,8) (0,12) (0,14) (0,2) (0,9) (0,1) (1,15) (1,20) (1,12) (2,20) (2,12) (2,7) (2,16) (3,15) (3,7) (3,16) (3,13) (3,14) (3,17) (3,21) (4,22) (4,8) (4,12) (4,17) (4,11) (6,23) (7,15) (7,17) (7,11) (7,21) (7,18) (8,22) (8,15) (8,20) (8,16) (8,9) (9,22) (9,13) (9,11) (9,21) (9,18) (10,22) (10,13) (10,21) (11,22) (11,15) (11,20) (11,12) (11,21) (11,18) (12,15) (12,13) (13,20) (13,18) (14,20) (17,22) (17,18) (18,20) (19,23) (20,22) (21,22)\nQ: Is there a path between node 23 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1028"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,4) (0,1) (1,2) (1,5) (1,4) (2,5) (2,4) (4,5)\nQ: Is there a path between node 4 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1029"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,1) (1,11) (1,5) (1,8) (2,14) (2,10) (2,6) (2,3) (2,13) (2,4) (3,7) (3,14) (3,6) (3,12) (3,13) (3,4) (4,9) (4,7) (4,10) (4,12) (4,13) (5,11) (5,8) (6,7) (6,10) (6,12) (6,13) (7,9) (7,14) (7,10) (7,13) (8,11) (10,14) (10,12) (10,13) (12,14) (12,13) (13,14)\nQ: Is there a path between node 10 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1030"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,2) (0,3) (1,5) (2,4) (2,3) (3,4)\nQ: Is there a path between node 5 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1031"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,8) (0,5) (0,4) (0,25) (0,22) (0,16) (0,24) (0,21) (2,15) (2,23) (2,26) (2,10) (2,3) (2,11) (2,6) (2,27) (3,15) (3,23) (3,14) (3,26) (3,10) (3,11) (3,27) (4,8) (4,13) (4,5) (4,20) (4,18) (4,7) (4,22) (4,16) (4,24) (5,8) (5,13) (5,20) (5,7) (5,22) (5,24) (5,21) (6,15) (6,23) (6,14) (6,26) (6,10) (6,11) (6,27) (7,12) (7,20) (7,25) (7,16) (7,21) (8,12) (8,20) (8,25) (8,16) (8,24) (10,15) (10,23) (10,14) (10,26) (10,19) (10,11) (10,27) (11,15) (11,23) (11,26) (11,27) (12,16) (12,24) (12,21) (13,20) (13,18) (13,25) (13,22) (13,16) (13,24) (13,21) (14,15) (14,26) (15,26) (15,27) (16,22) (16,24) (16,21) (18,25) (18,22) (18,21) (19,23) (19,26) (19,27) (20,25) (20,24) (21,25) (21,24) (22,25) (22,24) (23,26) (23,27) (24,25) (26,27)\nQ: Is there a path between node 18 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1032"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,3) (0,2) (0,1) (1,6) (1,3) (1,2) (2,6) (2,3) (3,6) (4,5)\nQ: Is there a path between node 5 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1033"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,4) (0,1) (0,11) (0,9) (0,12) (1,2) (1,4) (1,11) (1,9) (1,13) (1,8) (1,12) (2,6) (2,3) (2,4) (2,11) (2,9) (2,13) (2,8) (3,6) (3,9) (3,13) (3,8) (3,12) (4,6) (4,11) (4,9) (4,13) (4,8) (4,12) (5,7) (5,10) (6,11) (6,9) (6,8) (6,12) (8,9) (8,12) (9,11) (9,12) (11,13) (12,13)\nQ: Is there a path between node 10 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1034"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,34) (0,4) (0,7) (0,28) (0,8) (0,15) (0,23) (0,13) (0,22) (0,32) (0,11) (0,18) (1,7) (1,2) (1,13) (1,27) (1,26) (1,9) (2,14) (2,31) (2,15) (2,23) (2,13) (2,9) (2,22) (2,17) (2,32) (2,18) (3,24) (4,7) (4,27) (4,17) (5,16) (5,12) (5,29) (5,20) (6,34) (6,7) (6,14) (6,31) (6,10) (6,23) (6,26) (6,21) (6,17) (6,18) (7,33) (7,14) (7,28) (7,15) (7,26) (7,19) (8,14) (8,28) (8,31) (8,10) (8,13) (8,25) (8,30) (8,18) (9,14) (9,21) (9,25) (9,22) (9,11) (10,31) (10,15) (10,27) (10,25) (10,17) (10,32) (11,28) (11,31) (11,15) (11,13) (11,27) (11,21) (11,25) (11,22) (12,16) (13,33) (13,14) (13,28) (13,26) (13,21) (13,17) (13,32) (13,18) (14,33) (14,31) (14,23) (14,27) (14,25) (15,34) (15,30) (15,17) (15,19) (16,24) (17,23) (17,26) (17,19) (18,34) (18,21) (18,30) (19,33) (19,21) (19,25) (19,30) (21,33) (21,28) (21,25) (21,30) (22,33) (22,23) (22,26) (22,25) (23,34) (23,25) (25,33) (25,32) (26,33) (26,28) (26,31) (26,32) (27,33) (27,32) (32,33)\nQ: Is there a path between node 15 and node 26?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1035"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,13) (2,25) (2,28) (2,21) (2,5) (2,23) (3,22) (3,8) (3,6) (3,19) (3,21) (3,31) (3,15) (5,20) (5,16) (5,21) (5,23) (6,18) (6,17) (6,23) (7,10) (8,21) (9,24) (12,22) (12,18) (13,30) (13,27) (14,26) (15,16) (15,19) (15,31) (16,22) (16,20) (16,19) (17,20) (17,21) (17,31) (18,22) (18,25) (18,20) (18,21) (18,23) (19,25) (19,28) (20,28) (20,21) (21,25) (22,25) (22,28) (23,28) (27,29) (29,30) (30,32)\nQ: Is there a path between node 10 and node 26?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1036"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,11) (0,5) (0,9) (0,6) (1,2) (1,7) (1,3) (1,10) (1,8) (2,7) (2,3) (2,10) (2,8) (3,7) (3,10) (3,8) (4,11) (4,5) (4,9) (4,6) (5,11) (5,9) (5,6) (6,11) (6,9) (7,10) (7,8) (8,10) (9,11)\nQ: Is there a path between node 0 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1037"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,16) (0,22) (0,4) (0,15) (0,9) (1,8) (1,17) (1,12) (1,3) (1,5) (1,21) (1,6) (1,13) (1,19) (2,20) (2,16) (2,22) (2,4) (2,9) (3,8) (3,17) (3,14) (3,6) (3,10) (3,19) (4,20) (4,16) (4,22) (4,15) (4,9) (5,8) (5,17) (5,12) (5,14) (5,13) (5,10) (5,19) (6,17) (6,12) (6,14) (6,21) (6,13) (6,10) (6,19) (8,17) (8,12) (8,13) (8,19) (9,20) (9,22) (9,15) (10,17) (10,14) (10,21) (11,18) (11,23) (12,17) (12,21) (12,13) (12,19) (13,17) (13,14) (13,21) (15,20) (16,22) (17,21) (18,23)\nQ: Is there a path between node 1 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1038"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,15) (0,22) (0,18) (1,5) (1,14) (1,21) (1,16) (1,19) (1,3) (1,17) (1,13) (1,11) (1,2) (1,20) (1,8) (1,6) (1,12) (1,9) (1,7) (2,5) (2,14) (2,21) (2,16) (2,19) (2,3) (2,17) (2,13) (2,11) (2,20) (2,8) (2,6) (2,12) (2,9) (2,7) (3,5) (3,14) (3,21) (3,16) (3,19) (3,17) (3,13) (3,11) (3,20) (3,8) (3,6) (3,12) (3,9) (3,7) (5,14) (5,21) (5,16) (5,19) (5,17) (5,13) (5,11) (5,20) (5,8) (5,6) (5,12) (5,9) (5,7) (6,14) (6,21) (6,16) (6,19) (6,17) (6,13) (6,11) (6,20) (6,8) (6,12) (6,9) (6,7) (7,14) (7,21) (7,16) (7,19) (7,17) (7,13) (7,11) (7,20) (7,8) (7,12) (7,9) (8,14) (8,21) (8,16) (8,19) (8,17) (8,13) (8,11) (8,20) (8,12) (8,9) (9,14) (9,21) (9,16) (9,19) (9,17) (9,13) (9,11) (9,20) (9,12) (10,15) (10,22) (10,18) (11,14) (11,21) (11,16) (11,19) (11,17) (11,13) (11,20) (11,12) (12,14) (12,21) (12,16) (12,19) (12,17) (12,13) (12,20) (13,14) (13,21) (13,16) (13,19) (13,17) (13,20) (14,21) (14,16) (14,19) (14,17) (14,20) (15,22) (15,18) (16,21) (16,19) (16,17) (16,20) (17,21) (17,19) (17,20) (18,22) (19,21) (19,20) (20,21)\nQ: Is there a path between node 17 and node 18?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1039"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,18) (0,25) (0,19) (0,16) (0,22) (0,8) (0,10) (0,31) (0,13) (0,5) (0,14) (0,24) (0,27) (0,1) (0,15) (0,23) (1,9) (1,30) (1,25) (1,19) (1,16) (1,17) (1,22) (1,8) (1,21) (1,4) (1,31) (1,13) (1,14) (1,24) (1,12) (1,27) (1,15) (2,11) (2,28) (2,29) (2,7) (3,9) (3,18) (3,25) (3,19) (3,16) (3,22) (3,10) (3,4) (3,31) (3,13) (3,5) (3,14) (3,24) (3,12) (3,20) (3,27) (3,15) (3,23) (4,18) (4,30) (4,19) (4,22) (4,8) (4,21) (4,31) (4,5) (4,24) (4,12) (4,27) (4,23) (5,18) (5,30) (5,25) (5,19) (5,17) (5,10) (5,21) (5,31) (5,12) (5,20) (5,15) (5,23) (6,28) (6,29) (6,7) (6,26) (7,28) (8,9) (8,25) (8,19) (8,16) (8,22) (8,10) (8,13) (8,14) (8,24) (8,12) (8,27) (8,15) (8,23) (9,18) (9,30) (9,19) (9,16) (9,17) (9,22) (9,10) (9,31) (9,13) (9,27) (9,15) (9,23) (10,18) (10,30) (10,25) (10,16) (10,22) (10,21) (10,31) (10,14) (10,24) (10,12) (10,20) (10,15) (11,28) (11,26) (12,19) (12,22) (12,21) (12,13) (12,24) (12,15) (12,23) (13,25) (13,19) (13,16) (13,17) (13,22) (13,31) (13,14) (13,27) (14,30) (14,25) (14,16) (14,17) (14,22) (14,31) (14,24) (14,20) (14,15) (14,23) (15,18) (15,30) (15,25) (15,19) (15,16) (15,22) (15,31) (15,24) (16,18) (16,30) (16,22) (16,21) (16,31) (16,20) (16,27) (17,18) (17,30) (17,25) (17,19) (17,22) (17,21) (17,31) (17,24) (17,27) (17,23) (18,30) (18,25) (18,19) (18,22) (18,21) (18,31) (18,24) (18,27) (18,23) (19,30) (19,25) (19,21) (19,24) (19,20) (19,27) (19,23) (20,21) (20,31) (20,24) (20,27) (20,23) (21,25) (21,22) (21,31) (21,24) (21,27) (21,23) (22,30) (22,31) (22,24) (22,23) (23,30) (23,25) (23,24) (23,27) (24,30) (24,25) (24,31) (24,27) (25,30) (25,27) (26,28) (27,30) (27,31) (28,29) (30,31)\nQ: Is there a path between node 20 and node 25?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1040"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,2) (0,1) (1,5) (1,6) (2,6) (3,7) (4,7) (5,6)\nQ: Is there a path between node 5 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1041"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,3) (0,2) (0,9) (0,8) (1,6) (1,4) (2,7) (2,10) (2,3) (2,8) (2,5) (3,10) (3,9) (3,8) (4,6) (5,7) (5,10) (5,9) (7,8) (8,9)\nQ: Is there a path between node 5 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1042"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,11) (0,1) (0,25) (0,28) (0,16) (0,31) (0,2) (0,23) (1,20) (1,26) (1,24) (1,10) (1,31) (1,21) (2,26) (2,19) (2,11) (2,5) (2,15) (2,32) (2,33) (2,8) (2,16) (2,31) (2,21) (2,30) (3,12) (3,4) (4,18) (5,11) (5,24) (6,14) (6,12) (6,9) (6,13) (7,26) (7,25) (7,33) (7,8) (7,21) (8,26) (8,19) (8,32) (8,31) (9,12) (10,19) (10,11) (10,25) (11,33) (11,24) (12,14) (14,18) (15,19) (15,17) (15,32) (15,25) (15,31) (15,21) (16,26) (16,32) (17,20) (17,19) (17,23) (19,24) (19,31) (19,21) (19,30) (21,32) (21,25) (21,24) (21,31) (23,31) (24,28) (25,32) (25,33) (25,28) (26,32) (26,33) (26,28) (26,31) (26,30) (28,33) (28,30) (31,32)\nQ: Is there a path between node 30 and node 33?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1043"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,3) (0,5) (1,2) (1,10) (1,3) (1,5) (2,6) (2,10) (3,17) (3,14) (3,6) (3,9) (4,14) (4,7) (4,9) (5,17) (5,14) (5,6) (5,10) (5,7) (6,14) (6,16) (6,7) (9,17) (9,16) (9,10) (10,14) (11,15) (12,13) (14,17) (14,16) (14,15) (15,17)\nQ: Is there a path between node 17 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1044"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,18) (1,12) (1,15) (1,7) (2,17) (2,3) (3,17) (4,12) (5,17) (5,19) (6,18) (6,10) (6,9) (6,12) (6,16) (7,18) (7,9) (7,13) (7,8) (8,14) (9,18) (9,14) (9,12) (9,13) (10,12) (10,15) (11,17) (12,16) (14,18)\nQ: Is there a path between node 12 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1045"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,21) (1,17) (1,15) (1,2) (1,4) (1,18) (2,8) (2,13) (2,17) (2,15) (2,23) (2,22) (2,4) (2,18) (2,12) (4,21) (4,8) (4,13) (4,15) (4,23) (4,22) (4,18) (4,12) (5,21) (5,8) (5,13) (5,17) (5,15) (5,22) (5,18) (7,14) (7,16) (7,10) (7,11) (7,19) (8,21) (8,17) (8,23) (8,18) (9,14) (9,24) (10,14) (10,24) (10,19) (11,14) (11,16) (11,24) (12,21) (12,13) (12,17) (12,15) (12,23) (12,22) (12,18) (13,21) (13,17) (13,15) (13,23) (13,22) (14,24) (15,21) (15,17) (15,23) (15,22) (15,18) (16,19) (17,21) (17,18) (18,21) (18,23) (21,22) (22,23)\nQ: Is there a path between node 4 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1046"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,11) (0,1) (0,25) (0,28) (0,16) (0,31) (0,2) (0,23) (1,20) (1,26) (1,24) (1,10) (1,31) (1,21) (2,26) (2,19) (2,11) (2,5) (2,15) (2,32) (2,33) (2,8) (2,16) (2,31) (2,21) (2,30) (3,12) (3,4) (4,18) (5,11) (5,24) (6,14) (6,12) (6,9) (6,13) (7,26) (7,25) (7,33) (7,8) (7,21) (8,26) (8,19) (8,32) (8,31) (9,12) (10,19) (10,11) (10,25) (11,33) (11,24) (12,14) (14,18) (15,19) (15,17) (15,32) (15,25) (15,31) (15,21) (16,26) (16,32) (17,20) (17,19) (17,23) (19,24) (19,31) (19,21) (19,30) (21,32) (21,25) (21,24) (21,31) (23,31) (24,28) (25,32) (25,33) (25,28) (26,32) (26,33) (26,28) (26,31) (26,30) (28,33) (28,30) (31,32)\nQ: Is there a path between node 16 and node 30?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1047"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,27) (0,13) (0,10) (0,15) (0,2) (0,17) (1,5) (1,22) (1,8) (1,19) (1,26) (1,24) (1,18) (1,16) (1,14) (1,12) (1,4) (1,9) (2,7) (2,27) (2,13) (2,3) (2,6) (2,10) (2,11) (2,17) (3,7) (3,27) (3,20) (3,6) (3,10) (3,15) (3,21) (3,17) (4,5) (4,8) (4,19) (4,26) (4,25) (4,18) (4,14) (4,12) (5,8) (5,26) (5,18) (5,16) (5,14) (5,12) (6,7) (6,13) (6,10) (6,21) (7,20) (7,13) (7,10) (7,15) (7,11) (8,19) (8,26) (8,18) (8,16) (8,14) (8,9) (9,22) (9,19) (9,26) (9,25) (9,16) (9,14) (9,12) (10,13) (10,21) (10,17) (11,27) (11,13) (11,15) (11,21) (11,17) (12,22) (12,19) (12,26) (12,24) (12,25) (12,16) (12,14) (13,27) (13,15) (14,22) (14,19) (14,26) (15,27) (15,20) (15,21) (15,17) (16,22) (16,19) (16,24) (16,25) (16,18) (17,27) (17,20) (17,21) (18,22) (18,19) (18,26) (18,24) (19,26) (19,25) (20,27) (20,21) (21,27) (22,26) (22,24) (24,26)\nQ: Is there a path between node 7 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1048"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,13) (0,12) (0,14) (0,8) (0,3) (0,6) (0,2) (0,9) (0,5) (1,10) (1,7) (1,11) (2,4) (2,13) (2,12) (2,14) (2,8) (2,3) (2,6) (2,9) (2,5) (3,4) (3,13) (3,12) (3,14) (3,8) (3,6) (3,9) (3,5) (4,13) (4,12) (4,14) (4,8) (4,6) (4,9) (4,5) (5,13) (5,12) (5,14) (5,8) (5,6) (5,9) (6,13) (6,12) (6,14) (6,8) (6,9) (7,10) (7,11) (8,13) (8,12) (8,14) (8,9) (9,13) (9,12) (9,14) (10,11) (12,13) (12,14) (13,14)\nQ: Is there a path between node 7 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1049"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,8) (0,11) (0,17) (0,1) (0,2) (0,12) (0,6) (0,18) (0,7) (0,15) (1,19) (1,8) (1,9) (1,11) (1,2) (1,12) (1,6) (1,7) (1,15) (2,19) (2,4) (2,9) (2,11) (2,17) (2,12) (2,6) (2,18) (2,15) (3,5) (3,13) (3,10) (4,19) (4,8) (4,9) (4,11) (4,17) (4,12) (4,6) (4,7) (4,15) (5,13) (5,10) (6,9) (6,11) (6,12) (6,18) (7,19) (7,8) (7,9) (7,11) (7,17) (7,15) (8,19) (8,11) (8,17) (8,12) (9,17) (9,12) (9,18) (10,13) (11,17) (11,15) (12,19) (12,17) (12,18) (12,15) (14,20) (14,21) (15,17) (15,18) (17,19) (17,18) (18,19) (20,21)\nQ: Is there a path between node 8 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1050"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,9) (0,13) (0,3) (0,1) (0,2) (0,7) (0,8) (0,11) (1,14) (1,13) (1,8) (1,10) (1,11) (1,5) (2,9) (2,13) (2,3) (2,7) (2,8) (2,10) (3,14) (3,9) (3,13) (3,8) (3,11) (3,5) (4,6) (4,12) (5,14) (5,9) (5,7) (5,8) (5,10) (5,11) (6,12) (7,14) (7,13) (7,8) (7,10) (8,14) (8,9) (8,10) (9,14) (9,13) (10,14) (10,13) (11,14) (13,14)\nQ: Is there a path between node 4 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1051"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,13) (0,19) (0,11) (0,16) (0,20) (0,8) (0,5) (0,3) (0,2) (0,7) (0,6) (0,17) (0,14) (0,12) (0,1) (0,18) (0,10) (0,23) (0,9) (1,4) (1,13) (1,19) (1,11) (1,16) (1,20) (1,8) (1,5) (1,3) (1,2) (1,7) (1,6) (1,17) (1,14) (1,12) (1,18) (1,10) (1,23) (1,9) (2,4) (2,13) (2,19) (2,11) (2,16) (2,20) (2,8) (2,5) (2,3) (2,7) (2,6) (2,17) (2,14) (2,12) (2,18) (2,10) (2,23) (2,9) (3,4) (3,13) (3,19) (3,11) (3,16) (3,20) (3,8) (3,5) (3,7) (3,6) (3,17) (3,14) (3,12) (3,18) (3,10) (3,23) (3,9) (4,13) (4,19) (4,11) (4,16) (4,20) (4,8) (4,5) (4,7) (4,6) (4,17) (4,14) (4,12) (4,18) (4,10) (4,23) (4,9) (5,13) (5,19) (5,11) (5,16) (5,20) (5,8) (5,7) (5,6) (5,17) (5,14) (5,12) (5,18) (5,10) (5,23) (5,9) (6,13) (6,19) (6,11) (6,16) (6,20) (6,8) (6,7) (6,17) (6,14) (6,12) (6,18) (6,10) (6,23) (6,9) (7,13) (7,19) (7,11) (7,16) (7,20) (7,8) (7,17) (7,14) (7,12) (7,18) (7,10) (7,23) (7,9) (8,13) (8,19) (8,11) (8,16) (8,20) (8,17) (8,14) (8,12) (8,18) (8,10) (8,23) (8,9) (9,13) (9,19) (9,11) (9,16) (9,20) (9,17) (9,14) (9,12) (9,18) (9,10) (9,23) (10,13) (10,19) (10,11) (10,16) (10,20) (10,17) (10,14) (10,12) (10,18) (10,23) (11,13) (11,19) (11,16) (11,20) (11,17) (11,14) (11,12) (11,18) (11,23) (12,13) (12,19) (12,16) (12,20) (12,17) (12,14) (12,18) (12,23) (13,19) (13,16) (13,20) (13,17) (13,14) (13,18) (13,23) (14,19) (14,16) (14,20) (14,17) (14,18) (14,23) (15,21) (15,22) (16,19) (16,20) (16,17) (16,18) (16,23) (17,19) (17,20) (17,18) (17,23) (18,19) (18,20) (18,23) (19,20) (19,23) (20,23) (21,22)\nQ: Is there a path between node 11 and node 22?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1052"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,9) (0,4) (0,14) (0,6) (0,10) (0,12) (0,2) (1,13) (1,11) (1,3) (1,5) (1,7) (1,16) (1,8) (1,17) (2,15) (2,9) (2,4) (2,14) (2,6) (2,10) (2,12) (3,13) (3,11) (3,5) (3,7) (3,16) (3,8) (3,17) (4,15) (4,9) (4,14) (4,6) (4,10) (4,12) (5,13) (5,11) (5,7) (5,16) (5,8) (5,17) (6,15) (6,9) (6,14) (6,10) (6,12) (7,13) (7,11) (7,16) (7,8) (7,17) (8,13) (8,11) (8,16) (8,17) (9,15) (9,14) (9,10) (9,12) (10,15) (10,14) (10,12) (11,13) (11,16) (11,17) (12,15) (12,14) (13,16) (13,17) (14,15) (16,17)\nQ: Is there a path between node 16 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1053"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,5) (0,1) (0,9) (0,3) (0,4) (1,6) (1,5) (1,9) (1,3) (1,4) (2,7) (2,8) (2,10) (3,6) (3,5) (3,9) (3,4) (4,6) (4,5) (4,9) (5,6) (5,9) (6,9) (7,8) (7,10) (8,10)\nQ: Is there a path between node 8 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1054"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,17) (0,10) (0,28) (0,30) (0,29) (0,3) (1,14) (1,2) (2,25) (2,20) (2,7) (2,32) (2,22) (3,24) (3,19) (3,23) (3,4) (3,12) (3,29) (4,26) (4,24) (4,23) (4,8) (4,13) (5,26) (5,19) (5,23) (5,8) (5,15) (5,21) (6,14) (7,32) (8,16) (8,12) (8,29) (9,26) (9,13) (9,18) (9,29) (9,31) (10,17) (10,11) (10,30) (10,23) (10,13) (11,16) (11,17) (11,19) (11,28) (11,23) (12,26) (12,24) (12,21) (13,26) (13,17) (13,19) (13,30) (13,31) (14,25) (14,22) (15,16) (15,17) (15,23) (15,18) (15,29) (16,26) (16,24) (16,18) (16,21) (17,24) (17,19) (17,28) (17,30) (17,23) (18,24) (18,21) (19,26) (19,24) (19,28) (19,23) (20,32) (22,32) (22,27) (24,26) (24,30) (26,29) (28,29)\nQ: Is there a path between node 4 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1055"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,5) (3,5)\nQ: Is there a path between node 0 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1056"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,2) (2,3)\nQ: Is there a path between node 4 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1057"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,28) (0,1) (0,22) (0,20) (0,15) (0,18) (0,2) (0,5) (0,10) (0,8) (0,14) (0,6) (1,27) (1,12) (1,19) (1,28) (1,25) (1,29) (1,22) (1,4) (1,7) (1,15) (1,18) (1,3) (1,2) (1,24) (1,5) (1,11) (1,14) (1,13) (1,6) (2,12) (2,19) (2,28) (2,29) (2,4) (2,15) (2,16) (2,18) (2,3) (2,10) (2,13) (2,21) (2,6) (3,27) (3,19) (3,28) (3,20) (3,4) (3,7) (3,16) (3,18) (3,9) (3,24) (3,5) (3,11) (3,10) (3,8) (3,14) (3,23) (3,21) (3,6) (4,27) (4,12) (4,19) (4,28) (4,25) (4,20) (4,7) (4,15) (4,16) (4,5) (4,8) (4,14) (4,13) (4,21) (4,6) (5,27) (5,12) (5,19) (5,28) (5,25) (5,29) (5,22) (5,20) (5,7) (5,15) (5,16) (5,24) (5,11) (5,10) (5,8) (5,14) (5,23) (5,13) (5,21) (5,6) (6,27) (6,12) (6,28) (6,25) (6,29) (6,22) (6,20) (6,7) (6,16) (6,18) (6,9) (6,24) (6,8) (6,14) (6,21) (7,19) (7,25) (7,29) (7,22) (7,20) (7,15) (7,16) (7,24) (7,11) (7,10) (7,14) (7,23) (7,21) (8,27) (8,12) (8,19) (8,29) (8,22) (8,20) (8,15) (8,16) (8,9) (8,24) (8,11) (8,10) (8,14) (8,13) (9,12) (9,19) (9,25) (9,22) (9,20) (9,18) (9,24) (9,11) (9,10) (9,14) (9,23) (9,13) (9,21) (10,27) (10,12) (10,19) (10,28) (10,25) (10,29) (10,16) (10,18) (10,24) (10,14) (10,23) (10,13) (10,21) (11,27) (11,12) (11,25) (11,22) (11,20) (11,18) (11,24) (12,19) (12,28) (12,29) (12,22) (12,15) (12,16) (12,18) (12,14) (12,23) (12,13) (12,21) (13,27) (13,28) (13,25) (13,29) (13,22) (13,20) (13,15) (13,18) (13,24) (14,19) (14,28) (14,25) (14,29) (14,15) (14,16) (14,18) (14,24) (14,23) (15,27) (15,28) (15,25) (15,29) (15,20) (15,18) (15,23) (15,21) (16,27) (16,19) (16,28) (16,25) (16,29) (16,22) (16,20) (16,18) (16,24) (16,21) (18,19) (18,28) (18,29) (18,22) (18,20) (18,24) (18,23) (18,21) (19,27) (19,28) (19,25) (19,29) (19,22) (19,20) (19,24) (19,23) (19,21) (20,27) (20,28) (20,29) (20,22) (20,23) (20,21) (21,27) (21,28) (21,24) (21,23) (22,27) (22,28) (22,29) (22,23) (23,27) (23,28) (23,25) (23,29) (24,27) (24,28) (24,25) (24,29) (25,27) (25,29) (27,28) (27,29)\nQ: Is there a path between node 2 and node 18?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1058"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,6) (0,2) (0,5) (1,7) (1,16) (1,14) (1,17) (1,3) (1,9) (1,13) (1,10) (2,11) (2,6) (2,5) (3,7) (3,16) (3,14) (3,17) (3,9) (3,13) (3,10) (4,8) (4,15) (4,12) (5,11) (5,6) (6,11) (7,16) (7,14) (7,17) (7,9) (7,13) (7,10) (8,15) (8,12) (9,16) (9,14) (9,17) (9,13) (9,10) (10,16) (10,14) (10,17) (10,13) (12,15) (13,16) (13,14) (13,17) (14,16) (14,17) (16,17)\nQ: Is there a path between node 12 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1059"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,13) (2,25) (2,28) (2,21) (2,5) (2,23) (3,22) (3,8) (3,6) (3,19) (3,21) (3,31) (3,15) (5,20) (5,16) (5,21) (5,23) (6,18) (6,17) (6,23) (7,10) (8,21) (9,24) (12,22) (12,18) (13,30) (13,27) (14,26) (15,16) (15,19) (15,31) (16,22) (16,20) (16,19) (17,20) (17,21) (17,31) (18,22) (18,25) (18,20) (18,21) (18,23) (19,25) (19,28) (20,28) (20,21) (21,25) (22,25) (22,28) (23,28) (27,29) (29,30) (30,32)\nQ: Is there a path between node 32 and node 20?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1060"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,13) (0,19) (0,11) (0,16) (0,20) (0,8) (0,5) (0,3) (0,2) (0,7) (0,6) (0,17) (0,14) (0,12) (0,1) (0,18) (0,10) (0,23) (0,9) (1,4) (1,13) (1,19) (1,11) (1,16) (1,20) (1,8) (1,5) (1,3) (1,2) (1,7) (1,6) (1,17) (1,14) (1,12) (1,18) (1,10) (1,23) (1,9) (2,4) (2,13) (2,19) (2,11) (2,16) (2,20) (2,8) (2,5) (2,3) (2,7) (2,6) (2,17) (2,14) (2,12) (2,18) (2,10) (2,23) (2,9) (3,4) (3,13) (3,19) (3,11) (3,16) (3,20) (3,8) (3,5) (3,7) (3,6) (3,17) (3,14) (3,12) (3,18) (3,10) (3,23) (3,9) (4,13) (4,19) (4,11) (4,16) (4,20) (4,8) (4,5) (4,7) (4,6) (4,17) (4,14) (4,12) (4,18) (4,10) (4,23) (4,9) (5,13) (5,19) (5,11) (5,16) (5,20) (5,8) (5,7) (5,6) (5,17) (5,14) (5,12) (5,18) (5,10) (5,23) (5,9) (6,13) (6,19) (6,11) (6,16) (6,20) (6,8) (6,7) (6,17) (6,14) (6,12) (6,18) (6,10) (6,23) (6,9) (7,13) (7,19) (7,11) (7,16) (7,20) (7,8) (7,17) (7,14) (7,12) (7,18) (7,10) (7,23) (7,9) (8,13) (8,19) (8,11) (8,16) (8,20) (8,17) (8,14) (8,12) (8,18) (8,10) (8,23) (8,9) (9,13) (9,19) (9,11) (9,16) (9,20) (9,17) (9,14) (9,12) (9,18) (9,10) (9,23) (10,13) (10,19) (10,11) (10,16) (10,20) (10,17) (10,14) (10,12) (10,18) (10,23) (11,13) (11,19) (11,16) (11,20) (11,17) (11,14) (11,12) (11,18) (11,23) (12,13) (12,19) (12,16) (12,20) (12,17) (12,14) (12,18) (12,23) (13,19) (13,16) (13,20) (13,17) (13,14) (13,18) (13,23) (14,19) (14,16) (14,20) (14,17) (14,18) (14,23) (15,21) (15,22) (16,19) (16,20) (16,17) (16,18) (16,23) (17,19) (17,20) (17,18) (17,23) (18,19) (18,20) (18,23) (19,20) (19,23) (20,23) (21,22)\nQ: Is there a path between node 17 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1061"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,9) (1,10) (1,3) (2,6) (2,4) (2,7) (3,6) (3,10) (3,9) (3,12) (4,8) (5,9) (5,12) (6,9) (6,12) (6,7) (7,10) (7,9) (7,14) (8,10) (8,9) (8,14) (12,14)\nQ: Is there a path between node 0 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1062"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,3) (0,13) (0,15) (0,7) (1,4) (1,6) (2,9) (2,18) (2,13) (3,12) (4,11) (6,8) (6,17) (7,16) (7,12) (7,13) (7,14) (8,11) (8,17) (8,20) (9,18) (9,21) (9,14) (9,15) (10,12) (12,16) (12,15) (13,18) (13,15) (14,16) (14,21) (15,16) (15,18) (16,18)\nQ: Is there a path between node 7 and node 18?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1063"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,22) (0,6) (0,11) (0,10) (0,4) (0,5) (0,9) (0,1) (0,13) (0,21) (0,20) (0,12) (1,22) (1,11) (1,10) (1,5) (1,16) (1,9) (1,13) (1,21) (1,20) (2,8) (2,19) (2,3) (2,18) (2,24) (3,19) (3,17) (3,24) (3,23) (4,22) (4,6) (4,16) (4,9) (4,21) (4,20) (5,22) (5,6) (5,14) (5,11) (5,16) (5,15) (5,9) (5,13) (5,21) (5,20) (6,22) (6,11) (6,10) (6,16) (6,13) (6,21) (6,12) (7,8) (7,17) (7,18) (7,24) (7,23) (8,17) (8,24) (9,14) (9,11) (9,10) (9,16) (9,15) (9,21) (9,20) (9,12) (10,22) (10,14) (10,11) (10,16) (10,15) (10,21) (10,20) (11,22) (11,16) (11,15) (11,20) (12,22) (12,14) (12,15) (12,13) (12,21) (12,20) (13,14) (13,16) (13,15) (13,21) (13,20) (14,22) (14,16) (14,15) (14,21) (15,16) (15,21) (16,22) (16,21) (16,20) (17,19) (17,18) (17,24) (17,23) (18,23) (19,24) (23,24)\nQ: Is there a path between node 24 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1064"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,2) (0,8) (0,4) (0,7) (0,3) (0,1) (1,5) (1,2) (1,8) (1,4) (1,7) (1,3) (2,5) (2,8) (2,4) (2,7) (2,3) (3,5) (3,8) (3,4) (3,7) (4,5) (4,8) (4,7) (5,8) (5,7) (6,9) (7,8)\nQ: Is there a path between node 0 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1065"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,11) (0,1) (0,25) (0,28) (0,16) (0,31) (0,2) (0,23) (1,20) (1,26) (1,24) (1,10) (1,31) (1,21) (2,26) (2,19) (2,11) (2,5) (2,15) (2,32) (2,33) (2,8) (2,16) (2,31) (2,21) (2,30) (3,12) (3,4) (4,18) (5,11) (5,24) (6,14) (6,12) (6,9) (6,13) (7,26) (7,25) (7,33) (7,8) (7,21) (8,26) (8,19) (8,32) (8,31) (9,12) (10,19) (10,11) (10,25) (11,33) (11,24) (12,14) (14,18) (15,19) (15,17) (15,32) (15,25) (15,31) (15,21) (16,26) (16,32) (17,20) (17,19) (17,23) (19,24) (19,31) (19,21) (19,30) (21,32) (21,25) (21,24) (21,31) (23,31) (24,28) (25,32) (25,33) (25,28) (26,32) (26,33) (26,28) (26,31) (26,30) (28,33) (28,30) (31,32)\nQ: Is there a path between node 23 and node 16?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1066"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,9) (0,14) (0,18) (0,3) (0,1) (0,17) (0,4) (0,8) (0,7) (0,15) (0,11) (0,10) (0,13) (1,5) (1,9) (1,14) (1,18) (1,3) (1,17) (1,4) (1,8) (1,7) (1,15) (1,11) (1,10) (1,13) (3,5) (3,9) (3,14) (3,18) (3,17) (3,4) (3,8) (3,7) (3,15) (3,11) (3,10) (3,13) (4,5) (4,9) (4,14) (4,18) (4,17) (4,8) (4,7) (4,15) (4,11) (4,10) (4,13) (5,9) (5,14) (5,18) (5,17) (5,8) (5,7) (5,15) (5,11) (5,10) (5,13) (6,12) (6,16) (7,9) (7,14) (7,18) (7,17) (7,8) (7,15) (7,11) (7,10) (7,13) (8,9) (8,14) (8,18) (8,17) (8,15) (8,11) (8,10) (8,13) (9,14) (9,18) (9,17) (9,15) (9,11) (9,10) (9,13) (10,14) (10,18) (10,17) (10,15) (10,11) (10,13) (11,14) (11,18) (11,17) (11,15) (11,13) (12,16) (13,14) (13,18) (13,17) (13,15) (14,18) (14,17) (14,15) (15,18) (15,17) (17,18)\nQ: Is there a path between node 9 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1067"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,8) (1,5) (1,10) (1,8) (2,6) (2,7) (3,9) (3,10) (4,11) (4,8) (6,7) (8,9) (8,10) (11,12)\nQ: Is there a path between node 2 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1068"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,11) (1,9) (1,19) (1,31) (1,20) (2,15) (2,11) (2,27) (2,29) (2,16) (2,31) (3,8) (3,4) (3,12) (3,18) (3,17) (3,10) (3,25) (3,31) (3,20) (4,30) (4,24) (4,19) (5,26) (5,23) (6,13) (7,15) (7,9) (7,30) (7,12) (7,16) (7,19) (7,10) (7,25) (8,15) (8,11) (8,30) (8,24) (8,10) (8,31) (9,11) (9,30) (9,27) (9,29) (9,10) (10,15) (10,30) (10,12) (10,18) (10,19) (10,17) (10,14) (11,30) (11,29) (11,19) (12,15) (12,19) (12,14) (12,20) (13,28) (14,27) (14,24) (14,20) (15,27) (15,18) (15,25) (15,20) (16,29) (16,24) (16,19) (17,29) (17,19) (17,31) (18,30) (18,24) (18,19) (18,31) (19,30) (19,25) (21,28) (21,23) (22,23) (25,27) (25,31) (26,28) (29,31)\nQ: Is there a path between node 28 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1069"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,10) (0,17) (0,15) (0,4) (0,12) (0,24) (0,9) (0,3) (0,13) (0,23) (0,7) (0,19) (0,16) (0,6) (0,25) (0,8) (1,10) (1,17) (1,4) (1,12) (1,24) (1,3) (1,13) (1,23) (1,26) (1,22) (1,19) (1,6) (1,14) (1,25) (1,8) (1,20) (2,10) (2,17) (2,11) (2,4) (2,24) (2,9) (2,3) (2,13) (2,23) (2,26) (2,7) (2,22) (2,19) (2,6) (2,14) (2,25) (2,8) (3,10) (3,17) (3,11) (3,15) (3,4) (3,12) (3,24) (3,9) (3,13) (3,26) (3,7) (3,19) (3,16) (3,14) (3,25) (3,8) (3,20) (4,10) (4,17) (4,11) (4,15) (4,12) (4,24) (4,9) (4,7) (4,19) (4,16) (4,6) (4,25) (4,20) (5,18) (6,10) (6,17) (6,15) (6,12) (6,24) (6,9) (6,23) (6,7) (6,16) (6,25) (6,8) (7,10) (7,11) (7,15) (7,12) (7,13) (7,22) (7,19) (7,16) (7,25) (7,8) (7,20) (8,10) (8,17) (8,11) (8,15) (8,12) (8,24) (8,9) (8,23) (8,22) (8,19) (8,16) (8,14) (8,25) (8,20) (9,10) (9,17) (9,11) (9,12) (9,24) (9,13) (9,23) (9,26) (9,22) (9,19) (9,16) (9,20) (10,17) (10,11) (10,15) (10,12) (10,24) (10,13) (10,23) (10,26) (10,19) (10,14) (10,20) (11,15) (11,12) (11,24) (11,13) (11,23) (11,26) (11,19) (11,16) (11,14) (11,20) (12,15) (12,24) (12,23) (12,22) (12,19) (12,16) (12,14) (12,25) (12,20) (13,15) (13,24) (13,23) (13,19) (13,16) (13,14) (13,25) (13,20) (14,17) (14,15) (14,24) (14,23) (14,26) (14,22) (14,19) (14,16) (14,25) (14,20) (15,17) (15,24) (15,23) (15,26) (15,16) (15,20) (16,24) (16,23) (16,26) (16,19) (16,25) (16,20) (17,23) (17,20) (18,21) (19,23) (19,22) (19,25) (19,20) (20,24) (20,23) (20,22) (20,25) (22,26) (22,25) (23,24) (23,26) (23,25) (24,26) (24,25) (25,26)\nQ: Is there a path between node 17 and node 22?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1070"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (0,4) (1,32) (1,22) (1,34) (1,7) (1,5) (1,28) (1,11) (1,13) (1,30) (1,31) (1,26) (2,12) (2,3) (2,24) (2,15) (2,18) (2,8) (2,20) (2,25) (2,19) (2,17) (2,16) (3,10) (3,24) (3,15) (3,18) (3,8) (3,20) (3,14) (3,19) (3,21) (4,23) (4,6) (5,32) (5,22) (5,7) (5,33) (5,11) (5,13) (5,27) (5,31) (5,26) (6,23) (7,22) (7,34) (7,28) (7,13) (7,27) (7,30) (7,26) (7,29) (8,10) (8,24) (8,15) (8,18) (8,20) (8,14) (8,17) (8,21) (8,16) (9,32) (9,22) (9,34) (9,28) (9,13) (9,27) (9,31) (9,26) (9,29) (10,12) (10,24) (10,15) (10,18) (10,20) (10,25) (10,17) (11,32) (11,22) (11,34) (11,28) (11,13) (11,27) (11,30) (11,31) (11,26) (12,24) (12,25) (12,14) (12,17) (12,21) (12,16) (13,34) (13,33) (13,27) (13,30) (13,31) (13,29) (14,15) (14,18) (14,20) (14,25) (14,19) (14,17) (14,21) (14,16) (15,24) (15,18) (15,20) (15,17) (15,21) (16,24) (16,20) (16,19) (16,17) (17,24) (17,20) (17,21) (18,20) (18,25) (18,19) (20,24) (20,25) (20,21) (21,25) (22,32) (22,28) (22,27) (22,30) (22,31) (22,26) (24,25) (26,34) (26,33) (26,31) (27,34) (27,33) (27,28) (27,30) (27,31) (27,29) (28,32) (28,33) (28,30) (28,31) (28,29) (29,32) (29,33) (30,32) (31,32) (31,34) (32,34) (32,33) (33,34)\nQ: Is there a path between node 17 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1071"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,29) (0,1) (0,9) (0,20) (0,34) (0,7) (0,19) (0,22) (0,31) (1,11) (1,30) (1,6) (1,21) (1,14) (1,28) (1,19) (1,31) (1,4) (2,3) (2,11) (2,18) (2,21) (2,20) (2,14) (2,7) (2,17) (3,11) (3,33) (3,15) (3,30) (3,18) (3,21) (3,14) (3,5) (4,10) (4,26) (4,27) (4,21) (4,34) (5,9) (5,27) (5,30) (5,6) (5,24) (5,14) (5,34) (5,28) (5,17) (6,11) (6,25) (6,10) (6,26) (6,29) (6,15) (6,16) (6,14) (6,7) (6,12) (6,22) (7,10) (7,26) (7,27) (7,18) (7,24) (7,8) (7,31) (8,11) (8,33) (8,9) (8,30) (8,24) (8,20) (8,16) (8,22) (8,17) (9,10) (9,20) (9,16) (9,14) (10,25) (10,33) (10,30) (10,18) (10,24) (10,20) (10,31) (11,15) (11,12) (11,19) (11,17) (12,25) (12,29) (12,27) (12,30) (12,34) (12,28) (12,17) (14,25) (14,33) (14,26) (14,29) (14,30) (14,21) (14,17) (15,20) (15,17) (16,21) (16,28) (16,19) (16,22) (17,27) (17,30) (17,24) (17,19) (18,26) (18,21) (18,28) (19,33) (19,27) (19,34) (19,22) (20,25) (20,26) (20,27) (20,21) (20,28) (20,31) (21,22) (22,24) (22,31) (24,34) (24,28) (25,26) (25,29) (25,27) (26,33) (26,27) (26,30) (27,30) (27,28) (28,31) (29,30) (29,34) (29,31) (30,33) (30,34) (31,33) (31,34)\nQ: Is there a path between node 13 and node 24?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1072"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,14) (1,21) (1,3) (1,15) (1,7) (3,12) (4,10) (5,10) (6,22) (7,21) (7,15) (9,12) (11,13) (11,21) (14,20) (15,17) (15,21) (16,18) (18,22)\nQ: Is there a path between node 13 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1073"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,3) (0,2) (1,5) (1,3) (2,5) (2,3) (3,5)\nQ: Is there a path between node 3 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1074"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,13) (0,5) (0,11) (0,15) (0,10) (0,16) (0,14) (0,8) (0,9) (1,18) (1,12) (1,7) (1,6) (2,13) (2,11) (2,15) (2,17) (2,16) (2,14) (2,3) (2,8) (2,9) (3,5) (3,11) (3,4) (3,15) (3,10) (3,14) (3,8) (3,9) (4,13) (4,5) (4,17) (4,16) (4,14) (4,8) (5,17) (5,16) (5,14) (6,12) (6,19) (6,20) (6,7) (7,18) (8,15) (8,17) (8,16) (8,14) (8,9) (9,13) (9,11) (9,17) (9,16) (9,14) (10,11) (10,15) (10,17) (10,16) (10,14) (11,13) (11,15) (11,16) (12,18) (12,19) (12,20) (13,17) (13,14) (14,15) (14,17) (14,16) (15,17) (16,17) (18,19) (18,20) (19,20)\nQ: Is there a path between node 2 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1075"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,18) (0,15) (0,12) (0,5) (1,24) (2,21) (2,23) (2,9) (2,15) (2,19) (3,23) (3,15) (3,8) (3,16) (5,21) (5,22) (5,6) (5,19) (5,8) (5,10) (5,16) (6,14) (6,22) (6,9) (6,12) (6,17) (9,23) (9,22) (9,20) (9,10) (10,22) (10,18) (10,19) (11,24) (12,14) (13,14) (13,21) (13,23) (13,18) (13,15) (14,21) (14,18) (14,15) (14,16) (15,20) (15,17) (17,23) (17,22) (17,18) (17,20) (17,19) (18,19) (19,20) (21,23)\nQ: Is there a path between node 23 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1076"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,10) (0,25) (0,16) (0,24) (0,4) (0,8) (0,27) (0,19) (1,5) (1,28) (2,15) (3,12) (3,13) (3,21) (3,24) (3,4) (3,8) (4,26) (4,20) (4,21) (4,11) (4,9) (6,13) (6,14) (6,22) (6,21) (6,7) (6,23) (6,11) (7,12) (7,26) (7,20) (7,17) (7,14) (7,10) (7,25) (7,24) (7,8) (7,11) (7,19) (7,9) (8,25) (8,27) (8,11) (9,17) (9,14) (9,21) (9,23) (9,27) (9,11) (10,26) (10,20) (10,14) (10,25) (10,23) (10,24) (11,13) (11,17) (11,21) (11,25) (11,23) (11,19) (12,20) (12,17) (12,24) (13,26) (13,20) (13,17) (13,22) (13,25) (13,24) (13,19) (14,20) (14,16) (15,28) (15,18) (16,26) (16,21) (16,23) (17,26) (17,22) (17,23) (17,27) (18,28) (19,22) (20,23) (20,24) (20,27) (21,26) (21,27) (23,25) (24,25) (24,27) (25,27)\nQ: Is there a path between node 16 and node 18?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1077"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,23) (1,6) (1,19) (1,7) (2,17) (2,24) (2,10) (2,20) (3,22) (3,27) (4,17) (4,15) (5,19) (5,12) (5,25) (6,19) (6,7) (7,18) (7,23) (8,16) (8,13) (9,27) (9,13) (10,21) (10,15) (10,11) (11,17) (11,26) (11,24) (11,14) (12,25) (12,23) (14,17) (14,26) (15,21) (17,26) (17,21) (17,24) (20,21) (20,24) (21,26) (21,24) (23,25)\nQ: Is there a path between node 9 and node 25?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1078"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (0,1) (0,19) (0,15) (0,20) (0,9) (0,21) (0,3) (0,22) (0,32) (0,24) (0,14) (0,11) (0,17) (0,5) (0,34) (0,4) (0,26) (0,10) (0,8) (1,27) (1,23) (1,30) (1,6) (1,19) (1,20) (1,2) (1,9) (1,21) (1,3) (1,22) (1,24) (1,14) (1,11) (1,17) (1,5) (1,4) (1,26) (1,8) (2,27) (2,30) (2,6) (2,19) (2,20) (2,9) (2,21) (2,3) (2,22) (2,32) (2,7) (2,11) (2,17) (2,5) (2,34) (2,4) (2,26) (2,12) (2,10) (3,27) (3,23) (3,30) (3,6) (3,19) (3,15) (3,20) (3,9) (3,22) (3,24) (3,14) (3,34) (3,4) (3,12) (3,10) (3,8) (3,28) (4,27) (4,23) (4,30) (4,19) (4,15) (4,20) (4,9) (4,21) (4,32) (4,24) (4,14) (4,7) (4,11) (4,17) (4,5) (4,26) (4,12) (4,8) (4,28) (5,30) (5,19) (5,9) (5,21) (5,24) (5,7) (5,11) (5,17) (5,34) (5,12) (6,27) (6,23) (6,30) (6,19) (6,20) (6,9) (6,21) (6,22) (6,32) (6,24) (6,14) (6,7) (6,11) (6,17) (6,34) (6,26) (6,8) (6,28) (7,23) (7,30) (7,19) (7,15) (7,20) (7,21) (7,32) (7,24) (7,11) (7,17) (7,34) (7,12) (7,10) (7,8) (7,28) (8,23) (8,15) (8,20) (8,24) (8,14) (8,11) (8,17) (8,34) (8,26) (8,12) (8,10) (8,28) (9,30) (9,19) (9,15) (9,20) (9,22) (9,32) (9,24) (9,11) (9,34) (9,12) (9,10) (9,28) (10,27) (10,23) (10,30) (10,19) (10,21) (10,32) (10,24) (10,26) (10,12) (11,27) (11,30) (11,19) (11,20) (11,21) (11,22) (11,32) (11,24) (11,14) (11,17) (11,34) (11,12) (12,27) (12,30) (12,19) (12,20) (12,22) (12,32) (12,24) (12,14) (12,17) (12,34) (12,28) (14,27) (14,23) (14,30) (14,19) (14,15) (14,21) (14,22) (14,32) (14,17) (14,34) (14,28) (15,19) (15,20) (15,21) (15,22) (15,32) (15,24) (15,34) (15,26) (15,28) (16,33) (16,29) (16,18) (16,31) (17,27) (17,23) (17,30) (17,19) (17,20) (17,21) (17,22) (17,32) (17,24) (17,34) (17,28) (18,33) (18,31) (18,25) (19,27) (19,23) (19,30) (19,20) (19,22) (19,32) (19,34) (19,26) (19,28) (20,23) (20,30) (20,21) (20,22) (20,32) (20,24) (20,34) (20,26) (21,27) (21,23) (21,30) (21,22) (21,32) (21,24) (21,34) (21,26) (21,28) (22,27) (22,23) (22,24) (22,34) (22,26) (22,28) (23,32) (23,26) (23,28) (24,27) (24,32) (24,34) (24,26) (25,33) (26,30) (26,32) (26,34) (27,30) (27,32) (27,28) (28,30) (28,32) (28,34) (29,33) (29,31) (31,33) (32,34)\nQ: Is there a path between node 6 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1079"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (1,27) (1,24) (1,21) (1,3) (2,10) (2,22) (2,6) (2,18) (2,25) (2,12) (3,19) (3,27) (3,24) (4,10) (4,6) (4,18) (4,25) (5,28) (5,16) (6,10) (6,13) (6,25) (6,12) (6,9) (7,28) (8,10) (8,14) (8,18) (8,29) (8,25) (8,23) (9,13) (9,14) (10,29) (10,25) (12,22) (12,18) (12,17) (13,29) (13,26) (14,20) (14,17) (15,19) (17,25) (18,20) (18,25) (20,29) (20,26) (20,23) (21,27) (21,24) (23,26) (23,25) (24,27) (26,29)\nQ: Is there a path between node 7 and node 20?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1080"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,13) (0,8) (0,18) (0,25) (0,14) (0,17) (0,21) (1,13) (1,26) (1,14) (1,20) (1,17) (1,24) (1,6) (2,8) (2,18) (2,9) (2,26) (2,14) (2,10) (2,15) (3,16) (3,12) (4,13) (4,8) (4,18) (4,25) (4,6) (5,19) (5,13) (5,10) (5,20) (5,22) (5,17) (5,6) (6,8) (6,18) (6,9) (6,26) (6,14) (6,17) (6,21) (6,15) (6,23) (7,25) (7,14) (7,22) (7,24) (7,15) (7,23) (8,13) (8,25) (8,24) (8,23) (9,25) (9,27) (9,26) (9,14) (9,17) (9,24) (9,23) (10,19) (10,13) (10,25) (10,22) (11,12) (12,16) (13,19) (13,18) (13,21) (14,19) (14,18) (14,22) (15,19) (15,25) (15,23) (17,25) (17,22) (17,21) (17,24) (18,21) (18,24) (19,26) (19,22) (19,24) (19,23) (20,25) (20,26) (20,24) (20,23) (21,27) (21,23) (22,25) (22,26) (22,23) (25,27) (25,26)\nQ: Is there a path between node 1 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1081"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,18) (0,19) (0,20) (0,23) (0,9) (0,10) (0,22) (0,13) (0,1) (0,12) (0,5) (0,7) (0,15) (0,4) (1,11) (1,18) (1,19) (1,20) (1,23) (1,9) (1,10) (1,22) (1,13) (1,12) (1,5) (1,7) (1,15) (1,4) (2,8) (2,6) (2,3) (2,24) (2,16) (2,21) (2,17) (2,14) (3,8) (3,6) (3,24) (3,16) (3,21) (3,17) (3,14) (4,11) (4,18) (4,19) (4,20) (4,23) (4,9) (4,10) (4,22) (4,13) (4,12) (4,5) (4,7) (4,15) (5,11) (5,18) (5,19) (5,20) (5,23) (5,9) (5,10) (5,22) (5,13) (5,12) (5,7) (5,15) (6,8) (6,24) (6,16) (6,21) (6,17) (6,14) (7,11) (7,18) (7,19) (7,20) (7,23) (7,9) (7,10) (7,22) (7,13) (7,12) (7,15) (8,24) (8,16) (8,21) (8,17) (8,14) (9,11) (9,18) (9,19) (9,20) (9,23) (9,10) (9,22) (9,13) (9,12) (9,15) (10,11) (10,18) (10,19) (10,20) (10,23) (10,22) (10,13) (10,12) (10,15) (11,18) (11,19) (11,20) (11,23) (11,22) (11,13) (11,12) (11,15) (12,18) (12,19) (12,20) (12,23) (12,22) (12,13) (12,15) (13,18) (13,19) (13,20) (13,23) (13,22) (13,15) (14,24) (14,16) (14,21) (14,17) (15,18) (15,19) (15,20) (15,23) (15,22) (16,24) (16,21) (16,17) (17,24) (17,21) (18,19) (18,20) (18,23) (18,22) (19,20) (19,23) (19,22) (20,23) (20,22) (21,24) (22,23)\nQ: Is there a path between node 3 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1082"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,10) (0,19) (0,16) (0,7) (0,8) (0,4) (0,3) (0,11) (0,1) (0,18) (0,9) (0,5) (0,2) (0,13) (1,17) (1,10) (1,19) (1,16) (1,7) (1,8) (1,4) (1,3) (1,11) (1,18) (1,9) (1,5) (1,2) (1,13) (2,17) (2,10) (2,19) (2,16) (2,7) (2,8) (2,4) (2,3) (2,11) (2,18) (2,9) (2,5) (2,13) (3,17) (3,10) (3,19) (3,16) (3,7) (3,8) (3,4) (3,11) (3,18) (3,9) (3,5) (3,13) (4,17) (4,10) (4,19) (4,16) (4,7) (4,8) (4,11) (4,18) (4,9) (4,5) (4,13) (5,17) (5,10) (5,19) (5,16) (5,7) (5,8) (5,11) (5,18) (5,9) (5,13) (6,15) (7,17) (7,10) (7,19) (7,16) (7,8) (7,11) (7,18) (7,9) (7,13) (8,17) (8,10) (8,19) (8,16) (8,11) (8,18) (8,9) (8,13) (9,17) (9,10) (9,19) (9,16) (9,11) (9,18) (9,13) (10,17) (10,19) (10,16) (10,11) (10,18) (10,13) (11,17) (11,19) (11,16) (11,18) (11,13) (12,14) (13,17) (13,19) (13,16) (13,18) (16,17) (16,19) (16,18) (17,19) (17,18) (18,19)\nQ: Is there a path between node 17 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1083"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,31) (0,11) (0,27) (0,18) (1,4) (1,12) (1,31) (1,7) (1,25) (1,8) (1,18) (2,17) (2,14) (2,6) (2,10) (2,19) (3,17) (3,22) (3,9) (4,12) (4,30) (4,31) (4,13) (4,27) (4,18) (5,29) (5,16) (5,22) (5,21) (5,20) (5,28) (5,19) (6,29) (6,9) (6,10) (6,28) (7,11) (7,27) (7,15) (7,18) (8,30) (8,23) (8,11) (9,14) (9,21) (9,10) (11,23) (11,18) (12,30) (12,31) (12,27) (12,25) (12,15) (12,18) (13,23) (13,25) (13,15) (14,29) (14,17) (16,24) (16,17) (16,20) (17,29) (18,30) (18,26) (20,29) (21,24) (22,24) (23,27) (23,25) (25,26) (25,27) (26,31) (27,31) (28,29)\nQ: Is there a path between node 30 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1084"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (3,8) (3,9) (4,5) (8,9)\nQ: Is there a path between node 9 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1085"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,8) (0,10) (0,4) (0,16) (0,5) (0,2) (0,7) (0,9) (0,15) (0,13) (0,1) (0,12) (0,14) (0,3) (1,11) (1,8) (1,10) (1,4) (1,16) (1,5) (1,2) (1,7) (1,9) (1,15) (1,13) (1,12) (1,14) (1,3) (2,11) (2,8) (2,10) (2,4) (2,16) (2,5) (2,7) (2,9) (2,15) (2,13) (2,12) (2,14) (2,3) (3,11) (3,8) (3,10) (3,4) (3,16) (3,5) (3,7) (3,9) (3,15) (3,13) (3,12) (3,14) (4,11) (4,8) (4,10) (4,16) (4,5) (4,7) (4,9) (4,15) (4,13) (4,12) (4,14) (5,11) (5,8) (5,10) (5,16) (5,7) (5,9) (5,15) (5,13) (5,12) (5,14) (7,11) (7,8) (7,10) (7,16) (7,9) (7,15) (7,13) (7,12) (7,14) (8,11) (8,10) (8,16) (8,9) (8,15) (8,13) (8,12) (8,14) (9,11) (9,10) (9,16) (9,15) (9,13) (9,12) (9,14) (10,11) (10,16) (10,15) (10,13) (10,12) (10,14) (11,16) (11,15) (11,13) (11,12) (11,14) (12,16) (12,15) (12,13) (12,14) (13,16) (13,15) (13,14) (14,16) (14,15) (15,16)\nQ: Is there a path between node 11 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1086"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,8) (0,2) (0,20) (0,16) (0,14) (0,15) (0,7) (1,18) (1,24) (1,22) (1,5) (1,19) (1,11) (1,17) (2,6) (2,4) (2,23) (2,8) (2,20) (2,16) (2,21) (2,14) (2,15) (2,10) (3,6) (3,4) (3,23) (3,8) (3,16) (3,14) (3,25) (3,15) (3,7) (4,6) (4,23) (4,8) (4,20) (4,16) (4,21) (4,14) (4,15) (4,10) (4,7) (5,18) (5,24) (5,22) (5,13) (5,9) (5,11) (5,12) (6,23) (6,8) (6,20) (6,16) (6,14) (6,25) (6,15) (7,23) (7,20) (7,16) (7,21) (7,14) (7,25) (7,15) (7,10) (8,20) (8,16) (8,14) (8,25) (8,15) (9,18) (9,24) (9,22) (9,19) (9,11) (9,17) (9,12) (10,23) (10,20) (10,16) (10,21) (10,14) (10,25) (11,22) (11,19) (11,17) (11,12) (12,18) (12,13) (12,19) (13,18) (13,24) (13,22) (13,17) (14,23) (14,20) (14,16) (14,25) (15,20) (15,16) (15,21) (15,25) (16,23) (16,20) (16,25) (17,18) (17,22) (17,19) (18,24) (18,22) (18,19) (19,24) (19,22) (20,21) (20,25) (21,23) (21,25) (22,24) (23,25)\nQ: Is there a path between node 12 and node 21?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1087"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,10) (0,2) (2,15) (2,20) (2,23) (2,14) (2,17) (2,24) (2,18) (3,21) (4,27) (5,9) (5,22) (6,29) (6,8) (7,29) (7,25) (7,20) (7,17) (7,18) (7,8) (8,23) (8,24) (10,23) (10,18) (11,27) (12,13) (13,21) (14,25) (14,23) (14,17) (14,24) (15,29) (15,25) (15,23) (15,16) (16,29) (16,17) (17,25) (17,23) (17,24) (17,18) (18,29) (20,25) (22,26) (23,25) (24,29) (26,27)\nQ: Is there a path between node 28 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1088"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,15) (0,18) (0,27) (0,9) (0,13) (0,25) (0,3) (1,8) (1,5) (1,26) (1,12) (1,2) (1,16) (1,14) (2,8) (2,26) (2,12) (2,16) (2,14) (3,7) (3,4) (3,15) (3,18) (3,27) (3,13) (4,7) (4,15) (4,18) (4,27) (4,13) (5,8) (5,12) (5,11) (5,16) (5,14) (5,20) (6,17) (6,21) (6,29) (6,28) (7,15) (7,18) (7,27) (7,9) (7,13) (8,26) (8,23) (8,16) (8,14) (9,15) (10,29) (10,24) (11,12) (11,16) (11,14) (11,20) (12,22) (12,23) (12,14) (12,20) (13,18) (13,27) (14,26) (14,22) (14,23) (14,20) (15,18) (15,27) (15,25) (16,26) (16,22) (16,23) (16,20) (17,21) (17,19) (17,24) (17,28) (19,21) (19,29) (19,24) (19,28) (20,26) (20,22) (20,23) (21,29) (21,24) (22,26) (22,23) (24,29) (24,28) (25,27)\nQ: Is there a path between node 5 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1089"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,14) (1,21) (1,3) (1,15) (1,7) (3,12) (4,10) (5,10) (6,22) (7,21) (7,15) (9,12) (11,13) (11,21) (14,20) (15,17) (15,21) (16,18) (18,22)\nQ: Is there a path between node 10 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1090"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,12) (0,2) (0,3) (1,13) (1,22) (1,7) (1,11) (1,19) (1,6) (1,8) (2,14) (2,20) (2,3) (3,14) (3,20) (4,21) (4,18) (4,5) (4,17) (4,9) (4,15) (4,10) (5,21) (5,17) (5,9) (5,15) (5,10) (6,16) (6,13) (6,22) (6,7) (6,11) (6,19) (6,8) (7,16) (7,13) (7,22) (7,8) (8,16) (8,13) (8,11) (8,19) (9,18) (9,17) (9,15) (9,10) (10,21) (10,18) (11,16) (11,13) (11,22) (11,19) (12,14) (12,20) (13,16) (13,19) (14,20) (15,21) (15,18) (15,17) (16,22) (17,21) (17,18) (19,22)\nQ: Is there a path between node 21 and node 14?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1091"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,17) (0,10) (0,28) (0,30) (0,29) (0,3) (1,14) (1,2) (2,25) (2,20) (2,7) (2,32) (2,22) (3,24) (3,19) (3,23) (3,4) (3,12) (3,29) (4,26) (4,24) (4,23) (4,8) (4,13) (5,26) (5,19) (5,23) (5,8) (5,15) (5,21) (6,14) (7,32) (8,16) (8,12) (8,29) (9,26) (9,13) (9,18) (9,29) (9,31) (10,17) (10,11) (10,30) (10,23) (10,13) (11,16) (11,17) (11,19) (11,28) (11,23) (12,26) (12,24) (12,21) (13,26) (13,17) (13,19) (13,30) (13,31) (14,25) (14,22) (15,16) (15,17) (15,23) (15,18) (15,29) (16,26) (16,24) (16,18) (16,21) (17,24) (17,19) (17,28) (17,30) (17,23) (18,24) (18,21) (19,26) (19,24) (19,28) (19,23) (20,32) (22,32) (22,27) (24,26) (24,30) (26,29) (28,29)\nQ: Is there a path between node 13 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1092"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,18) (0,25) (0,19) (0,16) (0,22) (0,8) (0,10) (0,31) (0,13) (0,5) (0,14) (0,24) (0,27) (0,1) (0,15) (0,23) (1,9) (1,30) (1,25) (1,19) (1,16) (1,17) (1,22) (1,8) (1,21) (1,4) (1,31) (1,13) (1,14) (1,24) (1,12) (1,27) (1,15) (2,11) (2,28) (2,29) (2,7) (3,9) (3,18) (3,25) (3,19) (3,16) (3,22) (3,10) (3,4) (3,31) (3,13) (3,5) (3,14) (3,24) (3,12) (3,20) (3,27) (3,15) (3,23) (4,18) (4,30) (4,19) (4,22) (4,8) (4,21) (4,31) (4,5) (4,24) (4,12) (4,27) (4,23) (5,18) (5,30) (5,25) (5,19) (5,17) (5,10) (5,21) (5,31) (5,12) (5,20) (5,15) (5,23) (6,28) (6,29) (6,7) (6,26) (7,28) (8,9) (8,25) (8,19) (8,16) (8,22) (8,10) (8,13) (8,14) (8,24) (8,12) (8,27) (8,15) (8,23) (9,18) (9,30) (9,19) (9,16) (9,17) (9,22) (9,10) (9,31) (9,13) (9,27) (9,15) (9,23) (10,18) (10,30) (10,25) (10,16) (10,22) (10,21) (10,31) (10,14) (10,24) (10,12) (10,20) (10,15) (11,28) (11,26) (12,19) (12,22) (12,21) (12,13) (12,24) (12,15) (12,23) (13,25) (13,19) (13,16) (13,17) (13,22) (13,31) (13,14) (13,27) (14,30) (14,25) (14,16) (14,17) (14,22) (14,31) (14,24) (14,20) (14,15) (14,23) (15,18) (15,30) (15,25) (15,19) (15,16) (15,22) (15,31) (15,24) (16,18) (16,30) (16,22) (16,21) (16,31) (16,20) (16,27) (17,18) (17,30) (17,25) (17,19) (17,22) (17,21) (17,31) (17,24) (17,27) (17,23) (18,30) (18,25) (18,19) (18,22) (18,21) (18,31) (18,24) (18,27) (18,23) (19,30) (19,25) (19,21) (19,24) (19,20) (19,27) (19,23) (20,21) (20,31) (20,24) (20,27) (20,23) (21,25) (21,22) (21,31) (21,24) (21,27) (21,23) (22,30) (22,31) (22,24) (22,23) (23,30) (23,25) (23,24) (23,27) (24,30) (24,25) (24,31) (24,27) (25,30) (25,27) (26,28) (27,30) (27,31) (28,29) (30,31)\nQ: Is there a path between node 18 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1093"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (2,3)\nQ: Is there a path between node 3 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1094"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,1) (2,3) (4,6) (5,6) (5,7)\nQ: Is there a path between node 2 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1095"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,4) (0,9) (0,1) (0,11) (0,2) (1,10) (1,6) (1,9) (1,15) (1,13) (2,12) (2,9) (2,17) (2,15) (3,4) (3,6) (3,11) (4,12) (4,9) (4,11) (6,10) (6,12) (6,9) (6,15) (6,13) (8,12) (8,9) (8,15) (8,13) (9,10) (9,11) (10,13) (10,11) (11,13) (12,13) (14,16)\nQ: Is there a path between node 15 and node 13?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1096"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,6) (3,4) (4,5) (5,10) (6,8) (8,9)\nQ: Is there a path between node 5 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1097"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,18) (0,12) (0,2) (0,11) (0,8) (0,13) (1,4) (1,10) (1,17) (1,5) (1,14) (1,7) (1,6) (1,15) (2,3) (2,18) (2,12) (2,11) (2,8) (2,13) (3,18) (3,12) (3,11) (3,8) (3,13) (4,10) (4,17) (4,5) (4,14) (4,7) (4,6) (4,15) (5,10) (5,17) (5,14) (5,7) (5,6) (5,15) (6,10) (6,17) (6,14) (6,7) (6,15) (7,10) (7,17) (7,14) (7,15) (8,18) (8,12) (8,11) (8,13) (9,16) (10,17) (10,14) (10,15) (11,18) (11,12) (11,13) (12,18) (12,13) (13,18) (14,17) (14,15) (15,17)\nQ: Is there a path between node 5 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1098"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,9) (0,14) (0,18) (0,3) (0,1) (0,17) (0,4) (0,8) (0,7) (0,15) (0,11) (0,10) (0,13) (1,5) (1,9) (1,14) (1,18) (1,3) (1,17) (1,4) (1,8) (1,7) (1,15) (1,11) (1,10) (1,13) (3,5) (3,9) (3,14) (3,18) (3,17) (3,4) (3,8) (3,7) (3,15) (3,11) (3,10) (3,13) (4,5) (4,9) (4,14) (4,18) (4,17) (4,8) (4,7) (4,15) (4,11) (4,10) (4,13) (5,9) (5,14) (5,18) (5,17) (5,8) (5,7) (5,15) (5,11) (5,10) (5,13) (6,12) (6,16) (7,9) (7,14) (7,18) (7,17) (7,8) (7,15) (7,11) (7,10) (7,13) (8,9) (8,14) (8,18) (8,17) (8,15) (8,11) (8,10) (8,13) (9,14) (9,18) (9,17) (9,15) (9,11) (9,10) (9,13) (10,14) (10,18) (10,17) (10,15) (10,11) (10,13) (11,14) (11,18) (11,17) (11,15) (11,13) (12,16) (13,14) (13,18) (13,17) (13,15) (14,18) (14,17) (14,15) (15,18) (15,17) (17,18)\nQ: Is there a path between node 0 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1099"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (1,4) (1,11) (2,21) (2,20) (2,24) (3,24) (4,13) (4,15) (4,8) (5,19) (5,24) (6,20) (6,24) (7,25) (7,21) (8,17) (8,15) (8,12) (9,13) (9,12) (10,16) (11,13) (11,18) (11,23) (11,14) (11,12) (13,17) (14,23) (15,18) (15,23) (18,23) (19,25) (19,24) (20,21) (21,25) (24,25)\nQ: Is there a path between node 17 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1100"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,1) (1,11) (1,5) (1,8) (2,14) (2,10) (2,6) (2,3) (2,13) (2,4) (3,7) (3,14) (3,6) (3,12) (3,13) (3,4) (4,9) (4,7) (4,10) (4,12) (4,13) (5,11) (5,8) (6,7) (6,10) (6,12) (6,13) (7,9) (7,14) (7,10) (7,13) (8,11) (10,14) (10,12) (10,13) (12,14) (12,13) (13,14)\nQ: Is there a path between node 11 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1101"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,20) (0,13) (0,24) (0,4) (1,21) (1,3) (1,11) (1,10) (1,23) (1,8) (1,2) (1,22) (1,19) (1,18) (2,21) (2,3) (2,11) (2,10) (2,23) (2,8) (2,22) (2,19) (2,18) (3,21) (3,11) (3,10) (3,23) (3,8) (3,22) (3,19) (3,18) (4,14) (4,20) (4,13) (4,24) (5,7) (5,9) (5,12) (5,16) (5,15) (5,17) (5,6) (6,7) (6,9) (6,12) (6,16) (6,15) (6,17) (7,9) (7,12) (7,16) (7,15) (7,17) (8,21) (8,11) (8,10) (8,23) (8,22) (8,19) (8,18) (9,12) (9,16) (9,15) (9,17) (10,21) (10,11) (10,23) (10,22) (10,19) (10,18) (11,21) (11,23) (11,22) (11,19) (11,18) (12,16) (12,15) (12,17) (13,14) (13,20) (13,24) (14,20) (14,24) (15,16) (15,17) (16,17) (18,21) (18,23) (18,22) (18,19) (19,21) (19,23) (19,22) (20,24) (21,23) (21,22) (22,23)\nQ: Is there a path between node 13 and node 19?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1102"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,11) (1,9) (1,19) (1,31) (1,20) (2,15) (2,11) (2,27) (2,29) (2,16) (2,31) (3,8) (3,4) (3,12) (3,18) (3,17) (3,10) (3,25) (3,31) (3,20) (4,30) (4,24) (4,19) (5,26) (5,23) (6,13) (7,15) (7,9) (7,30) (7,12) (7,16) (7,19) (7,10) (7,25) (8,15) (8,11) (8,30) (8,24) (8,10) (8,31) (9,11) (9,30) (9,27) (9,29) (9,10) (10,15) (10,30) (10,12) (10,18) (10,19) (10,17) (10,14) (11,30) (11,29) (11,19) (12,15) (12,19) (12,14) (12,20) (13,28) (14,27) (14,24) (14,20) (15,27) (15,18) (15,25) (15,20) (16,29) (16,24) (16,19) (17,29) (17,19) (17,31) (18,30) (18,24) (18,19) (18,31) (19,30) (19,25) (21,28) (21,23) (22,23) (25,27) (25,31) (26,28) (29,31)\nQ: Is there a path between node 24 and node 31?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1103"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,19) (0,17) (0,3) (0,10) (0,14) (1,7) (1,8) (1,15) (1,13) (2,9) (2,12) (2,18) (2,4) (3,6) (3,19) (3,17) (3,16) (3,10) (3,14) (4,12) (4,18) (5,9) (5,18) (6,19) (6,17) (6,16) (6,14) (6,20) (7,8) (7,15) (7,13) (9,12) (9,18) (10,16) (10,14) (10,20) (11,15) (12,18) (13,15) (14,19) (14,17) (14,20) (16,19) (16,17) (17,20) (19,20)\nQ: Is there a path between node 8 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1104"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,4) (0,1) (0,5) (0,24) (0,3) (0,21) (0,19) (0,9) (0,15) (0,20) (0,27) (0,13) (1,24) (1,21) (1,31) (1,10) (1,7) (1,20) (1,27) (1,13) (2,6) (2,5) (2,24) (2,3) (2,21) (2,19) (2,9) (2,31) (2,15) (2,7) (2,27) (2,13) (3,6) (3,4) (3,5) (3,22) (3,24) (3,21) (3,19) (3,9) (3,31) (3,18) (3,7) (3,20) (4,5) (4,21) (4,19) (4,9) (4,31) (4,7) (4,20) (4,27) (4,13) (5,6) (5,22) (5,24) (5,21) (5,9) (5,31) (5,10) (5,15) (5,18) (5,20) (5,27) (5,13) (6,22) (6,21) (6,19) (6,9) (6,31) (6,10) (6,15) (6,18) (6,7) (6,27) (6,13) (7,22) (7,9) (7,10) (7,15) (7,18) (7,20) (7,27) (7,13) (8,16) (8,11) (8,28) (8,12) (8,25) (8,30) (8,14) (8,32) (8,29) (9,22) (9,24) (9,21) (9,19) (9,31) (9,10) (9,15) (9,18) (9,20) (10,22) (10,19) (10,31) (10,15) (10,20) (10,27) (10,13) (11,16) (11,28) (11,26) (11,23) (11,30) (11,14) (11,32) (11,17) (12,16) (12,28) (12,23) (12,30) (12,14) (12,33) (12,32) (12,17) (12,29) (13,22) (13,24) (13,21) (13,19) (13,15) (13,18) (13,20) (14,28) (14,26) (14,23) (14,25) (14,33) (14,32) (14,29) (15,22) (15,24) (15,21) (15,19) (15,20) (15,27) (16,26) (16,25) (16,30) (16,33) (16,32) (16,17) (16,29) (17,28) (17,26) (17,25) (17,30) (17,33) (17,32) (17,29) (18,24) (18,19) (18,31) (19,22) (19,24) (19,31) (19,20) (19,27) (20,21) (20,31) (20,27) (21,31) (23,28) (23,26) (23,25) (23,30) (24,31) (24,27) (25,26) (25,30) (25,33) (25,32) (25,29) (26,28) (26,33) (26,32) (28,30) (28,29) (29,30) (29,33) (29,32) (30,32)\nQ: Is there a path between node 16 and node 30?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1105"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,7) (0,4) (0,10) (0,5) (0,13) (0,12) (0,1) (0,2) (0,3) (0,15) (0,6) (0,8) (0,14) (1,11) (1,7) (1,4) (1,10) (1,5) (1,13) (1,12) (1,2) (1,3) (1,15) (1,6) (1,8) (1,14) (2,11) (2,7) (2,4) (2,10) (2,5) (2,13) (2,12) (2,3) (2,15) (2,6) (2,8) (2,14) (3,11) (3,7) (3,4) (3,10) (3,5) (3,13) (3,12) (3,15) (3,6) (3,8) (3,14) (4,11) (4,7) (4,10) (4,5) (4,13) (4,12) (4,15) (4,6) (4,8) (4,14) (5,11) (5,7) (5,10) (5,13) (5,12) (5,15) (5,6) (5,8) (5,14) (6,11) (6,7) (6,10) (6,13) (6,12) (6,15) (6,8) (6,14) (7,11) (7,10) (7,13) (7,12) (7,15) (7,8) (7,14) (8,11) (8,10) (8,13) (8,12) (8,15) (8,14) (10,11) (10,13) (10,12) (10,15) (10,14) (11,13) (11,12) (11,15) (11,14) (12,13) (12,15) (12,14) (13,15) (13,14) (14,15)\nQ: Is there a path between node 5 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1106"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (0,4) (1,32) (1,22) (1,34) (1,7) (1,5) (1,28) (1,11) (1,13) (1,30) (1,31) (1,26) (2,12) (2,3) (2,24) (2,15) (2,18) (2,8) (2,20) (2,25) (2,19) (2,17) (2,16) (3,10) (3,24) (3,15) (3,18) (3,8) (3,20) (3,14) (3,19) (3,21) (4,23) (4,6) (5,32) (5,22) (5,7) (5,33) (5,11) (5,13) (5,27) (5,31) (5,26) (6,23) (7,22) (7,34) (7,28) (7,13) (7,27) (7,30) (7,26) (7,29) (8,10) (8,24) (8,15) (8,18) (8,20) (8,14) (8,17) (8,21) (8,16) (9,32) (9,22) (9,34) (9,28) (9,13) (9,27) (9,31) (9,26) (9,29) (10,12) (10,24) (10,15) (10,18) (10,20) (10,25) (10,17) (11,32) (11,22) (11,34) (11,28) (11,13) (11,27) (11,30) (11,31) (11,26) (12,24) (12,25) (12,14) (12,17) (12,21) (12,16) (13,34) (13,33) (13,27) (13,30) (13,31) (13,29) (14,15) (14,18) (14,20) (14,25) (14,19) (14,17) (14,21) (14,16) (15,24) (15,18) (15,20) (15,17) (15,21) (16,24) (16,20) (16,19) (16,17) (17,24) (17,20) (17,21) (18,20) (18,25) (18,19) (20,24) (20,25) (20,21) (21,25) (22,32) (22,28) (22,27) (22,30) (22,31) (22,26) (24,25) (26,34) (26,33) (26,31) (27,34) (27,33) (27,28) (27,30) (27,31) (27,29) (28,32) (28,33) (28,30) (28,31) (28,29) (29,32) (29,33) (30,32) (31,32) (31,34) (32,34) (32,33) (33,34)\nQ: Is there a path between node 17 and node 30?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1107"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,1) (0,6) (0,2) (0,3) (0,7) (0,5) (1,8) (1,6) (1,2) (1,3) (1,7) (1,5) (2,8) (2,6) (2,3) (2,7) (2,5) (3,8) (3,6) (3,7) (3,5) (5,8) (5,6) (5,7) (6,8) (6,7) (7,8)\nQ: Is there a path between node 8 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1108"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,9) (0,4) (0,14) (0,6) (0,10) (0,12) (0,2) (1,13) (1,11) (1,3) (1,5) (1,7) (1,16) (1,8) (1,17) (2,15) (2,9) (2,4) (2,14) (2,6) (2,10) (2,12) (3,13) (3,11) (3,5) (3,7) (3,16) (3,8) (3,17) (4,15) (4,9) (4,14) (4,6) (4,10) (4,12) (5,13) (5,11) (5,7) (5,16) (5,8) (5,17) (6,15) (6,9) (6,14) (6,10) (6,12) (7,13) (7,11) (7,16) (7,8) (7,17) (8,13) (8,11) (8,16) (8,17) (9,15) (9,14) (9,10) (9,12) (10,15) (10,14) (10,12) (11,13) (11,16) (11,17) (12,15) (12,14) (13,16) (13,17) (14,15) (16,17)\nQ: Is there a path between node 11 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1109"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,31) (0,11) (0,27) (0,18) (1,4) (1,12) (1,31) (1,7) (1,25) (1,8) (1,18) (2,17) (2,14) (2,6) (2,10) (2,19) (3,17) (3,22) (3,9) (4,12) (4,30) (4,31) (4,13) (4,27) (4,18) (5,29) (5,16) (5,22) (5,21) (5,20) (5,28) (5,19) (6,29) (6,9) (6,10) (6,28) (7,11) (7,27) (7,15) (7,18) (8,30) (8,23) (8,11) (9,14) (9,21) (9,10) (11,23) (11,18) (12,30) (12,31) (12,27) (12,25) (12,15) (12,18) (13,23) (13,25) (13,15) (14,29) (14,17) (16,24) (16,17) (16,20) (17,29) (18,30) (18,26) (20,29) (21,24) (22,24) (23,27) (23,25) (25,26) (25,27) (26,31) (27,31) (28,29)\nQ: Is there a path between node 8 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1110"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (0,10) (0,23) (0,3) (0,9) (0,26) (1,8) (1,20) (1,6) (1,4) (1,19) (1,16) (1,13) (1,24) (2,8) (2,20) (2,4) (2,19) (2,16) (2,13) (2,24) (2,12) (3,10) (3,9) (3,21) (3,22) (4,6) (4,19) (4,13) (4,24) (4,12) (5,15) (5,25) (5,11) (5,7) (6,8) (6,20) (6,19) (6,16) (6,13) (6,24) (7,15) (7,25) (7,14) (8,19) (8,13) (8,24) (8,12) (9,18) (9,23) (10,18) (10,23) (10,21) (10,26) (11,15) (11,17) (11,25) (12,20) (12,19) (12,16) (12,24) (13,20) (13,19) (13,16) (13,24) (14,17) (14,25) (15,17) (15,25) (16,20) (16,24) (17,25) (18,21) (18,22) (19,20) (19,24) (20,24) (21,23) (22,23) (22,26) (23,26)\nQ: Is there a path between node 22 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1111"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,14) (0,20) (0,13) (1,2) (1,8) (1,9) (2,9) (4,10) (4,20) (5,21) (5,17) (5,9) (6,10) (6,14) (6,13) (7,21) (7,22) (8,9) (10,19) (10,18) (10,12) (10,13) (11,16) (11,18) (12,16) (12,19) (12,18) (13,19) (14,19) (16,18) (17,22) (18,19)\nQ: Is there a path between node 11 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1112"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,4) (1,13) (2,11) (3,4) (3,6) (3,19) (4,20) (4,12) (4,16) (5,14) (5,9) (6,18) (6,8) (7,13) (7,8) (7,19) (7,15) (8,18) (8,20) (8,15) (11,14) (12,20) (12,13) (12,19) (12,16) (13,18) (13,15) (15,18) (15,19) (18,20) (18,19)\nQ: Is there a path between node 8 and node 17?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1113"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,4) (0,9) (0,5) (0,13) (1,14) (1,15) (1,12) (1,5) (1,7) (2,4) (2,6) (2,9) (2,12) (2,13) (4,11) (4,6) (4,15) (4,7) (4,8) (4,13) (5,11) (5,10) (5,14) (5,6) (5,9) (5,15) (5,12) (5,7) (5,13) (6,14) (7,14) (7,8) (9,13) (10,14) (12,15)\nQ: Is there a path between node 13 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1114"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,6) (0,11) (0,19) (0,20) (0,1) (0,15) (0,12) (0,7) (0,22) (0,5) (0,21) (0,3) (0,4) (0,18) (0,17) (1,14) (1,6) (1,11) (1,19) (1,20) (1,15) (1,12) (1,7) (1,22) (1,5) (1,21) (1,3) (1,4) (1,18) (1,17) (2,13) (2,10) (2,8) (2,16) (2,9) (3,14) (3,6) (3,11) (3,19) (3,20) (3,15) (3,12) (3,7) (3,22) (3,5) (3,21) (3,4) (3,18) (3,17) (4,14) (4,6) (4,11) (4,19) (4,20) (4,15) (4,12) (4,7) (4,22) (4,5) (4,21) (4,18) (4,17) (5,14) (5,6) (5,11) (5,19) (5,20) (5,15) (5,12) (5,7) (5,22) (5,21) (5,18) (5,17) (6,14) (6,11) (6,19) (6,20) (6,15) (6,12) (6,7) (6,22) (6,21) (6,18) (6,17) (7,14) (7,11) (7,19) (7,20) (7,15) (7,12) (7,22) (7,21) (7,18) (7,17) (8,13) (8,10) (8,16) (8,9) (9,13) (9,10) (9,16) (10,13) (10,16) (11,14) (11,19) (11,20) (11,15) (11,12) (11,22) (11,21) (11,18) (11,17) (12,14) (12,19) (12,20) (12,15) (12,22) (12,21) (12,18) (12,17) (13,16) (14,19) (14,20) (14,15) (14,22) (14,21) (14,18) (14,17) (15,19) (15,20) (15,22) (15,21) (15,18) (15,17) (17,19) (17,20) (17,22) (17,21) (17,18) (18,19) (18,20) (18,22) (18,21) (19,20) (19,22) (19,21) (20,22) (20,21) (21,22)\nQ: Is there a path between node 22 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1115"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,7) (0,2) (0,8) (1,6) (2,3) (3,6) (3,7) (4,6) (4,5) (5,8) (7,8)\nQ: Is there a path between node 3 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1116"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,2) (2,3)\nQ: Is there a path between node 3 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1117"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,5) (3,5)\nQ: Is there a path between node 3 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1118"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (3,7) (4,6) (5,6)\nQ: Is there a path between node 5 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1119"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,8) (0,4) (0,5) (0,13) (0,2) (0,17) (1,15) (1,8) (1,3) (1,4) (1,5) (1,13) (1,17) (2,15) (2,8) (2,3) (2,4) (2,5) (2,13) (3,8) (3,5) (3,17) (4,15) (4,13) (4,17) (5,15) (5,8) (5,17) (6,14) (6,7) (6,10) (6,16) (6,9) (6,12) (7,14) (7,16) (7,9) (8,13) (9,14) (9,10) (9,11) (9,16) (9,12) (10,14) (10,12) (11,14) (11,12) (12,14) (12,16) (13,17) (15,17)\nQ: Is there a path between node 13 and node 14?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1120"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,34) (0,4) (0,7) (0,28) (0,8) (0,15) (0,23) (0,13) (0,22) (0,32) (0,11) (0,18) (1,7) (1,2) (1,13) (1,27) (1,26) (1,9) (2,14) (2,31) (2,15) (2,23) (2,13) (2,9) (2,22) (2,17) (2,32) (2,18) (3,24) (4,7) (4,27) (4,17) (5,16) (5,12) (5,29) (5,20) (6,34) (6,7) (6,14) (6,31) (6,10) (6,23) (6,26) (6,21) (6,17) (6,18) (7,33) (7,14) (7,28) (7,15) (7,26) (7,19) (8,14) (8,28) (8,31) (8,10) (8,13) (8,25) (8,30) (8,18) (9,14) (9,21) (9,25) (9,22) (9,11) (10,31) (10,15) (10,27) (10,25) (10,17) (10,32) (11,28) (11,31) (11,15) (11,13) (11,27) (11,21) (11,25) (11,22) (12,16) (13,33) (13,14) (13,28) (13,26) (13,21) (13,17) (13,32) (13,18) (14,33) (14,31) (14,23) (14,27) (14,25) (15,34) (15,30) (15,17) (15,19) (16,24) (17,23) (17,26) (17,19) (18,34) (18,21) (18,30) (19,33) (19,21) (19,25) (19,30) (21,33) (21,28) (21,25) (21,30) (22,33) (22,23) (22,26) (22,25) (23,34) (23,25) (25,33) (25,32) (26,33) (26,28) (26,31) (26,32) (27,33) (27,32) (32,33)\nQ: Is there a path between node 14 and node 17?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1121"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,1) (1,12) (1,15) (2,9) (2,6) (3,10) (3,17) (3,15) (5,7) (6,10) (6,9) (6,11) (7,13) (8,17) (8,16) (10,15) (11,12) (15,17)\nQ: Is there a path between node 13 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1122"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,20) (0,8) (0,31) (0,22) (1,4) (1,24) (1,19) (1,16) (1,5) (1,2) (1,8) (1,18) (1,27) (2,4) (2,19) (2,12) (2,17) (2,21) (2,31) (2,22) (3,25) (3,20) (3,14) (3,31) (3,22) (3,27) (4,7) (4,21) (4,26) (4,27) (5,11) (5,24) (5,20) (5,19) (5,12) (5,16) (5,17) (5,21) (5,9) (5,22) (6,15) (7,24) (7,20) (7,19) (7,16) (7,29) (7,17) (7,21) (7,14) (7,9) (7,8) (7,18) (7,22) (7,30) (8,20) (8,12) (8,14) (9,20) (9,16) (9,14) (9,18) (9,26) (9,23) (10,15) (11,25) (11,28) (11,20) (11,21) (11,26) (12,28) (12,24) (12,20) (12,29) (12,14) (12,18) (12,26) (12,22) (12,27) (12,23) (14,24) (14,16) (14,18) (14,31) (16,25) (16,26) (16,31) (16,23) (17,31) (17,27) (18,25) (18,28) (18,24) (18,21) (18,26) (18,27) (19,29) (19,21) (19,22) (20,25) (20,21) (20,26) (21,24) (21,29) (21,31) (21,23) (22,29) (22,26) (22,23) (23,25) (23,26) (24,25) (24,26) (24,30) (25,29) (25,31) (26,29) (26,31) (27,28) (27,31) (28,29) (29,31) (29,30) (30,31)\nQ: Is there a path between node 19 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1123"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,9) (0,4) (0,14) (0,6) (0,10) (0,12) (0,2) (1,13) (1,11) (1,3) (1,5) (1,7) (1,16) (1,8) (1,17) (2,15) (2,9) (2,4) (2,14) (2,6) (2,10) (2,12) (3,13) (3,11) (3,5) (3,7) (3,16) (3,8) (3,17) (4,15) (4,9) (4,14) (4,6) (4,10) (4,12) (5,13) (5,11) (5,7) (5,16) (5,8) (5,17) (6,15) (6,9) (6,14) (6,10) (6,12) (7,13) (7,11) (7,16) (7,8) (7,17) (8,13) (8,11) (8,16) (8,17) (9,15) (9,14) (9,10) (9,12) (10,15) (10,14) (10,12) (11,13) (11,16) (11,17) (12,15) (12,14) (13,16) (13,17) (14,15) (16,17)\nQ: Is there a path between node 5 and node 16?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1124"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,13) (0,19) (0,11) (0,16) (0,20) (0,8) (0,5) (0,3) (0,2) (0,7) (0,6) (0,17) (0,14) (0,12) (0,1) (0,18) (0,10) (0,23) (0,9) (1,4) (1,13) (1,19) (1,11) (1,16) (1,20) (1,8) (1,5) (1,3) (1,2) (1,7) (1,6) (1,17) (1,14) (1,12) (1,18) (1,10) (1,23) (1,9) (2,4) (2,13) (2,19) (2,11) (2,16) (2,20) (2,8) (2,5) (2,3) (2,7) (2,6) (2,17) (2,14) (2,12) (2,18) (2,10) (2,23) (2,9) (3,4) (3,13) (3,19) (3,11) (3,16) (3,20) (3,8) (3,5) (3,7) (3,6) (3,17) (3,14) (3,12) (3,18) (3,10) (3,23) (3,9) (4,13) (4,19) (4,11) (4,16) (4,20) (4,8) (4,5) (4,7) (4,6) (4,17) (4,14) (4,12) (4,18) (4,10) (4,23) (4,9) (5,13) (5,19) (5,11) (5,16) (5,20) (5,8) (5,7) (5,6) (5,17) (5,14) (5,12) (5,18) (5,10) (5,23) (5,9) (6,13) (6,19) (6,11) (6,16) (6,20) (6,8) (6,7) (6,17) (6,14) (6,12) (6,18) (6,10) (6,23) (6,9) (7,13) (7,19) (7,11) (7,16) (7,20) (7,8) (7,17) (7,14) (7,12) (7,18) (7,10) (7,23) (7,9) (8,13) (8,19) (8,11) (8,16) (8,20) (8,17) (8,14) (8,12) (8,18) (8,10) (8,23) (8,9) (9,13) (9,19) (9,11) (9,16) (9,20) (9,17) (9,14) (9,12) (9,18) (9,10) (9,23) (10,13) (10,19) (10,11) (10,16) (10,20) (10,17) (10,14) (10,12) (10,18) (10,23) (11,13) (11,19) (11,16) (11,20) (11,17) (11,14) (11,12) (11,18) (11,23) (12,13) (12,19) (12,16) (12,20) (12,17) (12,14) (12,18) (12,23) (13,19) (13,16) (13,20) (13,17) (13,14) (13,18) (13,23) (14,19) (14,16) (14,20) (14,17) (14,18) (14,23) (15,21) (15,22) (16,19) (16,20) (16,17) (16,18) (16,23) (17,19) (17,20) (17,18) (17,23) (18,19) (18,20) (18,23) (19,20) (19,23) (20,23) (21,22)\nQ: Is there a path between node 15 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1125"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,5) (0,7) (0,2) (0,8) (0,4) (0,9) (0,1) (0,12) (0,3) (0,11) (0,13) (1,10) (1,5) (1,7) (1,2) (1,8) (1,4) (1,9) (1,12) (1,3) (1,11) (1,13) (2,10) (2,5) (2,7) (2,8) (2,4) (2,9) (2,12) (2,3) (2,11) (2,13) (3,10) (3,5) (3,7) (3,8) (3,4) (3,9) (3,12) (3,11) (3,13) (4,10) (4,5) (4,7) (4,8) (4,9) (4,12) (4,11) (4,13) (5,10) (5,7) (5,8) (5,9) (5,12) (5,11) (5,13) (7,10) (7,8) (7,9) (7,12) (7,11) (7,13) (8,10) (8,9) (8,12) (8,11) (8,13) (9,10) (9,12) (9,11) (9,13) (10,12) (10,11) (10,13) (11,12) (11,13) (12,13)\nQ: Is there a path between node 10 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1126"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,13) (2,25) (2,28) (2,21) (2,5) (2,23) (3,22) (3,8) (3,6) (3,19) (3,21) (3,31) (3,15) (5,20) (5,16) (5,21) (5,23) (6,18) (6,17) (6,23) (7,10) (8,21) (9,24) (12,22) (12,18) (13,30) (13,27) (14,26) (15,16) (15,19) (15,31) (16,22) (16,20) (16,19) (17,20) (17,21) (17,31) (18,22) (18,25) (18,20) (18,21) (18,23) (19,25) (19,28) (20,28) (20,21) (21,25) (22,25) (22,28) (23,28) (27,29) (29,30) (30,32)\nQ: Is there a path between node 30 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1127"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (1,4) (2,4)\nQ: Is there a path between node 3 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1128"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,31) (0,11) (0,27) (0,18) (1,4) (1,12) (1,31) (1,7) (1,25) (1,8) (1,18) (2,17) (2,14) (2,6) (2,10) (2,19) (3,17) (3,22) (3,9) (4,12) (4,30) (4,31) (4,13) (4,27) (4,18) (5,29) (5,16) (5,22) (5,21) (5,20) (5,28) (5,19) (6,29) (6,9) (6,10) (6,28) (7,11) (7,27) (7,15) (7,18) (8,30) (8,23) (8,11) (9,14) (9,21) (9,10) (11,23) (11,18) (12,30) (12,31) (12,27) (12,25) (12,15) (12,18) (13,23) (13,25) (13,15) (14,29) (14,17) (16,24) (16,17) (16,20) (17,29) (18,30) (18,26) (20,29) (21,24) (22,24) (23,27) (23,25) (25,26) (25,27) (26,31) (27,31) (28,29)\nQ: Is there a path between node 7 and node 30?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1129"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,12) (0,2) (0,3) (1,13) (1,22) (1,7) (1,11) (1,19) (1,6) (1,8) (2,14) (2,20) (2,3) (3,14) (3,20) (4,21) (4,18) (4,5) (4,17) (4,9) (4,15) (4,10) (5,21) (5,17) (5,9) (5,15) (5,10) (6,16) (6,13) (6,22) (6,7) (6,11) (6,19) (6,8) (7,16) (7,13) (7,22) (7,8) (8,16) (8,13) (8,11) (8,19) (9,18) (9,17) (9,15) (9,10) (10,21) (10,18) (11,16) (11,13) (11,22) (11,19) (12,14) (12,20) (13,16) (13,19) (14,20) (15,21) (15,18) (15,17) (16,22) (17,21) (17,18) (19,22)\nQ: Is there a path between node 16 and node 17?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1130"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,11) (0,13) (0,3) (0,15) (0,4) (0,2) (1,7) (1,8) (2,14) (2,23) (2,21) (2,6) (2,10) (3,9) (3,17) (3,13) (3,5) (3,19) (3,4) (3,16) (3,10) (4,9) (4,22) (4,6) (5,11) (5,18) (5,23) (6,9) (6,14) (6,17) (6,20) (6,15) (6,21) (7,8) (9,17) (9,15) (9,21) (10,18) (10,12) (10,16) (11,17) (11,15) (11,22) (11,16) (12,15) (12,22) (13,23) (13,16) (14,17) (14,18) (14,20) (14,21) (14,22) (14,16) (15,20) (17,20) (17,19) (17,23) (18,19) (18,23) (19,20) (19,23) (21,23) (21,22)\nQ: Is there a path between node 20 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1131"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (1,8) (1,4) (1,5) (1,7) (1,2) (1,9) (1,6) (2,8) (2,4) (2,5) (2,7) (2,9) (2,6) (4,8) (4,5) (4,7) (4,9) (4,6) (5,8) (5,7) (5,9) (5,6) (6,8) (6,7) (6,9) (7,8) (7,9) (8,9)\nQ: Is there a path between node 1 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1132"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,17) (0,23) (0,22) (0,1) (0,9) (0,11) (0,14) (0,19) (0,12) (0,18) (0,8) (0,4) (0,16) (0,15) (0,10) (0,6) (1,20) (1,17) (1,23) (1,22) (1,9) (1,11) (1,14) (1,19) (1,12) (1,18) (1,8) (1,4) (1,16) (1,15) (1,10) (1,6) (2,13) (2,5) (2,3) (2,21) (2,7) (3,13) (3,5) (3,21) (3,7) (4,20) (4,17) (4,23) (4,22) (4,9) (4,11) (4,14) (4,19) (4,12) (4,18) (4,8) (4,16) (4,15) (4,10) (4,6) (5,13) (5,21) (5,7) (6,20) (6,17) (6,23) (6,22) (6,9) (6,11) (6,14) (6,19) (6,12) (6,18) (6,8) (6,16) (6,15) (6,10) (7,13) (7,21) (8,20) (8,17) (8,23) (8,22) (8,9) (8,11) (8,14) (8,19) (8,12) (8,18) (8,16) (8,15) (8,10) (9,20) (9,17) (9,23) (9,22) (9,11) (9,14) (9,19) (9,12) (9,18) (9,16) (9,15) (9,10) (10,20) (10,17) (10,23) (10,22) (10,11) (10,14) (10,19) (10,12) (10,18) (10,16) (10,15) (11,20) (11,17) (11,23) (11,22) (11,14) (11,19) (11,12) (11,18) (11,16) (11,15) (12,20) (12,17) (12,23) (12,22) (12,14) (12,19) (12,18) (12,16) (12,15) (13,21) (14,20) (14,17) (14,23) (14,22) (14,19) (14,18) (14,16) (14,15) (15,20) (15,17) (15,23) (15,22) (15,19) (15,18) (15,16) (16,20) (16,17) (16,23) (16,22) (16,19) (16,18) (17,20) (17,23) (17,22) (17,19) (17,18) (18,20) (18,23) (18,22) (18,19) (19,20) (19,23) (19,22) (20,23) (20,22) (22,23)\nQ: Is there a path between node 4 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1133"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,4) (0,1) (0,11) (0,9) (0,12) (1,2) (1,4) (1,11) (1,9) (1,13) (1,8) (1,12) (2,6) (2,3) (2,4) (2,11) (2,9) (2,13) (2,8) (3,6) (3,9) (3,13) (3,8) (3,12) (4,6) (4,11) (4,9) (4,13) (4,8) (4,12) (5,7) (5,10) (6,11) (6,9) (6,8) (6,12) (8,9) (8,12) (9,11) (9,12) (11,13) (12,13)\nQ: Is there a path between node 0 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1134"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,2) (1,5) (1,2) (2,5) (2,10) (3,10) (3,4) (3,8) (4,5) (5,10) (5,8) (7,11) (8,10) (9,11)\nQ: Is there a path between node 8 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1135"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,14) (0,5) (0,9) (0,8) (0,6) (0,21) (1,4) (1,15) (1,18) (1,11) (1,10) (1,12) (2,20) (2,14) (2,5) (2,9) (2,22) (2,6) (2,16) (3,9) (3,23) (3,22) (3,6) (3,21) (4,15) (4,11) (4,19) (4,13) (5,20) (5,14) (5,9) (5,8) (5,6) (5,21) (6,20) (6,14) (6,9) (6,23) (6,8) (6,16) (7,18) (7,11) (7,10) (7,12) (7,19) (7,13) (8,20) (8,14) (8,23) (8,21) (9,20) (9,23) (9,22) (9,21) (10,15) (10,18) (10,11) (10,12) (10,19) (10,13) (11,15) (11,13) (12,18) (12,19) (13,18) (13,19) (14,23) (14,22) (14,21) (15,19) (16,23) (16,22) (20,21) (22,23)\nQ: Is there a path between node 0 and node 15?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1136"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (1,2)\nQ: Is there a path between node 3 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1137"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,1) (1,12) (1,15) (2,9) (2,6) (3,10) (3,17) (3,15) (5,7) (6,10) (6,9) (6,11) (7,13) (8,17) (8,16) (10,15) (11,12) (15,17)\nQ: Is there a path between node 16 and node 14?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1138"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,4) (0,9) (0,1) (0,11) (0,2) (1,10) (1,6) (1,9) (1,15) (1,13) (2,12) (2,9) (2,17) (2,15) (3,4) (3,6) (3,11) (4,12) (4,9) (4,11) (6,10) (6,12) (6,9) (6,15) (6,13) (8,12) (8,9) (8,15) (8,13) (9,10) (9,11) (10,13) (10,11) (11,13) (12,13) (14,16)\nQ: Is there a path between node 13 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1139"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,4) (0,9) (0,5) (0,13) (1,14) (1,15) (1,12) (1,5) (1,7) (2,4) (2,6) (2,9) (2,12) (2,13) (4,11) (4,6) (4,15) (4,7) (4,8) (4,13) (5,11) (5,10) (5,14) (5,6) (5,9) (5,15) (5,12) (5,7) (5,13) (6,14) (7,14) (7,8) (9,13) (10,14) (12,15)\nQ: Is there a path between node 8 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1140"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,8) (0,10) (0,12) (0,13) (1,10) (2,5) (2,16) (3,13) (4,16) (5,7) (5,14) (6,7) (7,16) (7,14) (9,13) (10,15) (11,12) (12,15)\nQ: Is there a path between node 4 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1141"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,5) (0,2) (0,3) (0,10) (0,6) (0,1) (0,4) (0,9) (0,7) (0,12) (1,8) (1,5) (1,2) (1,3) (1,10) (1,6) (1,4) (1,9) (1,7) (1,12) (2,8) (2,5) (2,3) (2,10) (2,6) (2,4) (2,9) (2,7) (2,12) (3,8) (3,5) (3,10) (3,6) (3,4) (3,9) (3,7) (3,12) (4,8) (4,5) (4,10) (4,6) (4,9) (4,7) (4,12) (5,8) (5,10) (5,6) (5,9) (5,7) (5,12) (6,8) (6,10) (6,9) (6,7) (6,12) (7,8) (7,10) (7,9) (7,12) (8,10) (8,9) (8,12) (9,10) (9,12) (10,12) (11,13)\nQ: Is there a path between node 2 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1142"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,7) (0,8) (0,9) (0,13) (0,14) (0,15) (0,5) (1,2) (1,12) (1,16) (1,11) (1,3) (1,6) (1,14) (1,4) (2,12) (2,7) (2,9) (2,13) (2,14) (3,16) (3,11) (3,7) (3,8) (3,14) (3,15) (3,5) (3,4) (4,12) (4,11) (4,8) (4,9) (4,13) (4,14) (4,5) (5,12) (5,16) (5,11) (5,7) (5,8) (5,13) (5,14) (5,15) (6,12) (6,16) (6,11) (6,7) (6,14) (6,15) (7,12) (7,16) (7,11) (7,8) (7,9) (7,13) (8,12) (8,16) (8,11) (8,9) (8,13) (8,14) (9,12) (9,16) (9,11) (9,14) (9,15) (11,12) (11,16) (11,14) (12,13) (12,15) (13,16) (13,15) (14,16)\nQ: Is there a path between node 10 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1143"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,17) (0,23) (0,22) (0,1) (0,9) (0,11) (0,14) (0,19) (0,12) (0,18) (0,8) (0,4) (0,16) (0,15) (0,10) (0,6) (1,20) (1,17) (1,23) (1,22) (1,9) (1,11) (1,14) (1,19) (1,12) (1,18) (1,8) (1,4) (1,16) (1,15) (1,10) (1,6) (2,13) (2,5) (2,3) (2,21) (2,7) (3,13) (3,5) (3,21) (3,7) (4,20) (4,17) (4,23) (4,22) (4,9) (4,11) (4,14) (4,19) (4,12) (4,18) (4,8) (4,16) (4,15) (4,10) (4,6) (5,13) (5,21) (5,7) (6,20) (6,17) (6,23) (6,22) (6,9) (6,11) (6,14) (6,19) (6,12) (6,18) (6,8) (6,16) (6,15) (6,10) (7,13) (7,21) (8,20) (8,17) (8,23) (8,22) (8,9) (8,11) (8,14) (8,19) (8,12) (8,18) (8,16) (8,15) (8,10) (9,20) (9,17) (9,23) (9,22) (9,11) (9,14) (9,19) (9,12) (9,18) (9,16) (9,15) (9,10) (10,20) (10,17) (10,23) (10,22) (10,11) (10,14) (10,19) (10,12) (10,18) (10,16) (10,15) (11,20) (11,17) (11,23) (11,22) (11,14) (11,19) (11,12) (11,18) (11,16) (11,15) (12,20) (12,17) (12,23) (12,22) (12,14) (12,19) (12,18) (12,16) (12,15) (13,21) (14,20) (14,17) (14,23) (14,22) (14,19) (14,18) (14,16) (14,15) (15,20) (15,17) (15,23) (15,22) (15,19) (15,18) (15,16) (16,20) (16,17) (16,23) (16,22) (16,19) (16,18) (17,20) (17,23) (17,22) (17,19) (17,18) (18,20) (18,23) (18,22) (18,19) (19,20) (19,23) (19,22) (20,23) (20,22) (22,23)\nQ: Is there a path between node 4 and node 16?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1144"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,14) (0,20) (0,13) (1,2) (1,8) (1,9) (2,9) (4,10) (4,20) (5,21) (5,17) (5,9) (6,10) (6,14) (6,13) (7,21) (7,22) (8,9) (10,19) (10,18) (10,12) (10,13) (11,16) (11,18) (12,16) (12,19) (12,18) (13,19) (14,19) (16,18) (17,22) (18,19)\nQ: Is there a path between node 10 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1145"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,23) (0,8) (1,6) (1,26) (1,11) (2,6) (2,11) (3,12) (3,19) (3,20) (4,13) (4,21) (4,17) (4,10) (4,6) (4,23) (4,8) (5,13) (5,7) (5,21) (5,17) (5,28) (5,6) (5,23) (5,8) (5,26) (5,24) (5,11) (6,13) (6,17) (6,10) (6,23) (6,24) (7,17) (7,28) (7,23) (8,21) (8,10) (9,15) (10,13) (10,21) (10,23) (10,11) (11,13) (11,17) (12,19) (12,14) (12,27) (12,15) (12,22) (13,17) (13,16) (14,22) (15,19) (16,17) (16,28) (16,24) (17,24) (18,19) (18,27) (19,27) (21,26) (21,24) (22,25) (23,28) (24,28) (25,27)\nQ: Is there a path between node 9 and node 24?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1146"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,2) (2,3)\nQ: Is there a path between node 1 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1147"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,2) (0,14) (0,7) (0,13) (1,17) (1,3) (1,10) (1,6) (2,11) (2,12) (2,14) (2,13) (3,17) (3,10) (3,6) (4,9) (4,5) (5,9) (5,16) (6,17) (6,8) (6,10) (7,11) (7,12) (7,14) (7,13) (8,17) (8,15) (9,18) (9,16) (10,17) (12,14) (12,13) (13,14) (15,17)\nQ: Is there a path between node 17 and node 14?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1148"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,6) (0,2) (0,5) (1,7) (1,16) (1,14) (1,17) (1,3) (1,9) (1,13) (1,10) (2,11) (2,6) (2,5) (3,7) (3,16) (3,14) (3,17) (3,9) (3,13) (3,10) (4,8) (4,15) (4,12) (5,11) (5,6) (6,11) (7,16) (7,14) (7,17) (7,9) (7,13) (7,10) (8,15) (8,12) (9,16) (9,14) (9,17) (9,13) (9,10) (10,16) (10,14) (10,17) (10,13) (12,15) (13,16) (13,14) (13,17) (14,16) (14,17) (16,17)\nQ: Is there a path between node 9 and node 15?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1149"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,28) (0,26) (0,7) (0,22) (0,6) (0,1) (0,30) (0,3) (1,16) (1,28) (1,26) (1,22) (1,10) (1,30) (2,4) (2,29) (2,24) (2,14) (2,21) (2,25) (2,13) (2,12) (2,31) (2,19) (2,33) (2,27) (2,23) (2,8) (2,18) (3,16) (3,28) (3,26) (3,9) (3,7) (3,10) (4,29) (4,32) (4,24) (4,21) (4,25) (4,15) (4,12) (4,31) (4,19) (4,33) (4,27) (4,17) (4,23) (4,18) (5,32) (5,14) (5,21) (5,15) (5,12) (5,19) (5,33) (5,27) (5,23) (5,8) (6,28) (6,26) (6,7) (6,22) (6,10) (7,16) (7,9) (7,22) (7,10) (8,29) (8,32) (8,24) (8,21) (8,15) (8,13) (8,33) (8,27) (8,23) (8,18) (9,16) (9,28) (9,26) (9,22) (9,10) (10,28) (10,22) (10,30) (12,29) (12,14) (12,21) (12,25) (12,15) (12,13) (12,31) (12,19) (12,33) (12,17) (12,23) (12,18) (13,20) (13,29) (13,24) (13,21) (13,25) (13,15) (13,31) (13,19) (13,33) (13,27) (13,17) (13,23) (13,18) (14,20) (14,29) (14,32) (14,24) (14,21) (14,15) (14,31) (14,19) (14,33) (14,17) (14,18) (15,20) (15,29) (15,32) (15,24) (15,21) (15,25) (15,31) (15,19) (15,33) (15,27) (15,17) (15,23) (15,18) (16,28) (16,26) (16,22) (16,30) (17,20) (17,29) (17,32) (17,24) (17,21) (17,25) (17,31) (17,19) (17,18) (18,20) (18,29) (18,32) (18,24) (18,21) (18,25) (18,31) (18,19) (18,27) (18,23) (19,32) (19,24) (19,33) (19,27) (19,23) (20,29) (20,32) (20,24) (20,21) (20,25) (20,31) (20,33) (20,27) (20,23) (21,32) (21,24) (21,25) (21,31) (21,33) (21,27) (21,23) (22,26) (22,30) (23,29) (23,32) (23,24) (23,25) (23,31) (23,33) (23,27) (24,32) (24,25) (24,31) (24,27) (25,29) (25,33) (25,27) (26,28) (26,30) (27,29) (27,31) (27,33) (28,30) (29,32) (29,31) (29,33) (31,32) (31,33) (32,33)\nQ: Is there a path between node 10 and node 20?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1150"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,8) (1,5) (1,10) (1,8) (2,6) (2,7) (3,9) (3,10) (4,11) (4,8) (6,7) (8,9) (8,10) (11,12)\nQ: Is there a path between node 10 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1151"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,2) (3,5)\nQ: Is there a path between node 3 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1152"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,10) (0,17) (0,15) (0,4) (0,12) (0,24) (0,9) (0,3) (0,13) (0,23) (0,7) (0,19) (0,16) (0,6) (0,25) (0,8) (1,10) (1,17) (1,4) (1,12) (1,24) (1,3) (1,13) (1,23) (1,26) (1,22) (1,19) (1,6) (1,14) (1,25) (1,8) (1,20) (2,10) (2,17) (2,11) (2,4) (2,24) (2,9) (2,3) (2,13) (2,23) (2,26) (2,7) (2,22) (2,19) (2,6) (2,14) (2,25) (2,8) (3,10) (3,17) (3,11) (3,15) (3,4) (3,12) (3,24) (3,9) (3,13) (3,26) (3,7) (3,19) (3,16) (3,14) (3,25) (3,8) (3,20) (4,10) (4,17) (4,11) (4,15) (4,12) (4,24) (4,9) (4,7) (4,19) (4,16) (4,6) (4,25) (4,20) (5,18) (6,10) (6,17) (6,15) (6,12) (6,24) (6,9) (6,23) (6,7) (6,16) (6,25) (6,8) (7,10) (7,11) (7,15) (7,12) (7,13) (7,22) (7,19) (7,16) (7,25) (7,8) (7,20) (8,10) (8,17) (8,11) (8,15) (8,12) (8,24) (8,9) (8,23) (8,22) (8,19) (8,16) (8,14) (8,25) (8,20) (9,10) (9,17) (9,11) (9,12) (9,24) (9,13) (9,23) (9,26) (9,22) (9,19) (9,16) (9,20) (10,17) (10,11) (10,15) (10,12) (10,24) (10,13) (10,23) (10,26) (10,19) (10,14) (10,20) (11,15) (11,12) (11,24) (11,13) (11,23) (11,26) (11,19) (11,16) (11,14) (11,20) (12,15) (12,24) (12,23) (12,22) (12,19) (12,16) (12,14) (12,25) (12,20) (13,15) (13,24) (13,23) (13,19) (13,16) (13,14) (13,25) (13,20) (14,17) (14,15) (14,24) (14,23) (14,26) (14,22) (14,19) (14,16) (14,25) (14,20) (15,17) (15,24) (15,23) (15,26) (15,16) (15,20) (16,24) (16,23) (16,26) (16,19) (16,25) (16,20) (17,23) (17,20) (18,21) (19,23) (19,22) (19,25) (19,20) (20,24) (20,23) (20,22) (20,25) (22,26) (22,25) (23,24) (23,26) (23,25) (24,26) (24,25) (25,26)\nQ: Is there a path between node 18 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1153"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,20) (0,27) (0,29) (0,26) (0,17) (0,3) (0,1) (0,16) (1,6) (1,7) (1,20) (1,19) (1,3) (1,33) (1,4) (2,27) (2,34) (2,26) (2,19) (2,17) (2,3) (2,21) (2,4) (3,6) (3,7) (3,11) (3,28) (3,29) (4,6) (4,28) (4,27) (4,29) (4,26) (4,19) (4,33) (4,23) (5,7) (5,11) (5,28) (5,19) (5,33) (5,16) (6,7) (6,28) (6,27) (6,26) (6,21) (7,34) (8,13) (8,12) (8,22) (8,15) (9,24) (9,12) (9,10) (10,25) (11,16) (11,23) (12,32) (12,18) (12,22) (12,15) (13,14) (14,18) (14,15) (15,30) (15,18) (16,27) (16,17) (16,23) (17,29) (17,19) (17,33) (17,23) (18,31) (18,24) (19,28) (19,27) (19,34) (19,29) (19,33) (19,21) (20,21) (21,26) (21,33) (22,30) (22,25) (25,30) (25,31) (26,28) (26,34) (26,29) (27,28) (30,32) (31,32)\nQ: Is there a path between node 7 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1154"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,9) (0,14) (0,18) (0,3) (0,1) (0,17) (0,4) (0,8) (0,7) (0,15) (0,11) (0,10) (0,13) (1,5) (1,9) (1,14) (1,18) (1,3) (1,17) (1,4) (1,8) (1,7) (1,15) (1,11) (1,10) (1,13) (3,5) (3,9) (3,14) (3,18) (3,17) (3,4) (3,8) (3,7) (3,15) (3,11) (3,10) (3,13) (4,5) (4,9) (4,14) (4,18) (4,17) (4,8) (4,7) (4,15) (4,11) (4,10) (4,13) (5,9) (5,14) (5,18) (5,17) (5,8) (5,7) (5,15) (5,11) (5,10) (5,13) (6,12) (6,16) (7,9) (7,14) (7,18) (7,17) (7,8) (7,15) (7,11) (7,10) (7,13) (8,9) (8,14) (8,18) (8,17) (8,15) (8,11) (8,10) (8,13) (9,14) (9,18) (9,17) (9,15) (9,11) (9,10) (9,13) (10,14) (10,18) (10,17) (10,15) (10,11) (10,13) (11,14) (11,18) (11,17) (11,15) (11,13) (12,16) (13,14) (13,18) (13,17) (13,15) (14,18) (14,17) (14,15) (15,18) (15,17) (17,18)\nQ: Is there a path between node 12 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1155"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,10) (0,2) (2,15) (2,20) (2,23) (2,14) (2,17) (2,24) (2,18) (3,21) (4,27) (5,9) (5,22) (6,29) (6,8) (7,29) (7,25) (7,20) (7,17) (7,18) (7,8) (8,23) (8,24) (10,23) (10,18) (11,27) (12,13) (13,21) (14,25) (14,23) (14,17) (14,24) (15,29) (15,25) (15,23) (15,16) (16,29) (16,17) (17,25) (17,23) (17,24) (17,18) (18,29) (20,25) (22,26) (23,25) (24,29) (26,27)\nQ: Is there a path between node 11 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1156"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,8) (0,2) (0,20) (0,16) (0,14) (0,15) (0,7) (1,18) (1,24) (1,22) (1,5) (1,19) (1,11) (1,17) (2,6) (2,4) (2,23) (2,8) (2,20) (2,16) (2,21) (2,14) (2,15) (2,10) (3,6) (3,4) (3,23) (3,8) (3,16) (3,14) (3,25) (3,15) (3,7) (4,6) (4,23) (4,8) (4,20) (4,16) (4,21) (4,14) (4,15) (4,10) (4,7) (5,18) (5,24) (5,22) (5,13) (5,9) (5,11) (5,12) (6,23) (6,8) (6,20) (6,16) (6,14) (6,25) (6,15) (7,23) (7,20) (7,16) (7,21) (7,14) (7,25) (7,15) (7,10) (8,20) (8,16) (8,14) (8,25) (8,15) (9,18) (9,24) (9,22) (9,19) (9,11) (9,17) (9,12) (10,23) (10,20) (10,16) (10,21) (10,14) (10,25) (11,22) (11,19) (11,17) (11,12) (12,18) (12,13) (12,19) (13,18) (13,24) (13,22) (13,17) (14,23) (14,20) (14,16) (14,25) (15,20) (15,16) (15,21) (15,25) (16,23) (16,20) (16,25) (17,18) (17,22) (17,19) (18,24) (18,22) (18,19) (19,24) (19,22) (20,21) (20,25) (21,23) (21,25) (22,24) (23,25)\nQ: Is there a path between node 18 and node 23?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1157"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (0,4) (1,32) (1,22) (1,34) (1,7) (1,5) (1,28) (1,11) (1,13) (1,30) (1,31) (1,26) (2,12) (2,3) (2,24) (2,15) (2,18) (2,8) (2,20) (2,25) (2,19) (2,17) (2,16) (3,10) (3,24) (3,15) (3,18) (3,8) (3,20) (3,14) (3,19) (3,21) (4,23) (4,6) (5,32) (5,22) (5,7) (5,33) (5,11) (5,13) (5,27) (5,31) (5,26) (6,23) (7,22) (7,34) (7,28) (7,13) (7,27) (7,30) (7,26) (7,29) (8,10) (8,24) (8,15) (8,18) (8,20) (8,14) (8,17) (8,21) (8,16) (9,32) (9,22) (9,34) (9,28) (9,13) (9,27) (9,31) (9,26) (9,29) (10,12) (10,24) (10,15) (10,18) (10,20) (10,25) (10,17) (11,32) (11,22) (11,34) (11,28) (11,13) (11,27) (11,30) (11,31) (11,26) (12,24) (12,25) (12,14) (12,17) (12,21) (12,16) (13,34) (13,33) (13,27) (13,30) (13,31) (13,29) (14,15) (14,18) (14,20) (14,25) (14,19) (14,17) (14,21) (14,16) (15,24) (15,18) (15,20) (15,17) (15,21) (16,24) (16,20) (16,19) (16,17) (17,24) (17,20) (17,21) (18,20) (18,25) (18,19) (20,24) (20,25) (20,21) (21,25) (22,32) (22,28) (22,27) (22,30) (22,31) (22,26) (24,25) (26,34) (26,33) (26,31) (27,34) (27,33) (27,28) (27,30) (27,31) (27,29) (28,32) (28,33) (28,30) (28,31) (28,29) (29,32) (29,33) (30,32) (31,32) (31,34) (32,34) (32,33) (33,34)\nQ: Is there a path between node 17 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1158"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,6) (0,11) (0,19) (0,20) (0,1) (0,15) (0,12) (0,7) (0,22) (0,5) (0,21) (0,3) (0,4) (0,18) (0,17) (1,14) (1,6) (1,11) (1,19) (1,20) (1,15) (1,12) (1,7) (1,22) (1,5) (1,21) (1,3) (1,4) (1,18) (1,17) (2,13) (2,10) (2,8) (2,16) (2,9) (3,14) (3,6) (3,11) (3,19) (3,20) (3,15) (3,12) (3,7) (3,22) (3,5) (3,21) (3,4) (3,18) (3,17) (4,14) (4,6) (4,11) (4,19) (4,20) (4,15) (4,12) (4,7) (4,22) (4,5) (4,21) (4,18) (4,17) (5,14) (5,6) (5,11) (5,19) (5,20) (5,15) (5,12) (5,7) (5,22) (5,21) (5,18) (5,17) (6,14) (6,11) (6,19) (6,20) (6,15) (6,12) (6,7) (6,22) (6,21) (6,18) (6,17) (7,14) (7,11) (7,19) (7,20) (7,15) (7,12) (7,22) (7,21) (7,18) (7,17) (8,13) (8,10) (8,16) (8,9) (9,13) (9,10) (9,16) (10,13) (10,16) (11,14) (11,19) (11,20) (11,15) (11,12) (11,22) (11,21) (11,18) (11,17) (12,14) (12,19) (12,20) (12,15) (12,22) (12,21) (12,18) (12,17) (13,16) (14,19) (14,20) (14,15) (14,22) (14,21) (14,18) (14,17) (15,19) (15,20) (15,22) (15,21) (15,18) (15,17) (17,19) (17,20) (17,22) (17,21) (17,18) (18,19) (18,20) (18,22) (18,21) (19,20) (19,22) (19,21) (20,22) (20,21) (21,22)\nQ: Is there a path between node 0 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1159"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,13) (0,11) (0,21) (0,8) (0,18) (0,3) (0,7) (0,15) (0,20) (0,17) (0,10) (0,22) (0,1) (0,9) (0,6) (0,19) (1,23) (1,14) (1,5) (1,13) (1,11) (1,12) (1,21) (1,8) (1,18) (1,3) (1,25) (1,7) (1,28) (1,15) (1,20) (1,17) (1,10) (1,22) (1,9) (1,6) (1,16) (1,19) (3,27) (3,14) (3,5) (3,13) (3,4) (3,21) (3,18) (3,25) (3,28) (3,15) (3,20) (3,17) (3,22) (3,6) (3,16) (3,19) (4,27) (4,23) (4,5) (4,13) (4,11) (4,12) (4,8) (4,28) (4,15) (4,20) (4,17) (4,10) (4,24) (4,6) (5,27) (5,23) (5,14) (5,13) (5,11) (5,12) (5,21) (5,8) (5,18) (5,25) (5,7) (5,15) (5,10) (5,22) (5,24) (5,9) (5,6) (5,16) (5,19) (6,27) (6,14) (6,11) (6,12) (6,18) (6,25) (6,7) (6,20) (6,17) (6,10) (6,22) (6,24) (6,9) (6,16) (6,19) (7,23) (7,14) (7,13) (7,12) (7,21) (7,8) (7,25) (7,28) (7,20) (7,10) (7,22) (7,16) (7,19) (8,27) (8,13) (8,18) (8,25) (8,15) (8,17) (8,10) (8,22) (8,24) (8,9) (8,16) (8,19) (9,27) (9,23) (9,11) (9,21) (9,25) (9,28) (9,15) (9,20) (9,17) (9,10) (9,22) (9,24) (9,16) (9,19) (10,27) (10,14) (10,11) (10,12) (10,25) (10,28) (10,15) (10,20) (10,17) (10,24) (10,16) (10,19) (11,23) (11,21) (11,18) (11,25) (11,28) (11,15) (11,17) (11,22) (11,24) (11,19) (12,27) (12,23) (12,13) (12,21) (12,18) (12,25) (12,28) (12,15) (12,17) (12,22) (12,24) (12,16) (13,27) (13,14) (13,21) (13,18) (13,28) (13,15) (13,17) (13,24) (13,16) (13,19) (14,27) (14,25) (14,28) (14,15) (14,17) (14,22) (14,24) (14,16) (15,23) (15,21) (15,18) (15,25) (15,20) (15,24) (16,27) (16,23) (16,17) (16,24) (16,19) (17,27) (17,23) (17,18) (17,25) (17,28) (17,20) (17,22) (17,24) (17,19) (18,23) (18,21) (18,25) (18,28) (18,20) (18,22) (18,24) (18,19) (19,27) (19,23) (19,21) (19,25) (19,24) (20,27) (20,23) (20,21) (20,25) (20,24) (21,23) (21,22) (23,27) (23,24) (25,27) (25,28) (27,28)\nQ: Is there a path between node 14 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1160"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,5) (0,7) (0,2) (0,8) (0,4) (0,9) (0,1) (0,12) (0,3) (0,11) (0,13) (1,10) (1,5) (1,7) (1,2) (1,8) (1,4) (1,9) (1,12) (1,3) (1,11) (1,13) (2,10) (2,5) (2,7) (2,8) (2,4) (2,9) (2,12) (2,3) (2,11) (2,13) (3,10) (3,5) (3,7) (3,8) (3,4) (3,9) (3,12) (3,11) (3,13) (4,10) (4,5) (4,7) (4,8) (4,9) (4,12) (4,11) (4,13) (5,10) (5,7) (5,8) (5,9) (5,12) (5,11) (5,13) (7,10) (7,8) (7,9) (7,12) (7,11) (7,13) (8,10) (8,9) (8,12) (8,11) (8,13) (9,10) (9,12) (9,11) (9,13) (10,12) (10,11) (10,13) (11,12) (11,13) (12,13)\nQ: Is there a path between node 6 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1161"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,4) (0,12) (0,11) (0,10) (0,3) (0,17) (0,21) (0,27) (0,15) (0,23) (0,31) (0,29) (0,2) (0,8) (0,9) (0,14) (0,18) (1,5) (1,26) (1,13) (1,20) (1,32) (1,7) (2,19) (2,4) (2,28) (2,22) (2,16) (2,12) (2,10) (2,3) (2,17) (2,21) (2,27) (2,15) (2,23) (2,31) (2,29) (2,8) (2,9) (2,14) (2,18) (3,4) (3,22) (3,16) (3,12) (3,10) (3,17) (3,21) (3,27) (3,23) (3,31) (3,29) (3,6) (3,9) (3,14) (3,18) (4,16) (4,12) (4,11) (4,17) (4,21) (4,15) (4,30) (4,23) (4,29) (4,6) (4,8) (4,9) (4,18) (5,26) (5,13) (5,25) (5,24) (5,32) (5,7) (6,19) (6,22) (6,12) (6,11) (6,10) (6,17) (6,21) (6,27) (6,15) (6,30) (6,23) (6,31) (6,29) (6,9) (6,14) (7,26) (7,25) (7,32) (8,19) (8,28) (8,10) (8,17) (8,27) (8,15) (8,30) (8,23) (9,19) (9,28) (9,22) (9,16) (9,12) (9,10) (9,17) (9,21) (9,15) (9,30) (9,23) (9,29) (9,18) (10,19) (10,28) (10,22) (10,12) (10,11) (10,17) (10,21) (10,27) (10,15) (10,30) (10,23) (10,31) (10,29) (10,14) (10,18) (11,16) (11,12) (11,17) (11,21) (11,27) (11,15) (11,30) (11,31) (11,29) (11,14) (11,18) (12,19) (12,28) (12,22) (12,17) (12,27) (12,15) (12,30) (12,23) (12,31) (12,29) (12,14) (12,18) (13,26) (13,25) (13,20) (13,32) (14,28) (14,16) (14,17) (14,21) (14,27) (14,15) (14,31) (14,29) (14,18) (15,19) (15,22) (15,16) (15,17) (15,21) (15,27) (15,30) (15,23) (15,31) (15,29) (15,18) (16,19) (16,28) (16,22) (16,17) (16,21) (16,27) (16,30) (16,31) (16,18) (17,22) (17,21) (17,30) (17,31) (17,29) (17,18) (18,19) (18,28) (18,22) (18,21) (18,27) (18,29) (19,28) (19,22) (19,21) (19,30) (19,31) (19,29) (20,32) (21,28) (21,22) (21,27) (21,29) (22,28) (22,30) (22,23) (22,31) (22,29) (23,28) (23,27) (23,30) (23,31) (23,29) (24,26) (24,25) (25,26) (25,32) (26,32) (27,28) (27,30) (27,29) (28,30) (28,31) (28,29) (29,30) (29,31)\nQ: Is there a path between node 28 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1162"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (1,20) (2,11) (2,23) (2,14) (2,8) (3,17) (3,14) (3,16) (4,7) (4,16) (4,8) (4,24) (5,6) (5,10) (5,20) (6,20) (7,12) (7,16) (7,8) (7,24) (8,12) (8,23) (8,21) (9,18) (10,18) (10,20) (11,17) (11,19) (11,24) (12,22) (12,17) (12,14) (13,24) (14,23) (14,24) (15,17) (15,19) (15,24) (16,22) (16,19) (17,19) (17,24) (19,24) (23,24)\nQ: Is there a path between node 15 and node 16?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1163"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,9) (0,2) (0,5) (0,10) (0,1) (1,4) (1,9) (1,2) (1,5) (1,10) (2,4) (2,9) (2,5) (2,10) (3,11) (3,8) (3,12) (3,7) (3,6) (4,9) (4,5) (4,10) (5,9) (5,10) (6,11) (6,8) (6,12) (6,7) (7,11) (7,8) (7,12) (8,11) (8,12) (9,10) (11,12)\nQ: Is there a path between node 12 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1164"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,4) (0,9) (0,1) (0,11) (0,2) (1,10) (1,6) (1,9) (1,15) (1,13) (2,12) (2,9) (2,17) (2,15) (3,4) (3,6) (3,11) (4,12) (4,9) (4,11) (6,10) (6,12) (6,9) (6,15) (6,13) (8,12) (8,9) (8,15) (8,13) (9,10) (9,11) (10,13) (10,11) (11,13) (12,13) (14,16)\nQ: Is there a path between node 15 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1165"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,3) (1,20) (1,21) (1,8) (1,5) (1,16) (1,17) (1,19) (1,6) (1,12) (1,14) (1,9) (1,13) (1,18) (1,7) (1,11) (1,15) (1,2) (1,10) (2,20) (2,21) (2,8) (2,5) (2,16) (2,17) (2,19) (2,6) (2,12) (2,14) (2,9) (2,13) (2,18) (2,7) (2,11) (2,15) (2,10) (3,4) (5,20) (5,21) (5,8) (5,16) (5,17) (5,19) (5,6) (5,12) (5,14) (5,9) (5,13) (5,18) (5,7) (5,11) (5,15) (5,10) (6,20) (6,21) (6,8) (6,16) (6,17) (6,19) (6,12) (6,14) (6,9) (6,13) (6,18) (6,7) (6,11) (6,15) (6,10) (7,20) (7,21) (7,8) (7,16) (7,17) (7,19) (7,12) (7,14) (7,9) (7,13) (7,18) (7,11) (7,15) (7,10) (8,20) (8,21) (8,16) (8,17) (8,19) (8,12) (8,14) (8,9) (8,13) (8,18) (8,11) (8,15) (8,10) (9,20) (9,21) (9,16) (9,17) (9,19) (9,12) (9,14) (9,13) (9,18) (9,11) (9,15) (9,10) (10,20) (10,21) (10,16) (10,17) (10,19) (10,12) (10,14) (10,13) (10,18) (10,11) (10,15) (11,20) (11,21) (11,16) (11,17) (11,19) (11,12) (11,14) (11,13) (11,18) (11,15) (12,20) (12,21) (12,16) (12,17) (12,19) (12,14) (12,13) (12,18) (12,15) (13,20) (13,21) (13,16) (13,17) (13,19) (13,14) (13,18) (13,15) (14,20) (14,21) (14,16) (14,17) (14,19) (14,18) (14,15) (15,20) (15,21) (15,16) (15,17) (15,19) (15,18) (16,20) (16,21) (16,17) (16,19) (16,18) (17,20) (17,21) (17,19) (17,18) (18,20) (18,21) (18,19) (19,20) (19,21) (20,21)\nQ: Is there a path between node 6 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1166"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,12) (0,2) (0,3) (1,13) (1,22) (1,7) (1,11) (1,19) (1,6) (1,8) (2,14) (2,20) (2,3) (3,14) (3,20) (4,21) (4,18) (4,5) (4,17) (4,9) (4,15) (4,10) (5,21) (5,17) (5,9) (5,15) (5,10) (6,16) (6,13) (6,22) (6,7) (6,11) (6,19) (6,8) (7,16) (7,13) (7,22) (7,8) (8,16) (8,13) (8,11) (8,19) (9,18) (9,17) (9,15) (9,10) (10,21) (10,18) (11,16) (11,13) (11,22) (11,19) (12,14) (12,20) (13,16) (13,19) (14,20) (15,21) (15,18) (15,17) (16,22) (17,21) (17,18) (19,22)\nQ: Is there a path between node 4 and node 18?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1167"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,4) (0,12) (0,11) (0,10) (0,3) (0,17) (0,21) (0,27) (0,15) (0,23) (0,31) (0,29) (0,2) (0,8) (0,9) (0,14) (0,18) (1,5) (1,26) (1,13) (1,20) (1,32) (1,7) (2,19) (2,4) (2,28) (2,22) (2,16) (2,12) (2,10) (2,3) (2,17) (2,21) (2,27) (2,15) (2,23) (2,31) (2,29) (2,8) (2,9) (2,14) (2,18) (3,4) (3,22) (3,16) (3,12) (3,10) (3,17) (3,21) (3,27) (3,23) (3,31) (3,29) (3,6) (3,9) (3,14) (3,18) (4,16) (4,12) (4,11) (4,17) (4,21) (4,15) (4,30) (4,23) (4,29) (4,6) (4,8) (4,9) (4,18) (5,26) (5,13) (5,25) (5,24) (5,32) (5,7) (6,19) (6,22) (6,12) (6,11) (6,10) (6,17) (6,21) (6,27) (6,15) (6,30) (6,23) (6,31) (6,29) (6,9) (6,14) (7,26) (7,25) (7,32) (8,19) (8,28) (8,10) (8,17) (8,27) (8,15) (8,30) (8,23) (9,19) (9,28) (9,22) (9,16) (9,12) (9,10) (9,17) (9,21) (9,15) (9,30) (9,23) (9,29) (9,18) (10,19) (10,28) (10,22) (10,12) (10,11) (10,17) (10,21) (10,27) (10,15) (10,30) (10,23) (10,31) (10,29) (10,14) (10,18) (11,16) (11,12) (11,17) (11,21) (11,27) (11,15) (11,30) (11,31) (11,29) (11,14) (11,18) (12,19) (12,28) (12,22) (12,17) (12,27) (12,15) (12,30) (12,23) (12,31) (12,29) (12,14) (12,18) (13,26) (13,25) (13,20) (13,32) (14,28) (14,16) (14,17) (14,21) (14,27) (14,15) (14,31) (14,29) (14,18) (15,19) (15,22) (15,16) (15,17) (15,21) (15,27) (15,30) (15,23) (15,31) (15,29) (15,18) (16,19) (16,28) (16,22) (16,17) (16,21) (16,27) (16,30) (16,31) (16,18) (17,22) (17,21) (17,30) (17,31) (17,29) (17,18) (18,19) (18,28) (18,22) (18,21) (18,27) (18,29) (19,28) (19,22) (19,21) (19,30) (19,31) (19,29) (20,32) (21,28) (21,22) (21,27) (21,29) (22,28) (22,30) (22,23) (22,31) (22,29) (23,28) (23,27) (23,30) (23,31) (23,29) (24,26) (24,25) (25,26) (25,32) (26,32) (27,28) (27,30) (27,29) (28,30) (28,31) (28,29) (29,30) (29,31)\nQ: Is there a path between node 29 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1168"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,5) (0,2) (0,3) (0,10) (0,6) (0,1) (0,4) (0,9) (0,7) (0,12) (1,8) (1,5) (1,2) (1,3) (1,10) (1,6) (1,4) (1,9) (1,7) (1,12) (2,8) (2,5) (2,3) (2,10) (2,6) (2,4) (2,9) (2,7) (2,12) (3,8) (3,5) (3,10) (3,6) (3,4) (3,9) (3,7) (3,12) (4,8) (4,5) (4,10) (4,6) (4,9) (4,7) (4,12) (5,8) (5,10) (5,6) (5,9) (5,7) (5,12) (6,8) (6,10) (6,9) (6,7) (6,12) (7,8) (7,10) (7,9) (7,12) (8,10) (8,9) (8,12) (9,10) (9,12) (10,12) (11,13)\nQ: Is there a path between node 13 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1169"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 0 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1170"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,28) (0,26) (0,7) (0,22) (0,6) (0,1) (0,30) (0,3) (1,16) (1,28) (1,26) (1,22) (1,10) (1,30) (2,4) (2,29) (2,24) (2,14) (2,21) (2,25) (2,13) (2,12) (2,31) (2,19) (2,33) (2,27) (2,23) (2,8) (2,18) (3,16) (3,28) (3,26) (3,9) (3,7) (3,10) (4,29) (4,32) (4,24) (4,21) (4,25) (4,15) (4,12) (4,31) (4,19) (4,33) (4,27) (4,17) (4,23) (4,18) (5,32) (5,14) (5,21) (5,15) (5,12) (5,19) (5,33) (5,27) (5,23) (5,8) (6,28) (6,26) (6,7) (6,22) (6,10) (7,16) (7,9) (7,22) (7,10) (8,29) (8,32) (8,24) (8,21) (8,15) (8,13) (8,33) (8,27) (8,23) (8,18) (9,16) (9,28) (9,26) (9,22) (9,10) (10,28) (10,22) (10,30) (12,29) (12,14) (12,21) (12,25) (12,15) (12,13) (12,31) (12,19) (12,33) (12,17) (12,23) (12,18) (13,20) (13,29) (13,24) (13,21) (13,25) (13,15) (13,31) (13,19) (13,33) (13,27) (13,17) (13,23) (13,18) (14,20) (14,29) (14,32) (14,24) (14,21) (14,15) (14,31) (14,19) (14,33) (14,17) (14,18) (15,20) (15,29) (15,32) (15,24) (15,21) (15,25) (15,31) (15,19) (15,33) (15,27) (15,17) (15,23) (15,18) (16,28) (16,26) (16,22) (16,30) (17,20) (17,29) (17,32) (17,24) (17,21) (17,25) (17,31) (17,19) (17,18) (18,20) (18,29) (18,32) (18,24) (18,21) (18,25) (18,31) (18,19) (18,27) (18,23) (19,32) (19,24) (19,33) (19,27) (19,23) (20,29) (20,32) (20,24) (20,21) (20,25) (20,31) (20,33) (20,27) (20,23) (21,32) (21,24) (21,25) (21,31) (21,33) (21,27) (21,23) (22,26) (22,30) (23,29) (23,32) (23,24) (23,25) (23,31) (23,33) (23,27) (24,32) (24,25) (24,31) (24,27) (25,29) (25,33) (25,27) (26,28) (26,30) (27,29) (27,31) (27,33) (28,30) (29,32) (29,31) (29,33) (31,32) (31,33) (32,33)\nQ: Is there a path between node 28 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1171"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,26) (2,26) (2,30) (2,6) (3,19) (4,29) (4,8) (4,11) (4,9) (5,25) (6,30) (6,19) (6,13) (6,25) (7,23) (7,29) (7,10) (7,28) (7,14) (8,23) (8,15) (8,27) (8,18) (8,11) (8,28) (8,9) (9,23) (9,29) (9,15) (9,18) (9,12) (10,15) (11,29) (11,27) (11,28) (11,14) (12,27) (13,16) (13,26) (14,17) (15,29) (15,21) (15,28) (16,25) (17,23) (17,29) (17,18) (19,20) (19,22) (20,22) (21,27) (21,28) (22,26) (23,29) (23,28) (24,26) (24,30) (25,26) (25,30) (27,28)\nQ: Is there a path between node 3 and node 29?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1172"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,5) (0,11) (0,8) (0,6) (0,1) (1,10) (1,3) (1,5) (1,9) (1,6) (1,2) (2,10) (2,3) (2,5) (2,9) (2,8) (2,7) (2,6) (2,13) (3,9) (3,11) (3,8) (3,7) (4,12) (5,10) (5,9) (5,8) (5,7) (5,6) (6,10) (6,9) (6,11) (6,8) (7,10) (7,11) (7,8) (7,13) (8,10) (8,11) (8,13) (9,10) (9,11) (9,13) (10,11) (10,13)\nQ: Is there a path between node 2 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1173"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,3) (0,4) (1,3) (1,4) (3,4)\nQ: Is there a path between node 2 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1174"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,21) (1,17) (1,15) (1,2) (1,4) (1,18) (2,8) (2,13) (2,17) (2,15) (2,23) (2,22) (2,4) (2,18) (2,12) (4,21) (4,8) (4,13) (4,15) (4,23) (4,22) (4,18) (4,12) (5,21) (5,8) (5,13) (5,17) (5,15) (5,22) (5,18) (7,14) (7,16) (7,10) (7,11) (7,19) (8,21) (8,17) (8,23) (8,18) (9,14) (9,24) (10,14) (10,24) (10,19) (11,14) (11,16) (11,24) (12,21) (12,13) (12,17) (12,15) (12,23) (12,22) (12,18) (13,21) (13,17) (13,15) (13,23) (13,22) (14,24) (15,21) (15,17) (15,23) (15,22) (15,18) (16,19) (17,21) (17,18) (18,21) (18,23) (21,22) (22,23)\nQ: Is there a path between node 18 and node 12?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1175"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,13) (0,17) (0,10) (0,5) (0,4) (0,16) (0,19) (0,20) (0,7) (0,8) (0,15) (0,1) (0,18) (0,9) (0,12) (1,13) (1,17) (1,10) (1,5) (1,4) (1,16) (1,19) (1,20) (1,7) (1,8) (1,15) (1,18) (1,9) (1,12) (2,11) (2,21) (2,3) (2,14) (3,11) (3,21) (3,14) (4,13) (4,17) (4,10) (4,5) (4,16) (4,19) (4,20) (4,7) (4,8) (4,15) (4,18) (4,9) (4,12) (5,13) (5,17) (5,10) (5,16) (5,19) (5,20) (5,7) (5,8) (5,15) (5,18) (5,9) (5,12) (7,13) (7,17) (7,10) (7,16) (7,19) (7,20) (7,8) (7,15) (7,18) (7,9) (7,12) (8,13) (8,17) (8,10) (8,16) (8,19) (8,20) (8,15) (8,18) (8,9) (8,12) (9,13) (9,17) (9,10) (9,16) (9,19) (9,20) (9,15) (9,18) (9,12) (10,13) (10,17) (10,16) (10,19) (10,20) (10,15) (10,18) (10,12) (11,21) (11,14) (12,13) (12,17) (12,16) (12,19) (12,20) (12,15) (12,18) (13,17) (13,16) (13,19) (13,20) (13,15) (13,18) (14,21) (15,17) (15,16) (15,19) (15,20) (15,18) (16,17) (16,19) (16,20) (16,18) (17,19) (17,20) (17,18) (18,19) (18,20) (19,20)\nQ: Is there a path between node 13 and node 16?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1176"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,11) (0,1) (0,3) (0,10) (0,4) (1,11) (1,3) (1,10) (1,4) (2,7) (3,11) (3,4) (4,5) (4,11) (5,11) (6,9) (6,8) (7,9) (7,8) (8,9) (10,11)\nQ: Is there a path between node 9 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1177"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,23) (0,8) (1,6) (1,26) (1,11) (2,6) (2,11) (3,12) (3,19) (3,20) (4,13) (4,21) (4,17) (4,10) (4,6) (4,23) (4,8) (5,13) (5,7) (5,21) (5,17) (5,28) (5,6) (5,23) (5,8) (5,26) (5,24) (5,11) (6,13) (6,17) (6,10) (6,23) (6,24) (7,17) (7,28) (7,23) (8,21) (8,10) (9,15) (10,13) (10,21) (10,23) (10,11) (11,13) (11,17) (12,19) (12,14) (12,27) (12,15) (12,22) (13,17) (13,16) (14,22) (15,19) (16,17) (16,28) (16,24) (17,24) (18,19) (18,27) (19,27) (21,26) (21,24) (22,25) (23,28) (24,28) (25,27)\nQ: Is there a path between node 15 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1178"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,24) (0,1) (0,6) (0,14) (1,10) (2,25) (2,5) (2,20) (2,18) (3,22) (3,6) (3,19) (3,23) (4,9) (4,18) (5,15) (5,25) (5,17) (5,20) (6,11) (6,24) (6,14) (6,7) (6,21) (7,24) (8,25) (8,17) (8,20) (8,18) (9,25) (10,24) (10,22) (10,21) (11,22) (11,19) (11,23) (12,15) (12,16) (12,17) (13,19) (13,14) (14,22) (14,19) (15,16) (15,18) (16,17) (17,20) (18,25) (19,24) (19,22) (20,25) (21,23) (22,24) (22,23)\nQ: Is there a path between node 4 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1179"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,15) (0,18) (0,27) (0,9) (0,13) (0,25) (0,3) (1,8) (1,5) (1,26) (1,12) (1,2) (1,16) (1,14) (2,8) (2,26) (2,12) (2,16) (2,14) (3,7) (3,4) (3,15) (3,18) (3,27) (3,13) (4,7) (4,15) (4,18) (4,27) (4,13) (5,8) (5,12) (5,11) (5,16) (5,14) (5,20) (6,17) (6,21) (6,29) (6,28) (7,15) (7,18) (7,27) (7,9) (7,13) (8,26) (8,23) (8,16) (8,14) (9,15) (10,29) (10,24) (11,12) (11,16) (11,14) (11,20) (12,22) (12,23) (12,14) (12,20) (13,18) (13,27) (14,26) (14,22) (14,23) (14,20) (15,18) (15,27) (15,25) (16,26) (16,22) (16,23) (16,20) (17,21) (17,19) (17,24) (17,28) (19,21) (19,29) (19,24) (19,28) (20,26) (20,22) (20,23) (21,29) (21,24) (22,26) (22,23) (24,29) (24,28) (25,27)\nQ: Is there a path between node 26 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1180"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (1,3) (1,2) (1,6) (2,5) (2,6) (3,5) (5,6)\nQ: Is there a path between node 3 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1181"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,4) (1,23) (1,7) (1,18) (1,24) (1,32) (1,31) (1,21) (1,27) (1,11) (1,6) (1,29) (1,17) (1,20) (2,23) (2,7) (2,18) (2,33) (2,24) (2,31) (2,21) (2,8) (2,27) (2,11) (2,29) (2,17) (2,26) (3,9) (3,22) (3,13) (3,5) (3,30) (3,28) (3,16) (3,14) (3,15) (4,19) (4,10) (5,9) (5,22) (5,13) (5,28) (5,16) (5,14) (6,18) (6,32) (6,25) (6,21) (6,8) (6,11) (6,17) (6,20) (6,26) (7,18) (7,33) (7,24) (7,32) (7,25) (7,31) (7,21) (7,17) (7,20) (7,26) (8,18) (8,33) (8,32) (8,25) (8,31) (8,27) (8,11) (8,29) (8,20) (8,26) (9,22) (9,13) (9,30) (9,28) (9,14) (9,15) (10,19) (10,12) (11,18) (11,33) (11,24) (11,25) (11,31) (11,27) (11,29) (11,26) (12,19) (13,28) (13,15) (14,30) (14,28) (14,16) (14,15) (15,22) (15,30) (15,16) (16,22) (17,23) (17,18) (17,33) (17,25) (17,31) (17,21) (17,27) (17,29) (17,20) (17,26) (18,23) (18,32) (18,25) (18,21) (18,29) (18,20) (18,26) (20,23) (20,33) (20,32) (20,25) (20,31) (20,21) (20,27) (20,29) (20,26) (21,23) (21,33) (21,24) (21,25) (21,29) (23,33) (23,24) (23,25) (23,31) (23,27) (23,29) (23,26) (24,33) (24,32) (24,25) (24,27) (24,29) (24,26) (25,32) (25,31) (25,27) (25,29) (25,26) (26,33) (26,31) (26,27) (27,31) (27,29) (28,30) (31,32) (32,33)\nQ: Is there a path between node 16 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1182"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,1) (1,11) (1,5) (1,8) (2,14) (2,10) (2,6) (2,3) (2,13) (2,4) (3,7) (3,14) (3,6) (3,12) (3,13) (3,4) (4,9) (4,7) (4,10) (4,12) (4,13) (5,11) (5,8) (6,7) (6,10) (6,12) (6,13) (7,9) (7,14) (7,10) (7,13) (8,11) (10,14) (10,12) (10,13) (12,14) (12,13) (13,14)\nQ: Is there a path between node 2 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1183"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,4) (0,1) (1,2) (1,5) (1,4) (2,5) (2,4) (4,5)\nQ: Is there a path between node 3 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1184"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,8) (1,5) (1,10) (1,8) (2,6) (2,7) (3,9) (3,10) (4,11) (4,8) (6,7) (8,9) (8,10) (11,12)\nQ: Is there a path between node 1 and node 12?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1185"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,6) (0,2) (0,5) (1,7) (1,16) (1,14) (1,17) (1,3) (1,9) (1,13) (1,10) (2,11) (2,6) (2,5) (3,7) (3,16) (3,14) (3,17) (3,9) (3,13) (3,10) (4,8) (4,15) (4,12) (5,11) (5,6) (6,11) (7,16) (7,14) (7,17) (7,9) (7,13) (7,10) (8,15) (8,12) (9,16) (9,14) (9,17) (9,13) (9,10) (10,16) (10,14) (10,17) (10,13) (12,15) (13,16) (13,14) (13,17) (14,16) (14,17) (16,17)\nQ: Is there a path between node 7 and node 13?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1186"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,5) (0,7) (0,2) (0,8) (0,4) (0,9) (0,1) (0,12) (0,3) (0,11) (0,13) (1,10) (1,5) (1,7) (1,2) (1,8) (1,4) (1,9) (1,12) (1,3) (1,11) (1,13) (2,10) (2,5) (2,7) (2,8) (2,4) (2,9) (2,12) (2,3) (2,11) (2,13) (3,10) (3,5) (3,7) (3,8) (3,4) (3,9) (3,12) (3,11) (3,13) (4,10) (4,5) (4,7) (4,8) (4,9) (4,12) (4,11) (4,13) (5,10) (5,7) (5,8) (5,9) (5,12) (5,11) (5,13) (7,10) (7,8) (7,9) (7,12) (7,11) (7,13) (8,10) (8,9) (8,12) (8,11) (8,13) (9,10) (9,12) (9,11) (9,13) (10,12) (10,11) (10,13) (11,12) (11,13) (12,13)\nQ: Is there a path between node 10 and node 12?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1187"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,7) (0,12) (0,32) (0,22) (0,9) (0,20) (0,2) (0,5) (0,14) (0,4) (0,26) (0,21) (1,11) (1,8) (1,24) (1,3) (1,31) (1,28) (1,6) (2,16) (2,7) (2,32) (2,22) (2,9) (2,20) (2,14) (2,4) (2,21) (3,11) (3,8) (3,24) (3,31) (3,28) (4,16) (4,32) (4,22) (4,9) (4,20) (4,5) (4,14) (4,26) (5,16) (5,7) (5,12) (5,32) (5,22) (5,9) (5,20) (5,14) (5,26) (5,21) (6,8) (6,24) (6,31) (6,28) (7,12) (7,32) (7,22) (7,9) (7,14) (7,26) (7,21) (8,24) (8,31) (8,28) (9,16) (9,12) (9,32) (9,20) (9,26) (9,21) (10,23) (10,13) (10,29) (10,19) (10,25) (10,18) (12,32) (12,22) (12,20) (12,26) (12,21) (13,30) (13,27) (13,29) (13,19) (13,25) (13,18) (14,16) (14,32) (14,22) (14,20) (14,26) (15,30) (15,29) (15,25) (15,18) (16,32) (16,22) (16,20) (16,26) (16,21) (17,30) (17,27) (18,30) (18,29) (19,30) (19,23) (19,27) (19,25) (20,32) (20,22) (20,26) (21,32) (21,26) (22,32) (22,26) (23,30) (23,29) (23,25) (24,28) (26,32) (27,30) (27,29) (28,31) (29,30)\nQ: Is there a path between node 15 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1188"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,2) (0,14) (0,7) (0,13) (1,17) (1,3) (1,10) (1,6) (2,11) (2,12) (2,14) (2,13) (3,17) (3,10) (3,6) (4,9) (4,5) (5,9) (5,16) (6,17) (6,8) (6,10) (7,11) (7,12) (7,14) (7,13) (8,17) (8,15) (9,18) (9,16) (10,17) (12,14) (12,13) (13,14) (15,17)\nQ: Is there a path between node 12 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1189"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (0,13) (0,22) (1,12) (1,6) (2,20) (2,14) (2,11) (3,5) (3,23) (3,6) (5,17) (6,19) (7,23) (8,13) (8,15) (9,21) (9,18) (12,24) (12,17) (12,19) (13,21) (13,18) (13,25) (13,15) (13,16) (15,16) (16,21) (16,25) (17,23) (17,19) (19,26) (21,22) (22,25)\nQ: Is there a path between node 0 and node 17?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1190"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,18) (0,25) (0,19) (0,16) (0,22) (0,8) (0,10) (0,31) (0,13) (0,5) (0,14) (0,24) (0,27) (0,1) (0,15) (0,23) (1,9) (1,30) (1,25) (1,19) (1,16) (1,17) (1,22) (1,8) (1,21) (1,4) (1,31) (1,13) (1,14) (1,24) (1,12) (1,27) (1,15) (2,11) (2,28) (2,29) (2,7) (3,9) (3,18) (3,25) (3,19) (3,16) (3,22) (3,10) (3,4) (3,31) (3,13) (3,5) (3,14) (3,24) (3,12) (3,20) (3,27) (3,15) (3,23) (4,18) (4,30) (4,19) (4,22) (4,8) (4,21) (4,31) (4,5) (4,24) (4,12) (4,27) (4,23) (5,18) (5,30) (5,25) (5,19) (5,17) (5,10) (5,21) (5,31) (5,12) (5,20) (5,15) (5,23) (6,28) (6,29) (6,7) (6,26) (7,28) (8,9) (8,25) (8,19) (8,16) (8,22) (8,10) (8,13) (8,14) (8,24) (8,12) (8,27) (8,15) (8,23) (9,18) (9,30) (9,19) (9,16) (9,17) (9,22) (9,10) (9,31) (9,13) (9,27) (9,15) (9,23) (10,18) (10,30) (10,25) (10,16) (10,22) (10,21) (10,31) (10,14) (10,24) (10,12) (10,20) (10,15) (11,28) (11,26) (12,19) (12,22) (12,21) (12,13) (12,24) (12,15) (12,23) (13,25) (13,19) (13,16) (13,17) (13,22) (13,31) (13,14) (13,27) (14,30) (14,25) (14,16) (14,17) (14,22) (14,31) (14,24) (14,20) (14,15) (14,23) (15,18) (15,30) (15,25) (15,19) (15,16) (15,22) (15,31) (15,24) (16,18) (16,30) (16,22) (16,21) (16,31) (16,20) (16,27) (17,18) (17,30) (17,25) (17,19) (17,22) (17,21) (17,31) (17,24) (17,27) (17,23) (18,30) (18,25) (18,19) (18,22) (18,21) (18,31) (18,24) (18,27) (18,23) (19,30) (19,25) (19,21) (19,24) (19,20) (19,27) (19,23) (20,21) (20,31) (20,24) (20,27) (20,23) (21,25) (21,22) (21,31) (21,24) (21,27) (21,23) (22,30) (22,31) (22,24) (22,23) (23,30) (23,25) (23,24) (23,27) (24,30) (24,25) (24,31) (24,27) (25,30) (25,27) (26,28) (27,30) (27,31) (28,29) (30,31)\nQ: Is there a path between node 20 and node 19?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1191"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 3 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1192"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,9) (1,8) (1,4) (2,8) (2,4) (2,3) (3,7) (3,6) (3,10) (3,12) (3,11) (4,10) (4,12) (6,14) (6,8) (6,10) (7,14) (7,11) (8,14) (8,12) (10,14) (11,14) (12,14)\nQ: Is there a path between node 5 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1193"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,7) (0,4) (0,10) (0,5) (0,13) (0,12) (0,1) (0,2) (0,3) (0,15) (0,6) (0,8) (0,14) (1,11) (1,7) (1,4) (1,10) (1,5) (1,13) (1,12) (1,2) (1,3) (1,15) (1,6) (1,8) (1,14) (2,11) (2,7) (2,4) (2,10) (2,5) (2,13) (2,12) (2,3) (2,15) (2,6) (2,8) (2,14) (3,11) (3,7) (3,4) (3,10) (3,5) (3,13) (3,12) (3,15) (3,6) (3,8) (3,14) (4,11) (4,7) (4,10) (4,5) (4,13) (4,12) (4,15) (4,6) (4,8) (4,14) (5,11) (5,7) (5,10) (5,13) (5,12) (5,15) (5,6) (5,8) (5,14) (6,11) (6,7) (6,10) (6,13) (6,12) (6,15) (6,8) (6,14) (7,11) (7,10) (7,13) (7,12) (7,15) (7,8) (7,14) (8,11) (8,10) (8,13) (8,12) (8,15) (8,14) (10,11) (10,13) (10,12) (10,15) (10,14) (11,13) (11,12) (11,15) (11,14) (12,13) (12,15) (12,14) (13,15) (13,14) (14,15)\nQ: Is there a path between node 3 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1194"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,32) (0,29) (0,7) (0,15) (1,30) (1,10) (1,8) (2,27) (2,18) (2,20) (2,7) (2,26) (3,14) (3,9) (4,18) (4,11) (4,13) (4,15) (5,30) (5,21) (6,14) (6,21) (6,17) (7,18) (7,22) (7,31) (7,29) (7,26) (8,14) (8,10) (9,21) (10,12) (10,21) (10,17) (11,19) (11,22) (11,28) (11,32) (11,29) (11,15) (11,26) (12,30) (12,21) (13,27) (13,20) (13,28) (13,31) (14,17) (15,20) (15,31) (15,26) (16,27) (16,32) (17,30) (18,27) (18,28) (18,32) (18,26) (18,24) (18,23) (19,27) (19,20) (19,31) (19,29) (19,26) (19,24) (20,25) (20,28) (20,32) (20,26) (22,31) (22,23) (23,27) (23,28) (23,26) (25,26) (26,27) (26,28) (26,29) (28,32) (28,31) (29,31)\nQ: Is there a path between node 22 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1195"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (1,4) (1,11) (2,21) (2,20) (2,24) (3,24) (4,13) (4,15) (4,8) (5,19) (5,24) (6,20) (6,24) (7,25) (7,21) (8,17) (8,15) (8,12) (9,13) (9,12) (10,16) (11,13) (11,18) (11,23) (11,14) (11,12) (13,17) (14,23) (15,18) (15,23) (18,23) (19,25) (19,24) (20,21) (21,25) (24,25)\nQ: Is there a path between node 24 and node 25?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1196"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,6) (3,4) (4,5) (5,10) (6,8) (8,9)\nQ: Is there a path between node 4 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1197"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,6) (0,11) (0,19) (0,20) (0,1) (0,15) (0,12) (0,7) (0,22) (0,5) (0,21) (0,3) (0,4) (0,18) (0,17) (1,14) (1,6) (1,11) (1,19) (1,20) (1,15) (1,12) (1,7) (1,22) (1,5) (1,21) (1,3) (1,4) (1,18) (1,17) (2,13) (2,10) (2,8) (2,16) (2,9) (3,14) (3,6) (3,11) (3,19) (3,20) (3,15) (3,12) (3,7) (3,22) (3,5) (3,21) (3,4) (3,18) (3,17) (4,14) (4,6) (4,11) (4,19) (4,20) (4,15) (4,12) (4,7) (4,22) (4,5) (4,21) (4,18) (4,17) (5,14) (5,6) (5,11) (5,19) (5,20) (5,15) (5,12) (5,7) (5,22) (5,21) (5,18) (5,17) (6,14) (6,11) (6,19) (6,20) (6,15) (6,12) (6,7) (6,22) (6,21) (6,18) (6,17) (7,14) (7,11) (7,19) (7,20) (7,15) (7,12) (7,22) (7,21) (7,18) (7,17) (8,13) (8,10) (8,16) (8,9) (9,13) (9,10) (9,16) (10,13) (10,16) (11,14) (11,19) (11,20) (11,15) (11,12) (11,22) (11,21) (11,18) (11,17) (12,14) (12,19) (12,20) (12,15) (12,22) (12,21) (12,18) (12,17) (13,16) (14,19) (14,20) (14,15) (14,22) (14,21) (14,18) (14,17) (15,19) (15,20) (15,22) (15,21) (15,18) (15,17) (17,19) (17,20) (17,22) (17,21) (17,18) (18,19) (18,20) (18,22) (18,21) (19,20) (19,22) (19,21) (20,22) (20,21) (21,22)\nQ: Is there a path between node 12 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1198"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,13) (0,30) (0,1) (0,4) (0,2) (0,22) (1,30) (1,17) (1,5) (1,4) (1,25) (1,29) (2,3) (2,5) (2,23) (3,28) (3,24) (3,4) (3,6) (3,8) (3,12) (4,15) (4,24) (4,25) (4,7) (4,6) (4,29) (5,21) (5,23) (5,7) (5,12) (6,20) (6,28) (6,23) (7,13) (7,15) (7,16) (7,8) (7,12) (8,20) (8,30) (8,24) (8,17) (8,23) (10,19) (11,19) (11,26) (12,20) (12,16) (12,25) (12,18) (13,28) (13,18) (14,20) (15,28) (15,24) (15,23) (16,20) (16,30) (16,24) (16,29) (17,21) (17,28) (17,25) (18,21) (18,23) (18,29) (20,24) (20,23) (20,22) (20,29) (21,25) (21,23) (21,22) (22,25) (23,24) (23,29) (24,28) (24,29) (25,28) (26,27) (29,30)\nQ: Is there a path between node 10 and node 18?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1199"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,18) (0,15) (0,12) (0,5) (1,24) (2,21) (2,23) (2,9) (2,15) (2,19) (3,23) (3,15) (3,8) (3,16) (5,21) (5,22) (5,6) (5,19) (5,8) (5,10) (5,16) (6,14) (6,22) (6,9) (6,12) (6,17) (9,23) (9,22) (9,20) (9,10) (10,22) (10,18) (10,19) (11,24) (12,14) (13,14) (13,21) (13,23) (13,18) (13,15) (14,21) (14,18) (14,15) (14,16) (15,20) (15,17) (17,23) (17,22) (17,18) (17,20) (17,19) (18,19) (19,20) (21,23)\nQ: Is there a path between node 19 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1200"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,4) (0,1) (0,11) (0,9) (0,12) (1,2) (1,4) (1,11) (1,9) (1,13) (1,8) (1,12) (2,6) (2,3) (2,4) (2,11) (2,9) (2,13) (2,8) (3,6) (3,9) (3,13) (3,8) (3,12) (4,6) (4,11) (4,9) (4,13) (4,8) (4,12) (5,7) (5,10) (6,11) (6,9) (6,8) (6,12) (8,9) (8,12) (9,11) (9,12) (11,13) (12,13)\nQ: Is there a path between node 10 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1201"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,20) (0,27) (0,29) (0,26) (0,17) (0,3) (0,1) (0,16) (1,6) (1,7) (1,20) (1,19) (1,3) (1,33) (1,4) (2,27) (2,34) (2,26) (2,19) (2,17) (2,3) (2,21) (2,4) (3,6) (3,7) (3,11) (3,28) (3,29) (4,6) (4,28) (4,27) (4,29) (4,26) (4,19) (4,33) (4,23) (5,7) (5,11) (5,28) (5,19) (5,33) (5,16) (6,7) (6,28) (6,27) (6,26) (6,21) (7,34) (8,13) (8,12) (8,22) (8,15) (9,24) (9,12) (9,10) (10,25) (11,16) (11,23) (12,32) (12,18) (12,22) (12,15) (13,14) (14,18) (14,15) (15,30) (15,18) (16,27) (16,17) (16,23) (17,29) (17,19) (17,33) (17,23) (18,31) (18,24) (19,28) (19,27) (19,34) (19,29) (19,33) (19,21) (20,21) (21,26) (21,33) (22,30) (22,25) (25,30) (25,31) (26,28) (26,34) (26,29) (27,28) (30,32) (31,32)\nQ: Is there a path between node 15 and node 21?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1202"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,10) (0,1) (1,8) (1,3) (1,14) (3,5) (3,6) (3,9) (3,12) (4,9) (4,16) (6,7) (6,12) (7,14) (8,16) (8,14) (10,11) (10,14) (10,12) (11,14) (12,14)\nQ: Is there a path between node 8 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1203"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,21) (0,8) (0,11) (0,16) (0,13) (0,10) (0,20) (0,6) (0,4) (1,14) (1,17) (1,18) (1,5) (1,19) (1,2) (2,22) (2,14) (2,5) (3,8) (3,11) (3,10) (3,12) (3,6) (4,11) (4,13) (4,20) (4,12) (5,22) (5,14) (5,17) (5,18) (5,9) (5,19) (6,8) (6,11) (6,16) (6,13) (6,10) (6,20) (6,12) (7,15) (8,11) (8,13) (8,10) (8,20) (8,12) (9,22) (9,14) (9,17) (9,18) (9,19) (10,21) (10,13) (11,16) (11,13) (11,20) (11,12) (12,21) (12,16) (12,13) (12,20) (13,21) (13,16) (13,20) (14,22) (14,18) (16,21) (16,20) (17,22) (17,18) (17,19) (18,19) (20,21)\nQ: Is there a path between node 11 and node 19?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1204"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,12) (0,11) (0,4) (2,10) (2,8) (2,4) (4,6) (4,11) (5,9) (6,7) (6,10) (6,11) (7,8) (8,10) (8,9) (9,12) (10,11)\nQ: Is there a path between node 3 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1205"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,6) (0,1) (0,5) (1,7) (1,6) (1,8) (1,5) (2,7) (2,8) (2,5) (3,4) (5,7) (5,6) (5,8)\nQ: Is there a path between node 0 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1206"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,4) (0,1) (1,2) (1,5) (1,4) (2,5) (2,4) (4,5)\nQ: Is there a path between node 3 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1207"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,17) (0,23) (0,22) (0,1) (0,9) (0,11) (0,14) (0,19) (0,12) (0,18) (0,8) (0,4) (0,16) (0,15) (0,10) (0,6) (1,20) (1,17) (1,23) (1,22) (1,9) (1,11) (1,14) (1,19) (1,12) (1,18) (1,8) (1,4) (1,16) (1,15) (1,10) (1,6) (2,13) (2,5) (2,3) (2,21) (2,7) (3,13) (3,5) (3,21) (3,7) (4,20) (4,17) (4,23) (4,22) (4,9) (4,11) (4,14) (4,19) (4,12) (4,18) (4,8) (4,16) (4,15) (4,10) (4,6) (5,13) (5,21) (5,7) (6,20) (6,17) (6,23) (6,22) (6,9) (6,11) (6,14) (6,19) (6,12) (6,18) (6,8) (6,16) (6,15) (6,10) (7,13) (7,21) (8,20) (8,17) (8,23) (8,22) (8,9) (8,11) (8,14) (8,19) (8,12) (8,18) (8,16) (8,15) (8,10) (9,20) (9,17) (9,23) (9,22) (9,11) (9,14) (9,19) (9,12) (9,18) (9,16) (9,15) (9,10) (10,20) (10,17) (10,23) (10,22) (10,11) (10,14) (10,19) (10,12) (10,18) (10,16) (10,15) (11,20) (11,17) (11,23) (11,22) (11,14) (11,19) (11,12) (11,18) (11,16) (11,15) (12,20) (12,17) (12,23) (12,22) (12,14) (12,19) (12,18) (12,16) (12,15) (13,21) (14,20) (14,17) (14,23) (14,22) (14,19) (14,18) (14,16) (14,15) (15,20) (15,17) (15,23) (15,22) (15,19) (15,18) (15,16) (16,20) (16,17) (16,23) (16,22) (16,19) (16,18) (17,20) (17,23) (17,22) (17,19) (17,18) (18,20) (18,23) (18,22) (18,19) (19,20) (19,23) (19,22) (20,23) (20,22) (22,23)\nQ: Is there a path between node 11 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1208"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,10) (2,9) (2,5) (3,12) (3,14) (3,4) (3,8) (3,18) (4,19) (4,16) (4,11) (5,20) (5,12) (5,14) (5,11) (6,18) (6,16) (7,15) (8,20) (8,12) (8,18) (8,16) (9,20) (9,14) (9,19) (9,11) (11,13) (11,12) (11,18) (11,16) (12,18) (13,19) (13,18) (14,19) (16,20) (18,19)\nQ: Is there a path between node 17 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1209"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,10) (0,19) (0,16) (0,7) (0,8) (0,4) (0,3) (0,11) (0,1) (0,18) (0,9) (0,5) (0,2) (0,13) (1,17) (1,10) (1,19) (1,16) (1,7) (1,8) (1,4) (1,3) (1,11) (1,18) (1,9) (1,5) (1,2) (1,13) (2,17) (2,10) (2,19) (2,16) (2,7) (2,8) (2,4) (2,3) (2,11) (2,18) (2,9) (2,5) (2,13) (3,17) (3,10) (3,19) (3,16) (3,7) (3,8) (3,4) (3,11) (3,18) (3,9) (3,5) (3,13) (4,17) (4,10) (4,19) (4,16) (4,7) (4,8) (4,11) (4,18) (4,9) (4,5) (4,13) (5,17) (5,10) (5,19) (5,16) (5,7) (5,8) (5,11) (5,18) (5,9) (5,13) (6,15) (7,17) (7,10) (7,19) (7,16) (7,8) (7,11) (7,18) (7,9) (7,13) (8,17) (8,10) (8,19) (8,16) (8,11) (8,18) (8,9) (8,13) (9,17) (9,10) (9,19) (9,16) (9,11) (9,18) (9,13) (10,17) (10,19) (10,16) (10,11) (10,18) (10,13) (11,17) (11,19) (11,16) (11,18) (11,13) (12,14) (13,17) (13,19) (13,16) (13,18) (16,17) (16,19) (16,18) (17,19) (17,18) (18,19)\nQ: Is there a path between node 16 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1210"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,31) (1,4) (1,27) (1,25) (2,31) (2,24) (2,13) (2,10) (3,30) (3,32) (3,27) (3,15) (4,30) (4,6) (4,28) (4,8) (5,22) (6,27) (7,20) (7,11) (7,12) (8,15) (9,14) (10,17) (10,23) (10,13) (11,14) (12,18) (13,23) (14,22) (15,30) (15,27) (15,25) (15,16) (15,28) (17,23) (17,21) (18,22) (18,33) (20,22) (21,31) (23,24) (25,30) (25,27) (25,28) (26,31) (27,30) (27,32) (28,32)\nQ: Is there a path between node 17 and node 22?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1211"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (3,7) (4,6) (5,6)\nQ: Is there a path between node 2 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1212"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,1) (0,3) (1,5) (1,3) (2,4) (3,5)\nQ: Is there a path between node 1 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1213"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (1,24) (1,13) (1,7) (2,24) (2,15) (2,18) (2,8) (2,13) (2,7) (3,23) (3,6) (5,20) (5,14) (6,11) (6,23) (7,12) (7,10) (7,21) (7,8) (7,13) (8,10) (8,15) (8,18) (8,22) (8,13) (9,21) (9,13) (10,12) (10,15) (10,13) (12,24) (13,24) (13,22) (14,20) (15,24) (17,24) (19,20) (21,24)\nQ: Is there a path between node 4 and node 22?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1214"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,2) (0,8) (0,4) (0,7) (0,3) (0,1) (1,5) (1,2) (1,8) (1,4) (1,7) (1,3) (2,5) (2,8) (2,4) (2,7) (2,3) (3,5) (3,8) (3,4) (3,7) (4,5) (4,8) (4,7) (5,8) (5,7) (6,9) (7,8)\nQ: Is there a path between node 8 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1215"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,1) (2,3) (4,6) (5,6) (5,7)\nQ: Is there a path between node 7 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1216"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,21) (1,17) (1,15) (1,2) (1,4) (1,18) (2,8) (2,13) (2,17) (2,15) (2,23) (2,22) (2,4) (2,18) (2,12) (4,21) (4,8) (4,13) (4,15) (4,23) (4,22) (4,18) (4,12) (5,21) (5,8) (5,13) (5,17) (5,15) (5,22) (5,18) (7,14) (7,16) (7,10) (7,11) (7,19) (8,21) (8,17) (8,23) (8,18) (9,14) (9,24) (10,14) (10,24) (10,19) (11,14) (11,16) (11,24) (12,21) (12,13) (12,17) (12,15) (12,23) (12,22) (12,18) (13,21) (13,17) (13,15) (13,23) (13,22) (14,24) (15,21) (15,17) (15,23) (15,22) (15,18) (16,19) (17,21) (17,18) (18,21) (18,23) (21,22) (22,23)\nQ: Is there a path between node 2 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1217"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,11) (3,15) (3,8) (5,18) (5,7) (6,17) (6,7) (7,13) (7,8) (7,14) (8,18) (8,12) (9,11) (9,15) (9,13) (9,17) (10,18) (11,13) (11,17) (12,18) (12,17) (12,14) (13,17) (14,17) (17,18)\nQ: Is there a path between node 7 and node 17?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1218"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (1,11) (1,9) (1,14) (2,5) (2,6) (3,11) (3,13) (4,11) (4,13) (4,15) (5,7) (5,6) (7,10) (8,11) (8,9) (9,14) (9,12) (11,13) (13,14) (13,15)\nQ: Is there a path between node 0 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1219"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,4) (1,5)\nQ: Is there a path between node 6 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1220"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,4) (0,3) (0,6) (0,2) (0,8) (0,5) (0,11) (1,4) (1,3) (1,6) (1,2) (1,8) (1,5) (1,11) (2,4) (2,3) (2,6) (2,8) (2,5) (2,11) (3,4) (3,6) (3,8) (3,5) (3,11) (4,6) (4,8) (4,5) (4,11) (5,6) (5,8) (5,11) (6,8) (6,11) (7,9) (7,10) (8,11) (9,10)\nQ: Is there a path between node 6 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1221"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,18) (0,12) (0,2) (0,11) (0,8) (0,13) (1,4) (1,10) (1,17) (1,5) (1,14) (1,7) (1,6) (1,15) (2,3) (2,18) (2,12) (2,11) (2,8) (2,13) (3,18) (3,12) (3,11) (3,8) (3,13) (4,10) (4,17) (4,5) (4,14) (4,7) (4,6) (4,15) (5,10) (5,17) (5,14) (5,7) (5,6) (5,15) (6,10) (6,17) (6,14) (6,7) (6,15) (7,10) (7,17) (7,14) (7,15) (8,18) (8,12) (8,11) (8,13) (9,16) (10,17) (10,14) (10,15) (11,18) (11,12) (11,13) (12,18) (12,13) (13,18) (14,17) (14,15) (15,17)\nQ: Is there a path between node 17 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1222"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,3) (1,20) (1,21) (1,8) (1,5) (1,16) (1,17) (1,19) (1,6) (1,12) (1,14) (1,9) (1,13) (1,18) (1,7) (1,11) (1,15) (1,2) (1,10) (2,20) (2,21) (2,8) (2,5) (2,16) (2,17) (2,19) (2,6) (2,12) (2,14) (2,9) (2,13) (2,18) (2,7) (2,11) (2,15) (2,10) (3,4) (5,20) (5,21) (5,8) (5,16) (5,17) (5,19) (5,6) (5,12) (5,14) (5,9) (5,13) (5,18) (5,7) (5,11) (5,15) (5,10) (6,20) (6,21) (6,8) (6,16) (6,17) (6,19) (6,12) (6,14) (6,9) (6,13) (6,18) (6,7) (6,11) (6,15) (6,10) (7,20) (7,21) (7,8) (7,16) (7,17) (7,19) (7,12) (7,14) (7,9) (7,13) (7,18) (7,11) (7,15) (7,10) (8,20) (8,21) (8,16) (8,17) (8,19) (8,12) (8,14) (8,9) (8,13) (8,18) (8,11) (8,15) (8,10) (9,20) (9,21) (9,16) (9,17) (9,19) (9,12) (9,14) (9,13) (9,18) (9,11) (9,15) (9,10) (10,20) (10,21) (10,16) (10,17) (10,19) (10,12) (10,14) (10,13) (10,18) (10,11) (10,15) (11,20) (11,21) (11,16) (11,17) (11,19) (11,12) (11,14) (11,13) (11,18) (11,15) (12,20) (12,21) (12,16) (12,17) (12,19) (12,14) (12,13) (12,18) (12,15) (13,20) (13,21) (13,16) (13,17) (13,19) (13,14) (13,18) (13,15) (14,20) (14,21) (14,16) (14,17) (14,19) (14,18) (14,15) (15,20) (15,21) (15,16) (15,17) (15,19) (15,18) (16,20) (16,21) (16,17) (16,19) (16,18) (17,20) (17,21) (17,19) (17,18) (18,20) (18,21) (18,19) (19,20) (19,21) (20,21)\nQ: Is there a path between node 9 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1223"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,13) (0,2) (0,14) (0,23) (0,8) (0,1) (0,25) (0,27) (0,10) (1,29) (1,13) (1,19) (1,28) (1,23) (1,30) (1,25) (1,24) (2,12) (2,5) (2,14) (2,17) (2,23) (3,7) (3,12) (3,19) (3,23) (3,8) (3,30) (3,25) (3,24) (4,33) (5,20) (5,23) (5,30) (6,15) (6,11) (7,32) (7,17) (7,23) (7,8) (7,10) (8,29) (8,12) (8,32) (8,20) (8,19) (8,17) (8,30) (9,29) (9,28) (9,30) (9,24) (10,13) (10,20) (10,14) (10,22) (11,31) (12,13) (12,23) (12,27) (12,26) (13,29) (13,32) (13,14) (13,28) (13,30) (13,24) (14,17) (14,30) (14,22) (14,27) (15,16) (15,31) (15,33) (17,32) (17,20) (17,19) (17,27) (17,24) (17,26) (18,21) (20,28) (20,30) (20,25) (21,31) (22,32) (22,28) (22,30) (23,28) (23,25) (23,27) (24,29) (24,28) (24,26) (25,32) (26,29) (26,27) (27,32) (27,30) (28,32) (28,30)\nQ: Is there a path between node 15 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1224"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,7) (0,4) (0,10) (0,5) (0,13) (0,12) (0,1) (0,2) (0,3) (0,15) (0,6) (0,8) (0,14) (1,11) (1,7) (1,4) (1,10) (1,5) (1,13) (1,12) (1,2) (1,3) (1,15) (1,6) (1,8) (1,14) (2,11) (2,7) (2,4) (2,10) (2,5) (2,13) (2,12) (2,3) (2,15) (2,6) (2,8) (2,14) (3,11) (3,7) (3,4) (3,10) (3,5) (3,13) (3,12) (3,15) (3,6) (3,8) (3,14) (4,11) (4,7) (4,10) (4,5) (4,13) (4,12) (4,15) (4,6) (4,8) (4,14) (5,11) (5,7) (5,10) (5,13) (5,12) (5,15) (5,6) (5,8) (5,14) (6,11) (6,7) (6,10) (6,13) (6,12) (6,15) (6,8) (6,14) (7,11) (7,10) (7,13) (7,12) (7,15) (7,8) (7,14) (8,11) (8,10) (8,13) (8,12) (8,15) (8,14) (10,11) (10,13) (10,12) (10,15) (10,14) (11,13) (11,12) (11,15) (11,14) (12,13) (12,15) (12,14) (13,15) (13,14) (14,15)\nQ: Is there a path between node 9 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1225"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,2) (0,8) (0,4) (0,7) (0,3) (0,1) (1,5) (1,2) (1,8) (1,4) (1,7) (1,3) (2,5) (2,8) (2,4) (2,7) (2,3) (3,5) (3,8) (3,4) (3,7) (4,5) (4,8) (4,7) (5,8) (5,7) (6,9) (7,8)\nQ: Is there a path between node 9 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1226"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,7) (0,10) (0,6) (0,2) (0,8) (0,4) (0,1) (1,3) (1,7) (1,10) (1,6) (1,2) (1,8) (1,4) (2,3) (2,7) (2,10) (2,6) (2,8) (2,4) (3,7) (3,10) (3,6) (3,8) (3,4) (4,7) (4,10) (4,6) (4,8) (5,9) (6,7) (6,10) (6,8) (7,10) (7,8) (8,10)\nQ: Is there a path between node 6 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1227"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,22) (0,12) (0,24) (0,18) (0,19) (0,30) (0,1) (0,21) (0,9) (0,5) (0,6) (0,7) (0,2) (1,22) (1,24) (1,18) (1,19) (1,30) (1,21) (1,9) (1,5) (1,6) (1,11) (1,7) (1,31) (1,2) (2,12) (2,24) (2,18) (2,19) (2,21) (2,5) (2,6) (2,11) (2,7) (2,31) (3,26) (3,16) (3,4) (3,28) (3,13) (3,20) (4,26) (4,16) (4,8) (4,28) (5,12) (5,24) (5,30) (5,21) (5,9) (5,11) (5,7) (5,31) (6,22) (6,12) (6,24) (6,30) (6,21) (6,9) (6,11) (6,7) (7,12) (7,18) (7,30) (7,9) (7,11) (7,31) (8,26) (8,16) (8,28) (9,22) (9,12) (9,24) (9,18) (9,19) (9,30) (9,11) (9,31) (10,25) (10,14) (10,29) (10,32) (10,15) (10,23) (11,22) (11,12) (11,24) (11,18) (11,30) (11,21) (12,24) (12,30) (12,21) (12,31) (13,26) (13,28) (14,27) (14,17) (14,29) (14,32) (14,15) (15,25) (15,27) (15,17) (15,29) (15,32) (15,23) (16,26) (17,29) (18,22) (18,24) (18,19) (18,21) (19,22) (19,30) (19,21) (20,26) (21,22) (21,24) (21,31) (22,24) (23,25) (23,27) (23,32) (24,30) (24,31) (25,27) (25,29) (25,32) (26,28) (27,29) (27,32) (30,31)\nQ: Is there a path between node 21 and node 30?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1228"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,22) (0,6) (0,11) (0,10) (0,4) (0,5) (0,9) (0,1) (0,13) (0,21) (0,20) (0,12) (1,22) (1,11) (1,10) (1,5) (1,16) (1,9) (1,13) (1,21) (1,20) (2,8) (2,19) (2,3) (2,18) (2,24) (3,19) (3,17) (3,24) (3,23) (4,22) (4,6) (4,16) (4,9) (4,21) (4,20) (5,22) (5,6) (5,14) (5,11) (5,16) (5,15) (5,9) (5,13) (5,21) (5,20) (6,22) (6,11) (6,10) (6,16) (6,13) (6,21) (6,12) (7,8) (7,17) (7,18) (7,24) (7,23) (8,17) (8,24) (9,14) (9,11) (9,10) (9,16) (9,15) (9,21) (9,20) (9,12) (10,22) (10,14) (10,11) (10,16) (10,15) (10,21) (10,20) (11,22) (11,16) (11,15) (11,20) (12,22) (12,14) (12,15) (12,13) (12,21) (12,20) (13,14) (13,16) (13,15) (13,21) (13,20) (14,22) (14,16) (14,15) (14,21) (15,16) (15,21) (16,22) (16,21) (16,20) (17,19) (17,18) (17,24) (17,23) (18,23) (19,24) (23,24)\nQ: Is there a path between node 4 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1229"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,26) (2,26) (2,30) (2,6) (3,19) (4,29) (4,8) (4,11) (4,9) (5,25) (6,30) (6,19) (6,13) (6,25) (7,23) (7,29) (7,10) (7,28) (7,14) (8,23) (8,15) (8,27) (8,18) (8,11) (8,28) (8,9) (9,23) (9,29) (9,15) (9,18) (9,12) (10,15) (11,29) (11,27) (11,28) (11,14) (12,27) (13,16) (13,26) (14,17) (15,29) (15,21) (15,28) (16,25) (17,23) (17,29) (17,18) (19,20) (19,22) (20,22) (21,27) (21,28) (22,26) (23,29) (23,28) (24,26) (24,30) (25,26) (25,30) (27,28)\nQ: Is there a path between node 22 and node 30?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1230"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,4) (0,16) (0,21) (0,1) (0,25) (0,14) (0,9) (0,5) (0,6) (0,12) (0,17) (0,24) (0,23) (1,29) (1,4) (1,27) (1,16) (1,21) (1,14) (1,9) (1,6) (1,24) (1,23) (2,26) (2,10) (2,22) (2,15) (2,28) (2,8) (2,30) (2,19) (3,26) (3,10) (3,11) (3,22) (3,15) (3,28) (3,8) (3,30) (3,19) (3,20) (4,29) (4,27) (4,16) (4,21) (4,14) (4,9) (4,5) (4,6) (4,12) (4,24) (5,29) (5,27) (5,21) (5,7) (5,14) (5,12) (5,17) (5,24) (5,23) (6,29) (6,27) (6,7) (6,25) (6,14) (6,9) (6,12) (6,24) (6,23) (7,25) (7,14) (7,9) (7,12) (7,17) (7,23) (8,26) (8,10) (8,11) (8,13) (8,30) (8,19) (9,29) (9,27) (9,16) (9,14) (9,12) (9,24) (9,23) (10,26) (10,13) (10,15) (10,28) (10,19) (10,20) (11,26) (11,13) (11,15) (11,28) (11,30) (11,19) (11,20) (12,29) (12,27) (12,16) (12,21) (12,25) (12,17) (12,24) (12,23) (13,26) (13,28) (13,30) (14,29) (14,16) (14,21) (14,25) (14,17) (14,24) (14,23) (15,26) (15,28) (15,30) (15,20) (16,27) (16,21) (16,17) (16,24) (16,23) (17,29) (17,27) (17,21) (17,25) (17,24) (19,26) (19,22) (19,30) (19,20) (20,26) (20,22) (20,28) (21,29) (21,27) (21,25) (21,24) (21,23) (22,26) (22,28) (22,30) (23,29) (23,27) (23,25) (24,29) (24,27) (24,25) (25,29) (26,28) (28,30)\nQ: Is there a path between node 20 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1231"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,4) (0,15) (0,19) (0,8) (0,17) (0,13) (0,3) (0,14) (0,5) (0,2) (0,16) (0,1) (0,10) (1,20) (1,4) (1,15) (1,19) (1,8) (1,17) (1,13) (1,3) (1,14) (1,5) (1,2) (1,16) (1,10) (2,20) (2,4) (2,15) (2,19) (2,8) (2,17) (2,13) (2,3) (2,14) (2,5) (2,16) (2,10) (3,20) (3,4) (3,15) (3,19) (3,8) (3,17) (3,13) (3,14) (3,5) (3,16) (3,10) (4,20) (4,15) (4,19) (4,8) (4,17) (4,13) (4,14) (4,5) (4,16) (4,10) (5,20) (5,15) (5,19) (5,8) (5,17) (5,13) (5,14) (5,16) (5,10) (6,12) (6,22) (6,9) (6,18) (6,21) (6,7) (6,11) (7,12) (7,22) (7,9) (7,18) (7,21) (7,11) (8,20) (8,15) (8,19) (8,17) (8,13) (8,14) (8,16) (8,10) (9,12) (9,22) (9,18) (9,21) (9,11) (10,20) (10,15) (10,19) (10,17) (10,13) (10,14) (10,16) (11,12) (11,22) (11,18) (11,21) (12,22) (12,18) (12,21) (13,20) (13,15) (13,19) (13,17) (13,14) (13,16) (14,20) (14,15) (14,19) (14,17) (14,16) (15,20) (15,19) (15,17) (15,16) (16,20) (16,19) (16,17) (17,20) (17,19) (18,22) (18,21) (19,20) (21,22)\nQ: Is there a path between node 12 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1232"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,13) (0,30) (0,1) (0,4) (0,2) (0,22) (1,30) (1,17) (1,5) (1,4) (1,25) (1,29) (2,3) (2,5) (2,23) (3,28) (3,24) (3,4) (3,6) (3,8) (3,12) (4,15) (4,24) (4,25) (4,7) (4,6) (4,29) (5,21) (5,23) (5,7) (5,12) (6,20) (6,28) (6,23) (7,13) (7,15) (7,16) (7,8) (7,12) (8,20) (8,30) (8,24) (8,17) (8,23) (10,19) (11,19) (11,26) (12,20) (12,16) (12,25) (12,18) (13,28) (13,18) (14,20) (15,28) (15,24) (15,23) (16,20) (16,30) (16,24) (16,29) (17,21) (17,28) (17,25) (18,21) (18,23) (18,29) (20,24) (20,23) (20,22) (20,29) (21,25) (21,23) (21,22) (22,25) (23,24) (23,29) (24,28) (24,29) (25,28) (26,27) (29,30)\nQ: Is there a path between node 9 and node 29?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1233"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,22) (0,6) (0,11) (0,10) (0,4) (0,5) (0,9) (0,1) (0,13) (0,21) (0,20) (0,12) (1,22) (1,11) (1,10) (1,5) (1,16) (1,9) (1,13) (1,21) (1,20) (2,8) (2,19) (2,3) (2,18) (2,24) (3,19) (3,17) (3,24) (3,23) (4,22) (4,6) (4,16) (4,9) (4,21) (4,20) (5,22) (5,6) (5,14) (5,11) (5,16) (5,15) (5,9) (5,13) (5,21) (5,20) (6,22) (6,11) (6,10) (6,16) (6,13) (6,21) (6,12) (7,8) (7,17) (7,18) (7,24) (7,23) (8,17) (8,24) (9,14) (9,11) (9,10) (9,16) (9,15) (9,21) (9,20) (9,12) (10,22) (10,14) (10,11) (10,16) (10,15) (10,21) (10,20) (11,22) (11,16) (11,15) (11,20) (12,22) (12,14) (12,15) (12,13) (12,21) (12,20) (13,14) (13,16) (13,15) (13,21) (13,20) (14,22) (14,16) (14,15) (14,21) (15,16) (15,21) (16,22) (16,21) (16,20) (17,19) (17,18) (17,24) (17,23) (18,23) (19,24) (23,24)\nQ: Is there a path between node 19 and node 22?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1234"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,19) (0,17) (0,3) (0,10) (0,14) (1,7) (1,8) (1,15) (1,13) (2,9) (2,12) (2,18) (2,4) (3,6) (3,19) (3,17) (3,16) (3,10) (3,14) (4,12) (4,18) (5,9) (5,18) (6,19) (6,17) (6,16) (6,14) (6,20) (7,8) (7,15) (7,13) (9,12) (9,18) (10,16) (10,14) (10,20) (11,15) (12,18) (13,15) (14,19) (14,17) (14,20) (16,19) (16,17) (17,20) (19,20)\nQ: Is there a path between node 17 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1235"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,4) (0,9) (0,12) (0,11) (0,5) (1,6) (1,17) (1,8) (1,15) (1,3) (1,2) (1,18) (1,19) (1,13) (1,14) (1,10) (2,6) (2,17) (2,8) (2,15) (2,3) (2,18) (2,19) (2,13) (2,14) (2,10) (3,6) (3,17) (3,8) (3,15) (3,18) (3,19) (3,13) (3,14) (3,10) (4,7) (4,9) (4,12) (4,11) (4,5) (5,7) (5,9) (5,12) (5,11) (6,17) (6,8) (6,15) (6,18) (6,19) (6,13) (6,14) (6,10) (7,9) (7,12) (7,11) (8,17) (8,15) (8,18) (8,19) (8,13) (8,14) (8,10) (9,12) (9,11) (10,17) (10,15) (10,18) (10,19) (10,13) (10,14) (11,12) (13,17) (13,15) (13,18) (13,19) (13,14) (14,17) (14,15) (14,18) (14,19) (15,17) (15,18) (15,19) (17,18) (17,19) (18,19)\nQ: Is there a path between node 11 and node 15?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1236"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,8) (0,10) (0,4) (0,16) (0,5) (0,2) (0,7) (0,9) (0,15) (0,13) (0,1) (0,12) (0,14) (0,3) (1,11) (1,8) (1,10) (1,4) (1,16) (1,5) (1,2) (1,7) (1,9) (1,15) (1,13) (1,12) (1,14) (1,3) (2,11) (2,8) (2,10) (2,4) (2,16) (2,5) (2,7) (2,9) (2,15) (2,13) (2,12) (2,14) (2,3) (3,11) (3,8) (3,10) (3,4) (3,16) (3,5) (3,7) (3,9) (3,15) (3,13) (3,12) (3,14) (4,11) (4,8) (4,10) (4,16) (4,5) (4,7) (4,9) (4,15) (4,13) (4,12) (4,14) (5,11) (5,8) (5,10) (5,16) (5,7) (5,9) (5,15) (5,13) (5,12) (5,14) (7,11) (7,8) (7,10) (7,16) (7,9) (7,15) (7,13) (7,12) (7,14) (8,11) (8,10) (8,16) (8,9) (8,15) (8,13) (8,12) (8,14) (9,11) (9,10) (9,16) (9,15) (9,13) (9,12) (9,14) (10,11) (10,16) (10,15) (10,13) (10,12) (10,14) (11,16) (11,15) (11,13) (11,12) (11,14) (12,16) (12,15) (12,13) (12,14) (13,16) (13,15) (13,14) (14,16) (14,15) (15,16)\nQ: Is there a path between node 12 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1237"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,7) (0,4) (0,10) (0,5) (0,13) (0,12) (0,1) (0,2) (0,3) (0,15) (0,6) (0,8) (0,14) (1,11) (1,7) (1,4) (1,10) (1,5) (1,13) (1,12) (1,2) (1,3) (1,15) (1,6) (1,8) (1,14) (2,11) (2,7) (2,4) (2,10) (2,5) (2,13) (2,12) (2,3) (2,15) (2,6) (2,8) (2,14) (3,11) (3,7) (3,4) (3,10) (3,5) (3,13) (3,12) (3,15) (3,6) (3,8) (3,14) (4,11) (4,7) (4,10) (4,5) (4,13) (4,12) (4,15) (4,6) (4,8) (4,14) (5,11) (5,7) (5,10) (5,13) (5,12) (5,15) (5,6) (5,8) (5,14) (6,11) (6,7) (6,10) (6,13) (6,12) (6,15) (6,8) (6,14) (7,11) (7,10) (7,13) (7,12) (7,15) (7,8) (7,14) (8,11) (8,10) (8,13) (8,12) (8,15) (8,14) (10,11) (10,13) (10,12) (10,15) (10,14) (11,13) (11,12) (11,15) (11,14) (12,13) (12,15) (12,14) (13,15) (13,14) (14,15)\nQ: Is there a path between node 13 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1238"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,3) (0,14) (1,8) (1,6) (1,14) (2,6) (2,12) (2,18) (3,8) (3,6) (3,12) (3,18) (4,12) (4,9) (4,14) (5,15) (5,16) (5,7) (6,8) (6,12) (6,14) (7,10) (9,11) (9,18) (15,17) (15,16)\nQ: Is there a path between node 8 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1239"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,3) (0,12) (0,6) (0,11) (1,16) (1,3) (1,12) (1,6) (1,11) (1,14) (1,10) (2,15) (2,7) (2,13) (2,5) (2,9) (2,4) (2,18) (3,17) (3,12) (3,11) (3,14) (4,15) (4,7) (4,5) (4,9) (4,8) (5,15) (5,13) (5,9) (5,8) (5,18) (6,16) (6,17) (6,12) (6,14) (6,10) (7,15) (7,13) (7,9) (7,18) (8,15) (8,9) (8,18) (9,13) (9,18) (10,16) (10,17) (10,12) (10,11) (11,16) (11,17) (11,12) (12,16) (12,17) (12,14) (13,15) (13,18) (14,16) (14,17) (15,18) (16,17)\nQ: Is there a path between node 15 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1240"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,23) (1,6) (1,19) (1,7) (2,17) (2,24) (2,10) (2,20) (3,22) (3,27) (4,17) (4,15) (5,19) (5,12) (5,25) (6,19) (6,7) (7,18) (7,23) (8,16) (8,13) (9,27) (9,13) (10,21) (10,15) (10,11) (11,17) (11,26) (11,24) (11,14) (12,25) (12,23) (14,17) (14,26) (15,21) (17,26) (17,21) (17,24) (20,21) (20,24) (21,26) (21,24) (23,25)\nQ: Is there a path between node 6 and node 23?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1241"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,11) (0,1) (0,25) (0,28) (0,16) (0,31) (0,2) (0,23) (1,20) (1,26) (1,24) (1,10) (1,31) (1,21) (2,26) (2,19) (2,11) (2,5) (2,15) (2,32) (2,33) (2,8) (2,16) (2,31) (2,21) (2,30) (3,12) (3,4) (4,18) (5,11) (5,24) (6,14) (6,12) (6,9) (6,13) (7,26) (7,25) (7,33) (7,8) (7,21) (8,26) (8,19) (8,32) (8,31) (9,12) (10,19) (10,11) (10,25) (11,33) (11,24) (12,14) (14,18) (15,19) (15,17) (15,32) (15,25) (15,31) (15,21) (16,26) (16,32) (17,20) (17,19) (17,23) (19,24) (19,31) (19,21) (19,30) (21,32) (21,25) (21,24) (21,31) (23,31) (24,28) (25,32) (25,33) (25,28) (26,32) (26,33) (26,28) (26,31) (26,30) (28,33) (28,30) (31,32)\nQ: Is there a path between node 5 and node 14?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1242"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,14) (1,21) (1,3) (1,15) (1,7) (3,12) (4,10) (5,10) (6,22) (7,21) (7,15) (9,12) (11,13) (11,21) (14,20) (15,17) (15,21) (16,18) (18,22)\nQ: Is there a path between node 11 and node 22?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1243"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,13) (0,8) (0,18) (0,25) (0,14) (0,17) (0,21) (1,13) (1,26) (1,14) (1,20) (1,17) (1,24) (1,6) (2,8) (2,18) (2,9) (2,26) (2,14) (2,10) (2,15) (3,16) (3,12) (4,13) (4,8) (4,18) (4,25) (4,6) (5,19) (5,13) (5,10) (5,20) (5,22) (5,17) (5,6) (6,8) (6,18) (6,9) (6,26) (6,14) (6,17) (6,21) (6,15) (6,23) (7,25) (7,14) (7,22) (7,24) (7,15) (7,23) (8,13) (8,25) (8,24) (8,23) (9,25) (9,27) (9,26) (9,14) (9,17) (9,24) (9,23) (10,19) (10,13) (10,25) (10,22) (11,12) (12,16) (13,19) (13,18) (13,21) (14,19) (14,18) (14,22) (15,19) (15,25) (15,23) (17,25) (17,22) (17,21) (17,24) (18,21) (18,24) (19,26) (19,22) (19,24) (19,23) (20,25) (20,26) (20,24) (20,23) (21,27) (21,23) (22,25) (22,26) (22,23) (25,27) (25,26)\nQ: Is there a path between node 15 and node 24?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1244"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,21) (1,17) (1,15) (1,2) (1,4) (1,18) (2,8) (2,13) (2,17) (2,15) (2,23) (2,22) (2,4) (2,18) (2,12) (4,21) (4,8) (4,13) (4,15) (4,23) (4,22) (4,18) (4,12) (5,21) (5,8) (5,13) (5,17) (5,15) (5,22) (5,18) (7,14) (7,16) (7,10) (7,11) (7,19) (8,21) (8,17) (8,23) (8,18) (9,14) (9,24) (10,14) (10,24) (10,19) (11,14) (11,16) (11,24) (12,21) (12,13) (12,17) (12,15) (12,23) (12,22) (12,18) (13,21) (13,17) (13,15) (13,23) (13,22) (14,24) (15,21) (15,17) (15,23) (15,22) (15,18) (16,19) (17,21) (17,18) (18,21) (18,23) (21,22) (22,23)\nQ: Is there a path between node 9 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1245"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,2) (0,1) (0,4) (1,3) (1,2) (1,4) (1,6) (2,3) (2,4) (2,5) (3,4) (3,6) (4,6) (5,6)\nQ: Is there a path between node 2 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1246"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,11) (0,17) (0,3) (0,19) (0,9) (0,16) (0,15) (0,7) (0,12) (0,2) (1,11) (1,10) (1,3) (1,4) (1,8) (1,19) (1,13) (1,9) (1,16) (1,15) (1,7) (1,12) (1,2) (2,17) (2,5) (2,16) (2,15) (3,17) (3,10) (3,5) (3,6) (3,8) (3,13) (3,9) (3,16) (3,15) (3,7) (3,12) (4,11) (4,5) (4,8) (4,19) (4,13) (4,9) (4,7) (4,12) (5,11) (5,10) (5,6) (5,8) (5,19) (5,13) (5,7) (6,11) (6,17) (6,10) (6,8) (6,19) (6,13) (6,16) (6,15) (6,7) (6,12) (7,11) (7,17) (7,10) (7,19) (7,9) (7,16) (7,15) (8,11) (8,17) (8,10) (8,19) (8,13) (8,15) (8,12) (9,11) (9,17) (9,10) (9,13) (9,16) (9,15) (10,11) (10,17) (10,19) (10,13) (10,15) (10,12) (11,19) (11,15) (11,12) (12,17) (12,19) (12,13) (13,19) (13,16) (13,15) (14,18) (15,19) (15,16) (16,17) (17,19)\nQ: Is there a path between node 3 and node 18?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1247"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,17) (0,1) (0,4) (0,15) (0,2) (0,13) (0,10) (0,6) (0,18) (0,11) (0,12) (0,5) (1,19) (1,17) (1,4) (1,15) (1,2) (1,13) (1,10) (1,6) (1,18) (1,11) (1,12) (1,5) (2,19) (2,17) (2,4) (2,15) (2,13) (2,10) (2,6) (2,18) (2,11) (2,12) (2,5) (3,20) (3,16) (3,14) (3,8) (4,19) (4,17) (4,15) (4,13) (4,10) (4,6) (4,18) (4,11) (4,12) (4,5) (5,19) (5,17) (5,15) (5,13) (5,10) (5,6) (5,18) (5,11) (5,12) (6,19) (6,17) (6,15) (6,13) (6,10) (6,18) (6,11) (6,12) (7,9) (8,20) (8,16) (8,14) (10,19) (10,17) (10,15) (10,13) (10,18) (10,11) (10,12) (11,19) (11,17) (11,15) (11,13) (11,18) (11,12) (12,19) (12,17) (12,15) (12,13) (12,18) (13,19) (13,17) (13,15) (13,18) (14,20) (14,16) (15,19) (15,17) (15,18) (16,20) (17,19) (17,18) (18,19)\nQ: Is there a path between node 3 and node 18?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1248"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (1,18) (1,8) (1,4) (2,15) (2,18) (2,11) (2,23) (2,4) (3,12) (3,5) (4,23) (4,25) (5,12) (5,17) (6,22) (6,13) (7,18) (7,23) (7,8) (9,17) (10,19) (10,17) (11,15) (12,24) (14,20) (14,22) (15,18) (16,20) (16,22) (20,22) (21,22) (23,25)\nQ: Is there a path between node 15 and node 18?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1249"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,9) (0,2) (0,5) (0,10) (0,1) (1,4) (1,9) (1,2) (1,5) (1,10) (2,4) (2,9) (2,5) (2,10) (3,11) (3,8) (3,12) (3,7) (3,6) (4,9) (4,5) (4,10) (5,9) (5,10) (6,11) (6,8) (6,12) (6,7) (7,11) (7,8) (7,12) (8,11) (8,12) (9,10) (11,12)\nQ: Is there a path between node 3 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1250"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,5) (0,20) (0,7) (0,19) (0,1) (0,14) (0,12) (0,15) (0,18) (0,4) (1,10) (1,5) (1,7) (1,2) (1,14) (1,12) (1,3) (1,15) (1,16) (1,4) (2,10) (2,5) (2,20) (2,7) (2,19) (2,14) (2,12) (2,15) (2,16) (2,17) (2,18) (2,4) (3,5) (3,20) (3,7) (3,19) (3,14) (3,16) (3,17) (3,18) (4,10) (4,5) (4,20) (4,7) (4,19) (4,14) (4,12) (4,15) (4,16) (4,17) (5,20) (5,7) (5,19) (5,14) (5,12) (5,16) (5,17) (5,18) (6,11) (6,8) (7,10) (7,19) (7,14) (7,12) (7,15) (7,16) (7,17) (7,18) (8,11) (9,21) (9,13) (10,19) (10,14) (10,12) (10,16) (10,18) (12,20) (12,19) (12,14) (12,15) (12,16) (12,17) (14,20) (14,19) (14,15) (14,16) (14,17) (15,20) (15,19) (15,16) (15,17) (15,18) (16,20) (16,19) (16,17) (16,18) (17,20) (17,19) (17,18) (18,19) (19,20)\nQ: Is there a path between node 14 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1251"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,21) (0,7) (0,6) (0,3) (0,17) (0,20) (0,22) (0,16) (0,23) (0,25) (0,27) (1,5) (1,21) (1,4) (1,7) (1,15) (1,18) (1,2) (1,24) (1,20) (1,11) (1,16) (1,25) (1,27) (2,14) (2,5) (2,21) (2,4) (2,15) (2,24) (2,22) (2,11) (2,23) (2,25) (2,27) (3,14) (3,13) (3,21) (3,7) (3,15) (3,6) (3,17) (3,24) (3,22) (3,11) (3,16) (3,23) (4,14) (4,13) (4,5) (4,19) (4,7) (4,18) (4,17) (4,22) (4,11) (4,23) (4,25) (4,27) (5,13) (5,19) (5,15) (5,18) (5,24) (5,20) (5,22) (5,11) (5,23) (5,27) (6,14) (6,21) (6,19) (6,7) (6,15) (6,18) (6,17) (6,24) (6,20) (6,11) (6,16) (6,25) (6,27) (7,14) (7,13) (7,21) (7,19) (7,15) (7,18) (7,17) (7,20) (7,22) (7,11) (7,23) (7,27) (8,30) (8,28) (9,31) (9,10) (9,26) (9,29) (10,31) (10,26) (10,29) (11,13) (11,21) (11,19) (11,15) (11,24) (11,22) (11,25) (11,27) (12,28) (13,14) (13,21) (13,15) (13,18) (13,17) (13,24) (13,20) (13,16) (13,23) (13,25) (13,27) (14,21) (14,19) (14,24) (14,20) (14,22) (14,16) (14,23) (14,25) (15,21) (15,18) (15,17) (15,24) (15,20) (15,22) (15,16) (15,25) (15,27) (16,21) (16,18) (16,17) (16,24) (16,20) (16,22) (16,25) (17,21) (17,19) (17,18) (17,24) (17,20) (17,22) (17,23) (17,25) (17,27) (18,21) (18,24) (18,20) (18,25) (18,27) (19,21) (19,20) (19,22) (19,27) (20,21) (20,24) (20,22) (20,23) (20,27) (21,24) (21,22) (21,25) (21,27) (22,25) (23,25) (23,27) (25,27) (26,31) (26,29) (29,31)\nQ: Is there a path between node 30 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1252"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,11) (0,1) (0,25) (0,28) (0,16) (0,31) (0,2) (0,23) (1,20) (1,26) (1,24) (1,10) (1,31) (1,21) (2,26) (2,19) (2,11) (2,5) (2,15) (2,32) (2,33) (2,8) (2,16) (2,31) (2,21) (2,30) (3,12) (3,4) (4,18) (5,11) (5,24) (6,14) (6,12) (6,9) (6,13) (7,26) (7,25) (7,33) (7,8) (7,21) (8,26) (8,19) (8,32) (8,31) (9,12) (10,19) (10,11) (10,25) (11,33) (11,24) (12,14) (14,18) (15,19) (15,17) (15,32) (15,25) (15,31) (15,21) (16,26) (16,32) (17,20) (17,19) (17,23) (19,24) (19,31) (19,21) (19,30) (21,32) (21,25) (21,24) (21,31) (23,31) (24,28) (25,32) (25,33) (25,28) (26,32) (26,33) (26,28) (26,31) (26,30) (28,33) (28,30) (31,32)\nQ: Is there a path between node 16 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1253"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,15) (0,6) (0,17) (0,4) (0,12) (0,16) (0,9) (1,14) (1,23) (1,18) (1,19) (1,3) (1,21) (2,14) (2,5) (2,11) (2,23) (2,22) (2,8) (2,18) (2,19) (2,3) (2,20) (3,14) (3,5) (3,23) (3,22) (3,8) (3,18) (3,19) (3,20) (3,21) (4,7) (4,15) (4,6) (4,17) (4,13) (4,10) (4,16) (5,14) (5,8) (5,18) (5,19) (5,21) (6,13) (6,10) (6,16) (6,9) (7,15) (7,13) (7,9) (8,14) (8,11) (8,23) (8,22) (8,18) (8,19) (8,20) (8,21) (9,15) (9,13) (9,12) (9,16) (10,15) (10,17) (10,13) (10,12) (11,14) (11,23) (11,22) (11,18) (11,19) (12,17) (12,16) (13,17) (13,16) (14,23) (14,19) (15,17) (16,17) (18,23) (18,22) (18,19) (18,21) (19,23) (19,22) (19,20) (20,23) (20,21) (21,23) (22,23)\nQ: Is there a path between node 19 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1254"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,23) (0,8) (1,6) (1,26) (1,11) (2,6) (2,11) (3,12) (3,19) (3,20) (4,13) (4,21) (4,17) (4,10) (4,6) (4,23) (4,8) (5,13) (5,7) (5,21) (5,17) (5,28) (5,6) (5,23) (5,8) (5,26) (5,24) (5,11) (6,13) (6,17) (6,10) (6,23) (6,24) (7,17) (7,28) (7,23) (8,21) (8,10) (9,15) (10,13) (10,21) (10,23) (10,11) (11,13) (11,17) (12,19) (12,14) (12,27) (12,15) (12,22) (13,17) (13,16) (14,22) (15,19) (16,17) (16,28) (16,24) (17,24) (18,19) (18,27) (19,27) (21,26) (21,24) (22,25) (23,28) (24,28) (25,27)\nQ: Is there a path between node 11 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1255"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,17) (0,1) (0,4) (0,15) (0,2) (0,13) (0,10) (0,6) (0,18) (0,11) (0,12) (0,5) (1,19) (1,17) (1,4) (1,15) (1,2) (1,13) (1,10) (1,6) (1,18) (1,11) (1,12) (1,5) (2,19) (2,17) (2,4) (2,15) (2,13) (2,10) (2,6) (2,18) (2,11) (2,12) (2,5) (3,20) (3,16) (3,14) (3,8) (4,19) (4,17) (4,15) (4,13) (4,10) (4,6) (4,18) (4,11) (4,12) (4,5) (5,19) (5,17) (5,15) (5,13) (5,10) (5,6) (5,18) (5,11) (5,12) (6,19) (6,17) (6,15) (6,13) (6,10) (6,18) (6,11) (6,12) (7,9) (8,20) (8,16) (8,14) (10,19) (10,17) (10,15) (10,13) (10,18) (10,11) (10,12) (11,19) (11,17) (11,15) (11,13) (11,18) (11,12) (12,19) (12,17) (12,15) (12,13) (12,18) (13,19) (13,17) (13,15) (13,18) (14,20) (14,16) (15,19) (15,17) (15,18) (16,20) (17,19) (17,18) (18,19)\nQ: Is there a path between node 4 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1256"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,10) (0,17) (0,5) (0,13) (0,15) (0,16) (0,3) (0,7) (0,11) (0,1) (0,4) (0,14) (1,12) (1,10) (1,17) (1,5) (1,13) (1,15) (1,16) (1,3) (1,7) (1,11) (1,4) (1,14) (2,8) (2,6) (3,12) (3,10) (3,17) (3,5) (3,13) (3,15) (3,16) (3,7) (3,11) (3,4) (3,14) (4,12) (4,10) (4,17) (4,5) (4,13) (4,15) (4,16) (4,7) (4,11) (4,14) (5,12) (5,10) (5,17) (5,13) (5,15) (5,16) (5,7) (5,11) (5,14) (6,8) (7,12) (7,10) (7,17) (7,13) (7,15) (7,16) (7,11) (7,14) (10,12) (10,17) (10,13) (10,15) (10,16) (10,11) (10,14) (11,12) (11,17) (11,13) (11,15) (11,16) (11,14) (12,17) (12,13) (12,15) (12,16) (12,14) (13,17) (13,15) (13,16) (13,14) (14,17) (14,15) (14,16) (15,17) (15,16) (16,17)\nQ: Is there a path between node 8 and node 14?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1257"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,1) (2,3) (4,6) (5,6) (5,7)\nQ: Is there a path between node 9 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1258"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,8) (1,5) (1,10) (1,8) (2,6) (2,7) (3,9) (3,10) (4,11) (4,8) (6,7) (8,9) (8,10) (11,12)\nQ: Is there a path between node 8 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1259"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,2) (0,4) (0,5) (0,15) (0,7) (1,9) (1,13) (1,12) (1,3) (2,14) (2,10) (2,4) (2,8) (2,15) (2,7) (3,9) (3,13) (3,12) (3,11) (4,14) (4,6) (4,10) (4,8) (4,15) (5,6) (5,8) (5,7) (6,14) (6,8) (6,15) (7,14) (7,10) (7,8) (7,15) (8,14) (8,10) (8,15) (9,13) (9,12) (9,11) (10,14) (10,15) (11,13) (11,12) (12,13) (14,15)\nQ: Is there a path between node 2 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1260"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,9) (0,13) (0,3) (0,1) (0,2) (0,7) (0,8) (0,11) (1,14) (1,13) (1,8) (1,10) (1,11) (1,5) (2,9) (2,13) (2,3) (2,7) (2,8) (2,10) (3,14) (3,9) (3,13) (3,8) (3,11) (3,5) (4,6) (4,12) (5,14) (5,9) (5,7) (5,8) (5,10) (5,11) (6,12) (7,14) (7,13) (7,8) (7,10) (8,14) (8,9) (8,10) (9,14) (9,13) (10,14) (10,13) (11,14) (13,14)\nQ: Is there a path between node 10 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1261"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,11) (0,1) (0,3) (0,10) (0,4) (1,11) (1,3) (1,10) (1,4) (2,7) (3,11) (3,4) (4,5) (4,11) (5,11) (6,9) (6,8) (7,9) (7,8) (8,9) (10,11)\nQ: Is there a path between node 10 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1262"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,4) (0,16) (0,21) (0,1) (0,25) (0,14) (0,9) (0,5) (0,6) (0,12) (0,17) (0,24) (0,23) (1,29) (1,4) (1,27) (1,16) (1,21) (1,14) (1,9) (1,6) (1,24) (1,23) (2,26) (2,10) (2,22) (2,15) (2,28) (2,8) (2,30) (2,19) (3,26) (3,10) (3,11) (3,22) (3,15) (3,28) (3,8) (3,30) (3,19) (3,20) (4,29) (4,27) (4,16) (4,21) (4,14) (4,9) (4,5) (4,6) (4,12) (4,24) (5,29) (5,27) (5,21) (5,7) (5,14) (5,12) (5,17) (5,24) (5,23) (6,29) (6,27) (6,7) (6,25) (6,14) (6,9) (6,12) (6,24) (6,23) (7,25) (7,14) (7,9) (7,12) (7,17) (7,23) (8,26) (8,10) (8,11) (8,13) (8,30) (8,19) (9,29) (9,27) (9,16) (9,14) (9,12) (9,24) (9,23) (10,26) (10,13) (10,15) (10,28) (10,19) (10,20) (11,26) (11,13) (11,15) (11,28) (11,30) (11,19) (11,20) (12,29) (12,27) (12,16) (12,21) (12,25) (12,17) (12,24) (12,23) (13,26) (13,28) (13,30) (14,29) (14,16) (14,21) (14,25) (14,17) (14,24) (14,23) (15,26) (15,28) (15,30) (15,20) (16,27) (16,21) (16,17) (16,24) (16,23) (17,29) (17,27) (17,21) (17,25) (17,24) (19,26) (19,22) (19,30) (19,20) (20,26) (20,22) (20,28) (21,29) (21,27) (21,25) (21,24) (21,23) (22,26) (22,28) (22,30) (23,29) (23,27) (23,25) (24,29) (24,27) (24,25) (25,29) (26,28) (28,30)\nQ: Is there a path between node 11 and node 27?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1263"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,6) (0,1) (0,7) (0,4) (1,5) (1,6) (1,7) (1,4) (2,3) (4,5) (4,6) (4,7) (5,6) (5,7) (6,7)\nQ: Is there a path between node 6 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1264"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,5) (0,7) (0,6) (0,2) (0,4) (0,8) (0,9) (1,10) (2,3) (2,5) (2,7) (2,6) (2,4) (2,8) (2,9) (2,11) (3,5) (3,4) (3,8) (3,11) (4,5) (4,6) (4,9) (4,11) (5,6) (5,8) (5,9) (6,7) (6,8) (6,9) (6,11) (7,8) (7,11) (8,9) (9,11)\nQ: Is there a path between node 5 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1265"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,5) (3,5)\nQ: Is there a path between node 3 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1266"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (3,7) (4,6) (5,6)\nQ: Is there a path between node 2 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1267"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (1,11) (1,9) (1,14) (2,5) (2,6) (3,11) (3,13) (4,11) (4,13) (4,15) (5,7) (5,6) (7,10) (8,11) (8,9) (9,14) (9,12) (11,13) (13,14) (13,15)\nQ: Is there a path between node 8 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1268"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,3) (0,11) (0,8) (0,2) (0,12) (0,9) (0,1) (1,4) (1,3) (1,6) (1,11) (1,8) (1,7) (1,10) (1,2) (1,12) (2,3) (2,6) (2,11) (2,8) (2,9) (3,6) (3,11) (3,8) (3,7) (3,10) (3,9) (4,6) (4,11) (4,8) (4,7) (4,10) (4,12) (4,9) (6,8) (6,10) (7,10) (7,12) (7,9) (8,11) (8,10) (8,12) (9,10) (10,12)\nQ: Is there a path between node 5 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1269"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,10) (0,1) (1,8) (1,3) (1,14) (3,5) (3,6) (3,9) (3,12) (4,9) (4,16) (6,7) (6,12) (7,14) (8,16) (8,14) (10,11) (10,14) (10,12) (11,14) (12,14)\nQ: Is there a path between node 8 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1270"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,1) (0,6) (0,2) (0,3) (0,7) (0,5) (1,8) (1,6) (1,2) (1,3) (1,7) (1,5) (2,8) (2,6) (2,3) (2,7) (2,5) (3,8) (3,6) (3,7) (3,5) (5,8) (5,6) (5,7) (6,8) (6,7) (7,8)\nQ: Is there a path between node 6 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1271"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,10) (0,17) (0,5) (0,13) (0,15) (0,16) (0,3) (0,7) (0,11) (0,1) (0,4) (0,14) (1,12) (1,10) (1,17) (1,5) (1,13) (1,15) (1,16) (1,3) (1,7) (1,11) (1,4) (1,14) (2,8) (2,6) (3,12) (3,10) (3,17) (3,5) (3,13) (3,15) (3,16) (3,7) (3,11) (3,4) (3,14) (4,12) (4,10) (4,17) (4,5) (4,13) (4,15) (4,16) (4,7) (4,11) (4,14) (5,12) (5,10) (5,17) (5,13) (5,15) (5,16) (5,7) (5,11) (5,14) (6,8) (7,12) (7,10) (7,17) (7,13) (7,15) (7,16) (7,11) (7,14) (10,12) (10,17) (10,13) (10,15) (10,16) (10,11) (10,14) (11,12) (11,17) (11,13) (11,15) (11,16) (11,14) (12,17) (12,13) (12,15) (12,16) (12,14) (13,17) (13,15) (13,16) (13,14) (14,17) (14,15) (14,16) (15,17) (15,16) (16,17)\nQ: Is there a path between node 13 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1272"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (0,3) (0,4) (0,1) (1,2) (1,5) (1,6) (1,3) (1,4) (2,5) (2,6) (2,3) (2,4) (3,5) (3,6) (3,4) (4,5) (4,6) (5,6)\nQ: Is there a path between node 4 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1273"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,3) (0,12) (0,6) (0,11) (1,16) (1,3) (1,12) (1,6) (1,11) (1,14) (1,10) (2,15) (2,7) (2,13) (2,5) (2,9) (2,4) (2,18) (3,17) (3,12) (3,11) (3,14) (4,15) (4,7) (4,5) (4,9) (4,8) (5,15) (5,13) (5,9) (5,8) (5,18) (6,16) (6,17) (6,12) (6,14) (6,10) (7,15) (7,13) (7,9) (7,18) (8,15) (8,9) (8,18) (9,13) (9,18) (10,16) (10,17) (10,12) (10,11) (11,16) (11,17) (11,12) (12,16) (12,17) (12,14) (13,15) (13,18) (14,16) (14,17) (15,18) (16,17)\nQ: Is there a path between node 4 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1274"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,25) (0,13) (0,3) (0,1) (1,11) (1,25) (1,13) (1,2) (1,3) (1,8) (2,21) (2,22) (2,25) (2,13) (2,3) (3,18) (3,22) (3,11) (3,13) (4,23) (4,14) (4,6) (4,12) (4,27) (4,15) (4,5) (4,16) (4,26) (4,20) (4,7) (4,19) (5,14) (5,6) (5,12) (5,27) (5,15) (5,16) (5,9) (5,20) (5,7) (6,23) (6,14) (6,12) (6,24) (6,15) (6,16) (6,9) (6,17) (6,26) (6,20) (6,7) (6,19) (7,23) (7,14) (7,12) (7,24) (7,10) (7,16) (7,9) (7,17) (7,26) (7,20) (7,19) (8,21) (8,18) (8,22) (8,11) (8,25) (8,13) (9,23) (9,12) (9,10) (9,16) (9,17) (9,26) (9,20) (10,23) (10,14) (10,12) (10,24) (10,27) (10,16) (10,17) (10,26) (10,19) (11,21) (11,22) (11,25) (11,13) (12,23) (12,14) (12,24) (12,27) (12,16) (12,26) (12,20) (12,19) (13,22) (13,25) (14,23) (14,24) (14,16) (14,26) (14,19) (15,24) (15,27) (15,16) (15,26) (16,23) (16,27) (16,17) (16,26) (16,20) (17,27) (17,26) (17,20) (17,19) (18,22) (19,23) (19,24) (19,27) (19,26) (19,20) (20,23) (20,26) (21,22) (21,25) (22,25) (23,24) (23,27) (24,27) (24,26) (26,27)\nQ: Is there a path between node 22 and node 13?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1275"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,9) (1,8) (1,4) (2,8) (2,4) (2,3) (3,7) (3,6) (3,10) (3,12) (3,11) (4,10) (4,12) (6,14) (6,8) (6,10) (7,14) (7,11) (8,14) (8,12) (10,14) (11,14) (12,14)\nQ: Is there a path between node 14 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1276"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,1) (0,2) (0,7) (0,6) (1,2) (1,8) (1,7) (1,4) (1,6) (2,7) (2,4) (2,6) (3,5) (4,9) (4,8) (4,7) (6,9) (6,7) (7,8)\nQ: Is there a path between node 0 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1277"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (1,4) (1,11) (2,21) (2,20) (2,24) (3,24) (4,13) (4,15) (4,8) (5,19) (5,24) (6,20) (6,24) (7,25) (7,21) (8,17) (8,15) (8,12) (9,13) (9,12) (10,16) (11,13) (11,18) (11,23) (11,14) (11,12) (13,17) (14,23) (15,18) (15,23) (18,23) (19,25) (19,24) (20,21) (21,25) (24,25)\nQ: Is there a path between node 23 and node 18?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1278"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,27) (0,23) (0,4) (0,20) (0,17) (0,6) (1,5) (1,22) (1,11) (1,19) (1,24) (1,2) (1,15) (1,8) (1,30) (1,9) (1,28) (1,18) (2,5) (2,22) (2,24) (2,15) (2,8) (2,30) (2,9) (2,28) (2,18) (3,26) (3,13) (4,21) (4,29) (4,23) (4,20) (4,17) (4,6) (5,22) (5,19) (5,24) (5,14) (5,30) (5,28) (5,18) (6,21) (6,29) (6,27) (6,23) (6,20) (6,17) (7,26) (7,10) (7,13) (7,16) (7,12) (8,11) (8,24) (8,14) (8,30) (8,9) (8,28) (8,18) (9,22) (9,11) (9,19) (9,15) (9,28) (10,16) (10,12) (11,15) (11,30) (11,28) (11,18) (12,13) (12,16) (13,26) (13,16) (13,25) (14,22) (14,19) (14,15) (14,30) (15,19) (15,30) (15,28) (15,18) (16,26) (16,25) (17,29) (17,23) (18,19) (18,24) (18,28) (19,30) (19,28) (20,21) (20,27) (21,29) (21,27) (21,23) (22,24) (22,28) (23,27) (24,30) (24,28) (25,26) (28,30)\nQ: Is there a path between node 24 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1279"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (0,3) (0,4) (0,1) (1,2) (1,5) (1,6) (1,3) (1,4) (2,5) (2,6) (2,3) (2,4) (3,5) (3,6) (3,4) (4,5) (4,6) (5,6)\nQ: Is there a path between node 0 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1280"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,13) (2,25) (2,28) (2,21) (2,5) (2,23) (3,22) (3,8) (3,6) (3,19) (3,21) (3,31) (3,15) (5,20) (5,16) (5,21) (5,23) (6,18) (6,17) (6,23) (7,10) (8,21) (9,24) (12,22) (12,18) (13,30) (13,27) (14,26) (15,16) (15,19) (15,31) (16,22) (16,20) (16,19) (17,20) (17,21) (17,31) (18,22) (18,25) (18,20) (18,21) (18,23) (19,25) (19,28) (20,28) (20,21) (21,25) (22,25) (22,28) (23,28) (27,29) (29,30) (30,32)\nQ: Is there a path between node 31 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1281"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,9) (0,13) (0,3) (0,1) (0,2) (0,7) (0,8) (0,11) (1,14) (1,13) (1,8) (1,10) (1,11) (1,5) (2,9) (2,13) (2,3) (2,7) (2,8) (2,10) (3,14) (3,9) (3,13) (3,8) (3,11) (3,5) (4,6) (4,12) (5,14) (5,9) (5,7) (5,8) (5,10) (5,11) (6,12) (7,14) (7,13) (7,8) (7,10) (8,14) (8,9) (8,10) (9,14) (9,13) (10,14) (10,13) (11,14) (13,14)\nQ: Is there a path between node 12 and node 14?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1282"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,4) (0,12) (0,11) (0,10) (0,3) (0,17) (0,21) (0,27) (0,15) (0,23) (0,31) (0,29) (0,2) (0,8) (0,9) (0,14) (0,18) (1,5) (1,26) (1,13) (1,20) (1,32) (1,7) (2,19) (2,4) (2,28) (2,22) (2,16) (2,12) (2,10) (2,3) (2,17) (2,21) (2,27) (2,15) (2,23) (2,31) (2,29) (2,8) (2,9) (2,14) (2,18) (3,4) (3,22) (3,16) (3,12) (3,10) (3,17) (3,21) (3,27) (3,23) (3,31) (3,29) (3,6) (3,9) (3,14) (3,18) (4,16) (4,12) (4,11) (4,17) (4,21) (4,15) (4,30) (4,23) (4,29) (4,6) (4,8) (4,9) (4,18) (5,26) (5,13) (5,25) (5,24) (5,32) (5,7) (6,19) (6,22) (6,12) (6,11) (6,10) (6,17) (6,21) (6,27) (6,15) (6,30) (6,23) (6,31) (6,29) (6,9) (6,14) (7,26) (7,25) (7,32) (8,19) (8,28) (8,10) (8,17) (8,27) (8,15) (8,30) (8,23) (9,19) (9,28) (9,22) (9,16) (9,12) (9,10) (9,17) (9,21) (9,15) (9,30) (9,23) (9,29) (9,18) (10,19) (10,28) (10,22) (10,12) (10,11) (10,17) (10,21) (10,27) (10,15) (10,30) (10,23) (10,31) (10,29) (10,14) (10,18) (11,16) (11,12) (11,17) (11,21) (11,27) (11,15) (11,30) (11,31) (11,29) (11,14) (11,18) (12,19) (12,28) (12,22) (12,17) (12,27) (12,15) (12,30) (12,23) (12,31) (12,29) (12,14) (12,18) (13,26) (13,25) (13,20) (13,32) (14,28) (14,16) (14,17) (14,21) (14,27) (14,15) (14,31) (14,29) (14,18) (15,19) (15,22) (15,16) (15,17) (15,21) (15,27) (15,30) (15,23) (15,31) (15,29) (15,18) (16,19) (16,28) (16,22) (16,17) (16,21) (16,27) (16,30) (16,31) (16,18) (17,22) (17,21) (17,30) (17,31) (17,29) (17,18) (18,19) (18,28) (18,22) (18,21) (18,27) (18,29) (19,28) (19,22) (19,21) (19,30) (19,31) (19,29) (20,32) (21,28) (21,22) (21,27) (21,29) (22,28) (22,30) (22,23) (22,31) (22,29) (23,28) (23,27) (23,30) (23,31) (23,29) (24,26) (24,25) (25,26) (25,32) (26,32) (27,28) (27,30) (27,29) (28,30) (28,31) (28,29) (29,30) (29,31)\nQ: Is there a path between node 20 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1283"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,17) (0,23) (0,22) (0,1) (0,9) (0,11) (0,14) (0,19) (0,12) (0,18) (0,8) (0,4) (0,16) (0,15) (0,10) (0,6) (1,20) (1,17) (1,23) (1,22) (1,9) (1,11) (1,14) (1,19) (1,12) (1,18) (1,8) (1,4) (1,16) (1,15) (1,10) (1,6) (2,13) (2,5) (2,3) (2,21) (2,7) (3,13) (3,5) (3,21) (3,7) (4,20) (4,17) (4,23) (4,22) (4,9) (4,11) (4,14) (4,19) (4,12) (4,18) (4,8) (4,16) (4,15) (4,10) (4,6) (5,13) (5,21) (5,7) (6,20) (6,17) (6,23) (6,22) (6,9) (6,11) (6,14) (6,19) (6,12) (6,18) (6,8) (6,16) (6,15) (6,10) (7,13) (7,21) (8,20) (8,17) (8,23) (8,22) (8,9) (8,11) (8,14) (8,19) (8,12) (8,18) (8,16) (8,15) (8,10) (9,20) (9,17) (9,23) (9,22) (9,11) (9,14) (9,19) (9,12) (9,18) (9,16) (9,15) (9,10) (10,20) (10,17) (10,23) (10,22) (10,11) (10,14) (10,19) (10,12) (10,18) (10,16) (10,15) (11,20) (11,17) (11,23) (11,22) (11,14) (11,19) (11,12) (11,18) (11,16) (11,15) (12,20) (12,17) (12,23) (12,22) (12,14) (12,19) (12,18) (12,16) (12,15) (13,21) (14,20) (14,17) (14,23) (14,22) (14,19) (14,18) (14,16) (14,15) (15,20) (15,17) (15,23) (15,22) (15,19) (15,18) (15,16) (16,20) (16,17) (16,23) (16,22) (16,19) (16,18) (17,20) (17,23) (17,22) (17,19) (17,18) (18,20) (18,23) (18,22) (18,19) (19,20) (19,23) (19,22) (20,23) (20,22) (22,23)\nQ: Is there a path between node 11 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1284"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,11) (0,5) (0,9) (0,6) (1,2) (1,7) (1,3) (1,10) (1,8) (2,7) (2,3) (2,10) (2,8) (3,7) (3,10) (3,8) (4,11) (4,5) (4,9) (4,6) (5,11) (5,9) (5,6) (6,11) (6,9) (7,10) (7,8) (8,10) (9,11)\nQ: Is there a path between node 1 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1285"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,1) (0,12) (0,4) (1,13) (1,3) (1,6) (1,9) (2,15) (2,14) (2,11) (4,7) (5,16) (5,6) (5,9) (6,13) (6,8) (10,13) (10,12) (11,15) (11,14)\nQ: Is there a path between node 9 and node 13?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1286"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,17) (0,10) (0,28) (0,30) (0,29) (0,3) (1,14) (1,2) (2,25) (2,20) (2,7) (2,32) (2,22) (3,24) (3,19) (3,23) (3,4) (3,12) (3,29) (4,26) (4,24) (4,23) (4,8) (4,13) (5,26) (5,19) (5,23) (5,8) (5,15) (5,21) (6,14) (7,32) (8,16) (8,12) (8,29) (9,26) (9,13) (9,18) (9,29) (9,31) (10,17) (10,11) (10,30) (10,23) (10,13) (11,16) (11,17) (11,19) (11,28) (11,23) (12,26) (12,24) (12,21) (13,26) (13,17) (13,19) (13,30) (13,31) (14,25) (14,22) (15,16) (15,17) (15,23) (15,18) (15,29) (16,26) (16,24) (16,18) (16,21) (17,24) (17,19) (17,28) (17,30) (17,23) (18,24) (18,21) (19,26) (19,24) (19,28) (19,23) (20,32) (22,32) (22,27) (24,26) (24,30) (26,29) (28,29)\nQ: Is there a path between node 22 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1287"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,3) (0,7) (0,10) (0,13) (0,12) (0,16) (1,14) (1,2) (1,5) (1,9) (1,8) (1,15) (1,4) (1,6) (2,14) (2,5) (2,9) (2,8) (2,15) (2,4) (2,6) (3,11) (3,7) (3,10) (3,13) (3,12) (3,16) (4,14) (4,5) (4,9) (4,8) (4,15) (4,6) (5,14) (5,9) (5,8) (5,15) (5,6) (6,14) (6,9) (6,8) (6,15) (7,11) (7,10) (7,13) (7,12) (7,16) (8,14) (8,9) (8,15) (9,14) (9,15) (10,11) (10,13) (10,12) (10,16) (11,13) (11,12) (11,16) (12,13) (12,16) (13,16) (14,15)\nQ: Is there a path between node 6 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1288"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,19) (1,11) (2,4) (2,13) (3,17) (3,10) (3,11) (5,8) (5,13) (6,10) (6,12) (7,18) (7,9) (10,17) (10,12) (11,12) (12,17) (13,16) (13,15) (14,18)\nQ: Is there a path between node 7 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1289"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,10) (0,15) (0,21) (0,1) (0,7) (0,29) (0,24) (0,16) (0,23) (0,17) (1,26) (1,10) (1,15) (1,7) (1,28) (1,29) (1,12) (1,24) (1,16) (1,3) (1,23) (2,14) (2,27) (2,34) (3,26) (3,32) (3,15) (3,21) (3,7) (3,28) (3,29) (3,12) (3,24) (3,23) (3,17) (4,9) (4,14) (4,27) (4,31) (5,19) (5,22) (5,13) (5,20) (5,25) (5,30) (5,8) (5,33) (6,9) (6,27) (6,34) (6,31) (7,26) (7,32) (7,10) (7,15) (7,21) (7,29) (7,12) (7,24) (7,16) (7,23) (7,17) (8,19) (8,22) (8,13) (8,20) (8,25) (8,18) (8,30) (8,33) (9,14) (9,34) (10,32) (10,15) (10,21) (10,29) (10,24) (10,23) (10,17) (11,19) (11,22) (11,13) (11,25) (11,18) (11,30) (12,26) (12,32) (12,15) (12,21) (12,24) (12,16) (12,23) (13,19) (13,20) (13,25) (13,18) (13,33) (14,27) (14,31) (15,26) (15,21) (15,28) (15,24) (15,16) (15,23) (15,17) (16,26) (16,32) (16,23) (16,17) (17,26) (17,32) (17,21) (17,28) (17,24) (18,19) (18,22) (18,20) (18,30) (19,22) (19,20) (19,25) (19,30) (20,25) (20,30) (20,33) (21,26) (21,32) (21,28) (21,29) (22,25) (22,30) (22,33) (23,32) (23,28) (23,29) (23,24) (24,32) (24,28) (25,30) (25,33) (26,32) (26,28) (27,31) (28,29) (30,33)\nQ: Is there a path between node 1 and node 19?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1290"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,12) (1,25) (1,2) (1,10) (1,12) (1,3) (2,8) (2,22) (2,25) (2,26) (2,19) (2,11) (2,12) (2,7) (2,21) (3,25) (3,26) (3,10) (3,27) (3,21) (5,24) (5,6) (6,23) (6,9) (7,22) (7,25) (7,11) (8,20) (8,22) (8,25) (8,26) (8,27) (9,24) (10,14) (10,25) (10,13) (10,27) (10,21) (11,22) (11,12) (11,17) (11,21) (12,19) (12,18) (12,17) (12,27) (12,21) (13,17) (13,21) (14,17) (14,21) (15,23) (15,24) (16,22) (17,22) (17,25) (17,19) (18,20) (18,26) (18,21) (19,22) (19,26) (19,27) (20,27) (22,25) (25,26)\nQ: Is there a path between node 23 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1291"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,19) (0,17) (0,3) (0,10) (0,14) (1,7) (1,8) (1,15) (1,13) (2,9) (2,12) (2,18) (2,4) (3,6) (3,19) (3,17) (3,16) (3,10) (3,14) (4,12) (4,18) (5,9) (5,18) (6,19) (6,17) (6,16) (6,14) (6,20) (7,8) (7,15) (7,13) (9,12) (9,18) (10,16) (10,14) (10,20) (11,15) (12,18) (13,15) (14,19) (14,17) (14,20) (16,19) (16,17) (17,20) (19,20)\nQ: Is there a path between node 8 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1292"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,24) (0,2) (0,7) (0,15) (0,14) (0,22) (0,10) (0,18) (0,5) (0,9) (0,4) (0,11) (0,8) (0,20) (0,13) (1,2) (1,7) (1,15) (1,14) (1,18) (1,5) (1,16) (1,9) (1,4) (1,11) (1,8) (1,13) (2,24) (2,7) (2,15) (2,14) (2,22) (2,18) (2,16) (2,9) (2,4) (2,11) (2,8) (2,20) (2,23) (3,21) (4,7) (4,14) (4,22) (4,18) (4,16) (4,13) (4,23) (5,24) (5,7) (5,15) (5,14) (5,22) (5,10) (5,18) (5,20) (5,23) (6,12) (7,24) (7,15) (7,14) (7,10) (7,18) (7,16) (7,9) (7,11) (7,8) (7,20) (7,13) (7,23) (8,24) (8,14) (8,10) (8,18) (8,9) (8,13) (8,23) (9,24) (9,15) (9,14) (9,22) (9,10) (9,16) (9,20) (9,23) (10,24) (10,15) (10,14) (10,22) (10,18) (10,16) (10,20) (11,15) (11,14) (11,18) (11,16) (11,20) (11,13) (11,23) (13,24) (13,15) (13,18) (13,16) (13,23) (14,24) (14,15) (14,22) (14,18) (14,16) (14,23) (15,24) (15,22) (15,18) (15,16) (15,20) (15,23) (16,24) (16,20) (16,23) (18,22) (18,20) (18,23) (19,21) (20,22) (22,24) (22,23) (23,24)\nQ: Is there a path between node 8 and node 20?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1293"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,6) (0,2) (0,5) (1,7) (1,16) (1,14) (1,17) (1,3) (1,9) (1,13) (1,10) (2,11) (2,6) (2,5) (3,7) (3,16) (3,14) (3,17) (3,9) (3,13) (3,10) (4,8) (4,15) (4,12) (5,11) (5,6) (6,11) (7,16) (7,14) (7,17) (7,9) (7,13) (7,10) (8,15) (8,12) (9,16) (9,14) (9,17) (9,13) (9,10) (10,16) (10,14) (10,17) (10,13) (12,15) (13,16) (13,14) (13,17) (14,16) (14,17) (16,17)\nQ: Is there a path between node 3 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1294"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,19) (1,11) (2,4) (2,13) (3,17) (3,10) (3,11) (5,8) (5,13) (6,10) (6,12) (7,18) (7,9) (10,17) (10,12) (11,12) (12,17) (13,16) (13,15) (14,18)\nQ: Is there a path between node 19 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1295"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,1) (0,6) (0,2) (0,3) (0,7) (0,5) (1,8) (1,6) (1,2) (1,3) (1,7) (1,5) (2,8) (2,6) (2,3) (2,7) (2,5) (3,8) (3,6) (3,7) (3,5) (5,8) (5,6) (5,7) (6,8) (6,7) (7,8)\nQ: Is there a path between node 4 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1296"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,24) (0,2) (0,7) (0,15) (0,14) (0,22) (0,10) (0,18) (0,5) (0,9) (0,4) (0,11) (0,8) (0,20) (0,13) (1,2) (1,7) (1,15) (1,14) (1,18) (1,5) (1,16) (1,9) (1,4) (1,11) (1,8) (1,13) (2,24) (2,7) (2,15) (2,14) (2,22) (2,18) (2,16) (2,9) (2,4) (2,11) (2,8) (2,20) (2,23) (3,21) (4,7) (4,14) (4,22) (4,18) (4,16) (4,13) (4,23) (5,24) (5,7) (5,15) (5,14) (5,22) (5,10) (5,18) (5,20) (5,23) (6,12) (7,24) (7,15) (7,14) (7,10) (7,18) (7,16) (7,9) (7,11) (7,8) (7,20) (7,13) (7,23) (8,24) (8,14) (8,10) (8,18) (8,9) (8,13) (8,23) (9,24) (9,15) (9,14) (9,22) (9,10) (9,16) (9,20) (9,23) (10,24) (10,15) (10,14) (10,22) (10,18) (10,16) (10,20) (11,15) (11,14) (11,18) (11,16) (11,20) (11,13) (11,23) (13,24) (13,15) (13,18) (13,16) (13,23) (14,24) (14,15) (14,22) (14,18) (14,16) (14,23) (15,24) (15,22) (15,18) (15,16) (15,20) (15,23) (16,24) (16,20) (16,23) (18,22) (18,20) (18,23) (19,21) (20,22) (22,24) (22,23) (23,24)\nQ: Is there a path between node 15 and node 21?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1297"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,18) (0,19) (0,20) (0,23) (0,9) (0,10) (0,22) (0,13) (0,1) (0,12) (0,5) (0,7) (0,15) (0,4) (1,11) (1,18) (1,19) (1,20) (1,23) (1,9) (1,10) (1,22) (1,13) (1,12) (1,5) (1,7) (1,15) (1,4) (2,8) (2,6) (2,3) (2,24) (2,16) (2,21) (2,17) (2,14) (3,8) (3,6) (3,24) (3,16) (3,21) (3,17) (3,14) (4,11) (4,18) (4,19) (4,20) (4,23) (4,9) (4,10) (4,22) (4,13) (4,12) (4,5) (4,7) (4,15) (5,11) (5,18) (5,19) (5,20) (5,23) (5,9) (5,10) (5,22) (5,13) (5,12) (5,7) (5,15) (6,8) (6,24) (6,16) (6,21) (6,17) (6,14) (7,11) (7,18) (7,19) (7,20) (7,23) (7,9) (7,10) (7,22) (7,13) (7,12) (7,15) (8,24) (8,16) (8,21) (8,17) (8,14) (9,11) (9,18) (9,19) (9,20) (9,23) (9,10) (9,22) (9,13) (9,12) (9,15) (10,11) (10,18) (10,19) (10,20) (10,23) (10,22) (10,13) (10,12) (10,15) (11,18) (11,19) (11,20) (11,23) (11,22) (11,13) (11,12) (11,15) (12,18) (12,19) (12,20) (12,23) (12,22) (12,13) (12,15) (13,18) (13,19) (13,20) (13,23) (13,22) (13,15) (14,24) (14,16) (14,21) (14,17) (15,18) (15,19) (15,20) (15,23) (15,22) (16,24) (16,21) (16,17) (17,24) (17,21) (18,19) (18,20) (18,23) (18,22) (19,20) (19,23) (19,22) (20,23) (20,22) (21,24) (22,23)\nQ: Is there a path between node 20 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1298"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,7) (0,13) (0,24) (0,19) (0,5) (0,10) (0,4) (0,2) (0,21) (0,17) (0,23) (0,9) (0,20) (0,15) (0,22) (1,3) (1,18) (1,6) (1,14) (1,8) (1,11) (2,12) (2,7) (2,13) (2,24) (2,19) (2,5) (2,10) (2,4) (2,21) (2,17) (2,23) (2,9) (2,20) (2,15) (2,22) (3,18) (3,6) (3,14) (3,8) (3,11) (4,12) (4,7) (4,13) (4,24) (4,19) (4,5) (4,10) (4,21) (4,17) (4,23) (4,9) (4,20) (4,15) (4,22) (5,12) (5,7) (5,13) (5,24) (5,19) (5,10) (5,21) (5,17) (5,23) (5,9) (5,20) (5,15) (5,22) (6,18) (6,14) (6,8) (6,11) (7,12) (7,13) (7,24) (7,19) (7,10) (7,21) (7,17) (7,23) (7,9) (7,20) (7,15) (7,22) (8,18) (8,14) (8,11) (9,12) (9,13) (9,24) (9,19) (9,10) (9,21) (9,17) (9,23) (9,20) (9,15) (9,22) (10,12) (10,13) (10,24) (10,19) (10,21) (10,17) (10,23) (10,20) (10,15) (10,22) (11,18) (11,14) (12,13) (12,24) (12,19) (12,21) (12,17) (12,23) (12,20) (12,15) (12,22) (13,24) (13,19) (13,21) (13,17) (13,23) (13,20) (13,15) (13,22) (14,18) (15,24) (15,19) (15,21) (15,17) (15,23) (15,20) (15,22) (17,24) (17,19) (17,21) (17,23) (17,20) (17,22) (19,24) (19,21) (19,23) (19,20) (19,22) (20,24) (20,21) (20,23) (20,22) (21,24) (21,23) (21,22) (22,24) (22,23) (23,24)\nQ: Is there a path between node 14 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1299"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,1) (0,12) (0,4) (1,13) (1,3) (1,6) (1,9) (2,15) (2,14) (2,11) (4,7) (5,16) (5,6) (5,9) (6,13) (6,8) (10,13) (10,12) (11,15) (11,14)\nQ: Is there a path between node 16 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1300"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,18) (0,17) (0,10) (1,7) (1,24) (1,27) (2,4) (2,8) (2,13) (2,19) (2,27) (3,16) (3,28) (3,9) (4,18) (4,6) (4,10) (4,11) (4,27) (6,20) (6,8) (6,7) (6,27) (7,8) (7,18) (7,17) (7,23) (7,24) (7,10) (7,13) (7,19) (7,11) (7,14) (8,17) (8,22) (8,24) (8,10) (8,11) (10,18) (10,17) (10,12) (10,11) (10,27) (11,17) (11,12) (12,20) (12,18) (12,17) (12,14) (13,20) (13,18) (13,24) (13,27) (13,26) (14,18) (15,28) (15,25) (16,25) (17,20) (17,18) (17,26) (18,22) (18,23) (18,19) (18,27) (19,23) (19,27) (19,26) (20,24) (22,23) (22,24) (22,26) (26,27)\nQ: Is there a path between node 21 and node 24?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1301"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,10) (0,13) (0,12) (0,9) (0,18) (0,24) (0,5) (0,20) (0,21) (0,7) (0,3) (0,23) (1,2) (1,13) (1,16) (1,12) (1,18) (1,24) (1,20) (1,4) (1,7) (1,3) (1,19) (1,23) (2,13) (2,16) (2,12) (2,9) (2,11) (2,18) (2,24) (2,5) (2,20) (2,4) (2,21) (2,7) (2,3) (2,23) (3,13) (3,16) (3,12) (3,9) (3,11) (3,24) (3,5) (3,20) (3,21) (3,7) (3,19) (3,23) (4,10) (4,16) (4,12) (4,11) (4,18) (4,24) (4,5) (4,20) (4,21) (4,7) (4,19) (4,23) (5,13) (5,12) (5,11) (5,18) (5,24) (5,20) (5,21) (5,7) (5,23) (6,15) (6,25) (6,22) (6,8) (7,13) (7,12) (7,9) (7,11) (7,18) (7,20) (7,21) (7,19) (8,17) (8,15) (8,22) (8,14) (9,10) (9,13) (9,16) (9,11) (9,18) (9,21) (9,19) (9,23) (10,13) (10,12) (10,11) (10,24) (10,20) (10,21) (10,19) (10,23) (11,13) (11,16) (11,24) (11,20) (11,21) (11,19) (11,23) (12,13) (12,16) (12,18) (12,24) (12,20) (12,21) (12,19) (12,23) (13,16) (13,24) (13,21) (13,23) (14,17) (14,15) (14,22) (15,17) (15,25) (15,22) (16,18) (16,24) (16,21) (16,23) (17,25) (17,22) (18,20) (18,21) (18,19) (18,23) (19,20) (19,23) (20,24) (20,21) (21,23) (22,25) (23,24)\nQ: Is there a path between node 1 and node 14?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1302"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (1,2) (1,5) (5,6)\nQ: Is there a path between node 3 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1303"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,1) (0,15) (0,6) (0,9) (0,4) (0,16) (0,19) (1,20) (1,15) (1,6) (1,9) (1,4) (1,16) (1,19) (2,14) (2,10) (2,3) (2,11) (2,7) (2,18) (2,5) (2,12) (2,17) (2,8) (3,14) (3,10) (3,11) (3,7) (3,18) (3,5) (3,12) (3,17) (3,8) (4,20) (4,15) (4,6) (4,9) (4,16) (4,19) (5,14) (5,10) (5,11) (5,7) (5,18) (5,12) (5,17) (5,8) (6,20) (6,15) (6,9) (6,16) (6,19) (7,14) (7,10) (7,11) (7,18) (7,12) (7,17) (7,8) (8,14) (8,10) (8,11) (8,18) (8,12) (8,17) (9,20) (9,15) (9,16) (9,19) (10,14) (10,11) (10,18) (10,12) (10,17) (11,14) (11,18) (11,12) (11,17) (12,14) (12,18) (12,17) (14,18) (14,17) (15,20) (15,16) (15,19) (16,20) (16,19) (17,18) (19,20)\nQ: Is there a path between node 16 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1304"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,10) (0,1) (1,8) (1,3) (1,14) (3,5) (3,6) (3,9) (3,12) (4,9) (4,16) (6,7) (6,12) (7,14) (8,16) (8,14) (10,11) (10,14) (10,12) (11,14) (12,14)\nQ: Is there a path between node 6 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1305"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,19) (0,25) (0,2) (0,13) (0,1) (1,17) (1,24) (1,25) (1,11) (2,17) (2,25) (2,16) (2,13) (3,17) (4,23) (4,7) (4,14) (4,8) (5,18) (5,16) (6,18) (6,16) (6,21) (7,14) (7,15) (7,10) (8,23) (8,10) (9,14) (9,10) (10,23) (10,20) (11,17) (11,18) (11,25) (11,16) (11,13) (12,16) (13,17) (13,24) (13,25) (13,21) (14,15) (16,21) (17,19) (17,18) (17,25) (19,25) (19,21) (21,25)\nQ: Is there a path between node 12 and node 13?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1306"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,6) (0,3) (0,18) (0,1) (0,15) (0,12) (0,14) (0,9) (0,16) (0,8) (0,2) (0,11) (0,19) (1,7) (1,6) (1,3) (1,18) (1,15) (1,9) (1,8) (1,2) (1,20) (2,7) (2,3) (2,18) (2,15) (2,12) (2,14) (2,9) (2,16) (2,8) (2,11) (2,19) (2,20) (3,18) (3,15) (3,12) (3,9) (3,16) (3,8) (3,19) (3,20) (4,13) (4,17) (5,17) (6,7) (6,18) (6,15) (6,14) (6,9) (6,16) (6,11) (6,19) (6,20) (7,15) (7,12) (7,14) (7,9) (7,16) (8,18) (8,12) (8,14) (8,9) (8,16) (8,11) (8,19) (8,20) (9,18) (9,15) (9,12) (9,11) (9,19) (9,20) (10,13) (11,18) (11,12) (11,14) (11,16) (11,19) (11,20) (12,18) (12,15) (12,14) (12,19) (12,20) (13,17) (14,19) (16,18) (16,19) (18,20)\nQ: Is there a path between node 9 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1307"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (0,11) (0,8) (0,17) (0,13) (0,6) (0,3) (0,15) (0,7) (1,14) (1,19) (1,9) (1,21) (1,12) (1,22) (1,4) (1,18) (1,5) (1,10) (1,20) (2,16) (3,23) (3,11) (3,8) (3,17) (3,13) (3,6) (3,15) (3,7) (4,14) (4,19) (4,9) (4,21) (4,12) (4,22) (4,18) (4,5) (4,10) (4,20) (5,14) (5,19) (5,9) (5,21) (5,12) (5,22) (5,18) (5,10) (5,20) (6,23) (6,11) (6,8) (6,17) (6,13) (6,15) (6,7) (7,23) (7,11) (7,8) (7,17) (7,13) (7,15) (8,23) (8,11) (8,17) (8,13) (8,15) (9,14) (9,19) (9,21) (9,12) (9,22) (9,18) (9,10) (9,20) (10,14) (10,19) (10,21) (10,12) (10,22) (10,18) (10,20) (11,23) (11,17) (11,13) (11,15) (12,14) (12,19) (12,21) (12,22) (12,18) (12,20) (13,23) (13,17) (13,15) (14,19) (14,21) (14,22) (14,18) (14,20) (15,23) (15,17) (17,23) (18,19) (18,21) (18,22) (18,20) (19,21) (19,22) (19,20) (20,21) (20,22) (21,22)\nQ: Is there a path between node 20 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1308"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,5) (0,7) (0,2) (0,8) (0,4) (0,9) (0,1) (0,12) (0,3) (0,11) (0,13) (1,10) (1,5) (1,7) (1,2) (1,8) (1,4) (1,9) (1,12) (1,3) (1,11) (1,13) (2,10) (2,5) (2,7) (2,8) (2,4) (2,9) (2,12) (2,3) (2,11) (2,13) (3,10) (3,5) (3,7) (3,8) (3,4) (3,9) (3,12) (3,11) (3,13) (4,10) (4,5) (4,7) (4,8) (4,9) (4,12) (4,11) (4,13) (5,10) (5,7) (5,8) (5,9) (5,12) (5,11) (5,13) (7,10) (7,8) (7,9) (7,12) (7,11) (7,13) (8,10) (8,9) (8,12) (8,11) (8,13) (9,10) (9,12) (9,11) (9,13) (10,12) (10,11) (10,13) (11,12) (11,13) (12,13)\nQ: Is there a path between node 7 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1309"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,7) (0,8) (0,9) (0,13) (0,14) (0,15) (0,5) (1,2) (1,12) (1,16) (1,11) (1,3) (1,6) (1,14) (1,4) (2,12) (2,7) (2,9) (2,13) (2,14) (3,16) (3,11) (3,7) (3,8) (3,14) (3,15) (3,5) (3,4) (4,12) (4,11) (4,8) (4,9) (4,13) (4,14) (4,5) (5,12) (5,16) (5,11) (5,7) (5,8) (5,13) (5,14) (5,15) (6,12) (6,16) (6,11) (6,7) (6,14) (6,15) (7,12) (7,16) (7,11) (7,8) (7,9) (7,13) (8,12) (8,16) (8,11) (8,9) (8,13) (8,14) (9,12) (9,16) (9,11) (9,14) (9,15) (11,12) (11,16) (11,14) (12,13) (12,15) (13,16) (13,15) (14,16)\nQ: Is there a path between node 2 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1310"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,13) (0,2) (0,15) (0,6) (0,17) (0,8) (0,16) (0,18) (0,9) (0,12) (0,11) (1,10) (1,14) (1,7) (1,5) (1,4) (2,3) (2,13) (2,15) (2,6) (2,17) (2,8) (2,16) (2,18) (2,9) (2,12) (2,11) (3,13) (3,15) (3,6) (3,17) (3,8) (3,16) (3,18) (3,9) (3,12) (3,11) (4,10) (4,14) (4,7) (4,5) (5,10) (5,14) (5,7) (6,13) (6,15) (6,17) (6,8) (6,16) (6,18) (6,9) (6,12) (6,11) (7,10) (7,14) (8,13) (8,15) (8,17) (8,16) (8,18) (8,9) (8,12) (8,11) (9,13) (9,15) (9,17) (9,16) (9,18) (9,12) (9,11) (10,14) (11,13) (11,15) (11,17) (11,16) (11,18) (11,12) (12,13) (12,15) (12,17) (12,16) (12,18) (13,15) (13,17) (13,16) (13,18) (15,17) (15,16) (15,18) (16,17) (16,18) (17,18)\nQ: Is there a path between node 9 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1311"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,11) (1,9) (1,19) (1,31) (1,20) (2,15) (2,11) (2,27) (2,29) (2,16) (2,31) (3,8) (3,4) (3,12) (3,18) (3,17) (3,10) (3,25) (3,31) (3,20) (4,30) (4,24) (4,19) (5,26) (5,23) (6,13) (7,15) (7,9) (7,30) (7,12) (7,16) (7,19) (7,10) (7,25) (8,15) (8,11) (8,30) (8,24) (8,10) (8,31) (9,11) (9,30) (9,27) (9,29) (9,10) (10,15) (10,30) (10,12) (10,18) (10,19) (10,17) (10,14) (11,30) (11,29) (11,19) (12,15) (12,19) (12,14) (12,20) (13,28) (14,27) (14,24) (14,20) (15,27) (15,18) (15,25) (15,20) (16,29) (16,24) (16,19) (17,29) (17,19) (17,31) (18,30) (18,24) (18,19) (18,31) (19,30) (19,25) (21,28) (21,23) (22,23) (25,27) (25,31) (26,28) (29,31)\nQ: Is there a path between node 29 and node 30?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1312"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,2) (0,3) (1,5) (2,4) (2,3) (3,4)\nQ: Is there a path between node 5 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1313"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,11) (0,15) (0,25) (0,31) (0,23) (0,14) (1,28) (1,20) (1,12) (1,21) (1,19) (1,24) (1,27) (1,13) (1,6) (2,20) (2,22) (2,21) (2,19) (2,13) (2,6) (3,15) (3,4) (3,25) (3,23) (4,9) (4,15) (4,14) (5,8) (5,17) (5,10) (5,26) (5,7) (5,16) (6,20) (6,21) (6,19) (6,27) (6,13) (7,17) (7,16) (7,29) (8,17) (9,11) (9,15) (9,31) (9,23) (9,14) (10,17) (11,15) (11,30) (11,23) (11,14) (12,20) (12,22) (12,19) (12,27) (12,13) (12,18) (13,28) (13,22) (13,21) (13,24) (13,27) (13,18) (14,15) (14,25) (14,31) (14,23) (15,25) (15,30) (15,23) (16,26) (17,26) (17,29) (18,28) (18,20) (18,22) (18,21) (18,19) (18,24) (18,27) (19,22) (19,21) (19,24) (19,27) (20,28) (20,22) (20,21) (20,24) (20,27) (21,28) (21,22) (21,24) (22,24) (22,27) (23,30) (23,31) (24,28) (25,31) (27,28) (30,31)\nQ: Is there a path between node 8 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1314"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,28) (0,26) (0,7) (0,22) (0,6) (0,1) (0,30) (0,3) (1,16) (1,28) (1,26) (1,22) (1,10) (1,30) (2,4) (2,29) (2,24) (2,14) (2,21) (2,25) (2,13) (2,12) (2,31) (2,19) (2,33) (2,27) (2,23) (2,8) (2,18) (3,16) (3,28) (3,26) (3,9) (3,7) (3,10) (4,29) (4,32) (4,24) (4,21) (4,25) (4,15) (4,12) (4,31) (4,19) (4,33) (4,27) (4,17) (4,23) (4,18) (5,32) (5,14) (5,21) (5,15) (5,12) (5,19) (5,33) (5,27) (5,23) (5,8) (6,28) (6,26) (6,7) (6,22) (6,10) (7,16) (7,9) (7,22) (7,10) (8,29) (8,32) (8,24) (8,21) (8,15) (8,13) (8,33) (8,27) (8,23) (8,18) (9,16) (9,28) (9,26) (9,22) (9,10) (10,28) (10,22) (10,30) (12,29) (12,14) (12,21) (12,25) (12,15) (12,13) (12,31) (12,19) (12,33) (12,17) (12,23) (12,18) (13,20) (13,29) (13,24) (13,21) (13,25) (13,15) (13,31) (13,19) (13,33) (13,27) (13,17) (13,23) (13,18) (14,20) (14,29) (14,32) (14,24) (14,21) (14,15) (14,31) (14,19) (14,33) (14,17) (14,18) (15,20) (15,29) (15,32) (15,24) (15,21) (15,25) (15,31) (15,19) (15,33) (15,27) (15,17) (15,23) (15,18) (16,28) (16,26) (16,22) (16,30) (17,20) (17,29) (17,32) (17,24) (17,21) (17,25) (17,31) (17,19) (17,18) (18,20) (18,29) (18,32) (18,24) (18,21) (18,25) (18,31) (18,19) (18,27) (18,23) (19,32) (19,24) (19,33) (19,27) (19,23) (20,29) (20,32) (20,24) (20,21) (20,25) (20,31) (20,33) (20,27) (20,23) (21,32) (21,24) (21,25) (21,31) (21,33) (21,27) (21,23) (22,26) (22,30) (23,29) (23,32) (23,24) (23,25) (23,31) (23,33) (23,27) (24,32) (24,25) (24,31) (24,27) (25,29) (25,33) (25,27) (26,28) (26,30) (27,29) (27,31) (27,33) (28,30) (29,32) (29,31) (29,33) (31,32) (31,33) (32,33)\nQ: Is there a path between node 30 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1315"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,20) (0,27) (0,29) (0,26) (0,17) (0,3) (0,1) (0,16) (1,6) (1,7) (1,20) (1,19) (1,3) (1,33) (1,4) (2,27) (2,34) (2,26) (2,19) (2,17) (2,3) (2,21) (2,4) (3,6) (3,7) (3,11) (3,28) (3,29) (4,6) (4,28) (4,27) (4,29) (4,26) (4,19) (4,33) (4,23) (5,7) (5,11) (5,28) (5,19) (5,33) (5,16) (6,7) (6,28) (6,27) (6,26) (6,21) (7,34) (8,13) (8,12) (8,22) (8,15) (9,24) (9,12) (9,10) (10,25) (11,16) (11,23) (12,32) (12,18) (12,22) (12,15) (13,14) (14,18) (14,15) (15,30) (15,18) (16,27) (16,17) (16,23) (17,29) (17,19) (17,33) (17,23) (18,31) (18,24) (19,28) (19,27) (19,34) (19,29) (19,33) (19,21) (20,21) (21,26) (21,33) (22,30) (22,25) (25,30) (25,31) (26,28) (26,34) (26,29) (27,28) (30,32) (31,32)\nQ: Is there a path between node 13 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1316"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,13) (0,11) (0,21) (0,8) (0,18) (0,3) (0,7) (0,15) (0,20) (0,17) (0,10) (0,22) (0,1) (0,9) (0,6) (0,19) (1,23) (1,14) (1,5) (1,13) (1,11) (1,12) (1,21) (1,8) (1,18) (1,3) (1,25) (1,7) (1,28) (1,15) (1,20) (1,17) (1,10) (1,22) (1,9) (1,6) (1,16) (1,19) (3,27) (3,14) (3,5) (3,13) (3,4) (3,21) (3,18) (3,25) (3,28) (3,15) (3,20) (3,17) (3,22) (3,6) (3,16) (3,19) (4,27) (4,23) (4,5) (4,13) (4,11) (4,12) (4,8) (4,28) (4,15) (4,20) (4,17) (4,10) (4,24) (4,6) (5,27) (5,23) (5,14) (5,13) (5,11) (5,12) (5,21) (5,8) (5,18) (5,25) (5,7) (5,15) (5,10) (5,22) (5,24) (5,9) (5,6) (5,16) (5,19) (6,27) (6,14) (6,11) (6,12) (6,18) (6,25) (6,7) (6,20) (6,17) (6,10) (6,22) (6,24) (6,9) (6,16) (6,19) (7,23) (7,14) (7,13) (7,12) (7,21) (7,8) (7,25) (7,28) (7,20) (7,10) (7,22) (7,16) (7,19) (8,27) (8,13) (8,18) (8,25) (8,15) (8,17) (8,10) (8,22) (8,24) (8,9) (8,16) (8,19) (9,27) (9,23) (9,11) (9,21) (9,25) (9,28) (9,15) (9,20) (9,17) (9,10) (9,22) (9,24) (9,16) (9,19) (10,27) (10,14) (10,11) (10,12) (10,25) (10,28) (10,15) (10,20) (10,17) (10,24) (10,16) (10,19) (11,23) (11,21) (11,18) (11,25) (11,28) (11,15) (11,17) (11,22) (11,24) (11,19) (12,27) (12,23) (12,13) (12,21) (12,18) (12,25) (12,28) (12,15) (12,17) (12,22) (12,24) (12,16) (13,27) (13,14) (13,21) (13,18) (13,28) (13,15) (13,17) (13,24) (13,16) (13,19) (14,27) (14,25) (14,28) (14,15) (14,17) (14,22) (14,24) (14,16) (15,23) (15,21) (15,18) (15,25) (15,20) (15,24) (16,27) (16,23) (16,17) (16,24) (16,19) (17,27) (17,23) (17,18) (17,25) (17,28) (17,20) (17,22) (17,24) (17,19) (18,23) (18,21) (18,25) (18,28) (18,20) (18,22) (18,24) (18,19) (19,27) (19,23) (19,21) (19,25) (19,24) (20,27) (20,23) (20,21) (20,25) (20,24) (21,23) (21,22) (23,27) (23,24) (25,27) (25,28) (27,28)\nQ: Is there a path between node 12 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1317"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,3) (0,12) (0,6) (0,11) (1,16) (1,3) (1,12) (1,6) (1,11) (1,14) (1,10) (2,15) (2,7) (2,13) (2,5) (2,9) (2,4) (2,18) (3,17) (3,12) (3,11) (3,14) (4,15) (4,7) (4,5) (4,9) (4,8) (5,15) (5,13) (5,9) (5,8) (5,18) (6,16) (6,17) (6,12) (6,14) (6,10) (7,15) (7,13) (7,9) (7,18) (8,15) (8,9) (8,18) (9,13) (9,18) (10,16) (10,17) (10,12) (10,11) (11,16) (11,17) (11,12) (12,16) (12,17) (12,14) (13,15) (13,18) (14,16) (14,17) (15,18) (16,17)\nQ: Is there a path between node 2 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1318"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,27) (0,23) (0,4) (0,20) (0,17) (0,6) (1,5) (1,22) (1,11) (1,19) (1,24) (1,2) (1,15) (1,8) (1,30) (1,9) (1,28) (1,18) (2,5) (2,22) (2,24) (2,15) (2,8) (2,30) (2,9) (2,28) (2,18) (3,26) (3,13) (4,21) (4,29) (4,23) (4,20) (4,17) (4,6) (5,22) (5,19) (5,24) (5,14) (5,30) (5,28) (5,18) (6,21) (6,29) (6,27) (6,23) (6,20) (6,17) (7,26) (7,10) (7,13) (7,16) (7,12) (8,11) (8,24) (8,14) (8,30) (8,9) (8,28) (8,18) (9,22) (9,11) (9,19) (9,15) (9,28) (10,16) (10,12) (11,15) (11,30) (11,28) (11,18) (12,13) (12,16) (13,26) (13,16) (13,25) (14,22) (14,19) (14,15) (14,30) (15,19) (15,30) (15,28) (15,18) (16,26) (16,25) (17,29) (17,23) (18,19) (18,24) (18,28) (19,30) (19,28) (20,21) (20,27) (21,29) (21,27) (21,23) (22,24) (22,28) (23,27) (24,30) (24,28) (25,26) (28,30)\nQ: Is there a path between node 13 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1319"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,29) (0,1) (0,9) (0,20) (0,34) (0,7) (0,19) (0,22) (0,31) (1,11) (1,30) (1,6) (1,21) (1,14) (1,28) (1,19) (1,31) (1,4) (2,3) (2,11) (2,18) (2,21) (2,20) (2,14) (2,7) (2,17) (3,11) (3,33) (3,15) (3,30) (3,18) (3,21) (3,14) (3,5) (4,10) (4,26) (4,27) (4,21) (4,34) (5,9) (5,27) (5,30) (5,6) (5,24) (5,14) (5,34) (5,28) (5,17) (6,11) (6,25) (6,10) (6,26) (6,29) (6,15) (6,16) (6,14) (6,7) (6,12) (6,22) (7,10) (7,26) (7,27) (7,18) (7,24) (7,8) (7,31) (8,11) (8,33) (8,9) (8,30) (8,24) (8,20) (8,16) (8,22) (8,17) (9,10) (9,20) (9,16) (9,14) (10,25) (10,33) (10,30) (10,18) (10,24) (10,20) (10,31) (11,15) (11,12) (11,19) (11,17) (12,25) (12,29) (12,27) (12,30) (12,34) (12,28) (12,17) (14,25) (14,33) (14,26) (14,29) (14,30) (14,21) (14,17) (15,20) (15,17) (16,21) (16,28) (16,19) (16,22) (17,27) (17,30) (17,24) (17,19) (18,26) (18,21) (18,28) (19,33) (19,27) (19,34) (19,22) (20,25) (20,26) (20,27) (20,21) (20,28) (20,31) (21,22) (22,24) (22,31) (24,34) (24,28) (25,26) (25,29) (25,27) (26,33) (26,27) (26,30) (27,30) (27,28) (28,31) (29,30) (29,34) (29,31) (30,33) (30,34) (31,33) (31,34)\nQ: Is there a path between node 6 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1320"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,3) (0,14) (1,8) (1,6) (1,14) (2,6) (2,12) (2,18) (3,8) (3,6) (3,12) (3,18) (4,12) (4,9) (4,14) (5,15) (5,16) (5,7) (6,8) (6,12) (6,14) (7,10) (9,11) (9,18) (15,17) (15,16)\nQ: Is there a path between node 12 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1321"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,8) (0,5) (0,4) (0,25) (0,22) (0,16) (0,24) (0,21) (2,15) (2,23) (2,26) (2,10) (2,3) (2,11) (2,6) (2,27) (3,15) (3,23) (3,14) (3,26) (3,10) (3,11) (3,27) (4,8) (4,13) (4,5) (4,20) (4,18) (4,7) (4,22) (4,16) (4,24) (5,8) (5,13) (5,20) (5,7) (5,22) (5,24) (5,21) (6,15) (6,23) (6,14) (6,26) (6,10) (6,11) (6,27) (7,12) (7,20) (7,25) (7,16) (7,21) (8,12) (8,20) (8,25) (8,16) (8,24) (10,15) (10,23) (10,14) (10,26) (10,19) (10,11) (10,27) (11,15) (11,23) (11,26) (11,27) (12,16) (12,24) (12,21) (13,20) (13,18) (13,25) (13,22) (13,16) (13,24) (13,21) (14,15) (14,26) (15,26) (15,27) (16,22) (16,24) (16,21) (18,25) (18,22) (18,21) (19,23) (19,26) (19,27) (20,25) (20,24) (21,25) (21,24) (22,25) (22,24) (23,26) (23,27) (24,25) (26,27)\nQ: Is there a path between node 21 and node 18?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1322"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,22) (0,12) (0,24) (0,18) (0,19) (0,30) (0,1) (0,21) (0,9) (0,5) (0,6) (0,7) (0,2) (1,22) (1,24) (1,18) (1,19) (1,30) (1,21) (1,9) (1,5) (1,6) (1,11) (1,7) (1,31) (1,2) (2,12) (2,24) (2,18) (2,19) (2,21) (2,5) (2,6) (2,11) (2,7) (2,31) (3,26) (3,16) (3,4) (3,28) (3,13) (3,20) (4,26) (4,16) (4,8) (4,28) (5,12) (5,24) (5,30) (5,21) (5,9) (5,11) (5,7) (5,31) (6,22) (6,12) (6,24) (6,30) (6,21) (6,9) (6,11) (6,7) (7,12) (7,18) (7,30) (7,9) (7,11) (7,31) (8,26) (8,16) (8,28) (9,22) (9,12) (9,24) (9,18) (9,19) (9,30) (9,11) (9,31) (10,25) (10,14) (10,29) (10,32) (10,15) (10,23) (11,22) (11,12) (11,24) (11,18) (11,30) (11,21) (12,24) (12,30) (12,21) (12,31) (13,26) (13,28) (14,27) (14,17) (14,29) (14,32) (14,15) (15,25) (15,27) (15,17) (15,29) (15,32) (15,23) (16,26) (17,29) (18,22) (18,24) (18,19) (18,21) (19,22) (19,30) (19,21) (20,26) (21,22) (21,24) (21,31) (22,24) (23,25) (23,27) (23,32) (24,30) (24,31) (25,27) (25,29) (25,32) (26,28) (27,29) (27,32) (30,31)\nQ: Is there a path between node 18 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1323"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,13) (0,12) (0,14) (0,8) (0,3) (0,6) (0,2) (0,9) (0,5) (1,10) (1,7) (1,11) (2,4) (2,13) (2,12) (2,14) (2,8) (2,3) (2,6) (2,9) (2,5) (3,4) (3,13) (3,12) (3,14) (3,8) (3,6) (3,9) (3,5) (4,13) (4,12) (4,14) (4,8) (4,6) (4,9) (4,5) (5,13) (5,12) (5,14) (5,8) (5,6) (5,9) (6,13) (6,12) (6,14) (6,8) (6,9) (7,10) (7,11) (8,13) (8,12) (8,14) (8,9) (9,13) (9,12) (9,14) (10,11) (12,13) (12,14) (13,14)\nQ: Is there a path between node 14 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1324"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,2) (3,5)\nQ: Is there a path between node 2 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1325"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,2) (1,5) (1,2) (2,5) (2,10) (3,10) (3,4) (3,8) (4,5) (5,10) (5,8) (7,11) (8,10) (9,11)\nQ: Is there a path between node 1 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1326"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,27) (0,23) (0,4) (0,20) (0,17) (0,6) (1,5) (1,22) (1,11) (1,19) (1,24) (1,2) (1,15) (1,8) (1,30) (1,9) (1,28) (1,18) (2,5) (2,22) (2,24) (2,15) (2,8) (2,30) (2,9) (2,28) (2,18) (3,26) (3,13) (4,21) (4,29) (4,23) (4,20) (4,17) (4,6) (5,22) (5,19) (5,24) (5,14) (5,30) (5,28) (5,18) (6,21) (6,29) (6,27) (6,23) (6,20) (6,17) (7,26) (7,10) (7,13) (7,16) (7,12) (8,11) (8,24) (8,14) (8,30) (8,9) (8,28) (8,18) (9,22) (9,11) (9,19) (9,15) (9,28) (10,16) (10,12) (11,15) (11,30) (11,28) (11,18) (12,13) (12,16) (13,26) (13,16) (13,25) (14,22) (14,19) (14,15) (14,30) (15,19) (15,30) (15,28) (15,18) (16,26) (16,25) (17,29) (17,23) (18,19) (18,24) (18,28) (19,30) (19,28) (20,21) (20,27) (21,29) (21,27) (21,23) (22,24) (22,28) (23,27) (24,30) (24,28) (25,26) (28,30)\nQ: Is there a path between node 15 and node 20?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1327"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (1,11) (1,9) (1,14) (2,5) (2,6) (3,11) (3,13) (4,11) (4,13) (4,15) (5,7) (5,6) (7,10) (8,11) (8,9) (9,14) (9,12) (11,13) (13,14) (13,15)\nQ: Is there a path between node 1 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1328"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,9) (0,14) (0,18) (0,3) (0,1) (0,17) (0,4) (0,8) (0,7) (0,15) (0,11) (0,10) (0,13) (1,5) (1,9) (1,14) (1,18) (1,3) (1,17) (1,4) (1,8) (1,7) (1,15) (1,11) (1,10) (1,13) (3,5) (3,9) (3,14) (3,18) (3,17) (3,4) (3,8) (3,7) (3,15) (3,11) (3,10) (3,13) (4,5) (4,9) (4,14) (4,18) (4,17) (4,8) (4,7) (4,15) (4,11) (4,10) (4,13) (5,9) (5,14) (5,18) (5,17) (5,8) (5,7) (5,15) (5,11) (5,10) (5,13) (6,12) (6,16) (7,9) (7,14) (7,18) (7,17) (7,8) (7,15) (7,11) (7,10) (7,13) (8,9) (8,14) (8,18) (8,17) (8,15) (8,11) (8,10) (8,13) (9,14) (9,18) (9,17) (9,15) (9,11) (9,10) (9,13) (10,14) (10,18) (10,17) (10,15) (10,11) (10,13) (11,14) (11,18) (11,17) (11,15) (11,13) (12,16) (13,14) (13,18) (13,17) (13,15) (14,18) (14,17) (14,15) (15,18) (15,17) (17,18)\nQ: Is there a path between node 16 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1329"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,11) (0,1) (0,25) (0,28) (0,16) (0,31) (0,2) (0,23) (1,20) (1,26) (1,24) (1,10) (1,31) (1,21) (2,26) (2,19) (2,11) (2,5) (2,15) (2,32) (2,33) (2,8) (2,16) (2,31) (2,21) (2,30) (3,12) (3,4) (4,18) (5,11) (5,24) (6,14) (6,12) (6,9) (6,13) (7,26) (7,25) (7,33) (7,8) (7,21) (8,26) (8,19) (8,32) (8,31) (9,12) (10,19) (10,11) (10,25) (11,33) (11,24) (12,14) (14,18) (15,19) (15,17) (15,32) (15,25) (15,31) (15,21) (16,26) (16,32) (17,20) (17,19) (17,23) (19,24) (19,31) (19,21) (19,30) (21,32) (21,25) (21,24) (21,31) (23,31) (24,28) (25,32) (25,33) (25,28) (26,32) (26,33) (26,28) (26,31) (26,30) (28,33) (28,30) (31,32)\nQ: Is there a path between node 9 and node 23?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1330"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,3) (0,2) (0,1) (1,6) (1,3) (1,2) (2,6) (2,3) (3,6) (4,5)\nQ: Is there a path between node 2 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1331"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,12) (0,11) (0,4) (2,10) (2,8) (2,4) (4,6) (4,11) (5,9) (6,7) (6,10) (6,11) (7,8) (8,10) (8,9) (9,12) (10,11)\nQ: Is there a path between node 3 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1332"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (3,8) (3,9) (4,5) (8,9)\nQ: Is there a path between node 9 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1333"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,13) (0,1) (0,9) (0,5) (0,7) (0,3) (0,10) (0,23) (0,26) (0,27) (0,8) (0,14) (0,22) (0,20) (0,15) (0,4) (0,2) (1,25) (1,11) (1,21) (1,13) (1,9) (1,3) (1,10) (1,23) (1,26) (1,27) (1,14) (1,20) (1,15) (1,2) (1,28) (2,25) (2,11) (2,16) (2,21) (2,6) (2,13) (2,9) (2,7) (2,23) (2,26) (2,8) (2,20) (2,15) (3,25) (3,6) (3,13) (3,9) (3,10) (3,27) (3,20) (3,15) (3,4) (3,28) (4,11) (4,16) (4,6) (4,13) (4,10) (4,23) (4,26) (4,27) (4,8) (4,14) (4,22) (4,15) (4,28) (5,25) (5,16) (5,21) (5,6) (5,13) (5,9) (5,7) (5,26) (5,8) (5,22) (5,15) (5,28) (6,11) (6,16) (6,21) (6,13) (6,9) (6,7) (6,10) (6,27) (6,22) (6,20) (6,15) (7,25) (7,16) (7,21) (7,9) (7,10) (7,27) (7,8) (7,14) (7,22) (7,20) (7,15) (7,28) (8,25) (8,13) (8,23) (8,26) (8,27) (8,14) (8,20) (8,28) (9,25) (9,11) (9,16) (9,21) (9,10) (9,23) (9,26) (9,27) (9,22) (9,20) (9,28) (10,11) (10,16) (10,21) (10,13) (10,23) (10,26) (10,27) (10,14) (10,22) (10,20) (10,15) (10,28) (11,25) (11,16) (11,21) (11,13) (11,23) (11,26) (11,27) (11,14) (11,22) (11,20) (12,24) (12,19) (13,25) (13,16) (13,14) (13,22) (13,15) (13,28) (14,25) (14,21) (14,23) (14,26) (14,20) (14,15) (15,16) (15,21) (15,26) (15,27) (15,22) (15,28) (16,21) (16,23) (16,26) (16,27) (16,28) (17,18) (20,25) (20,23) (20,26) (20,27) (20,22) (20,28) (21,25) (21,23) (21,26) (21,22) (22,25) (22,23) (22,27) (23,25) (23,26) (23,27) (23,28) (25,26) (25,27) (26,27) (27,28)\nQ: Is there a path between node 25 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1334"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,1) (0,3) (1,5) (1,3) (2,4) (3,5)\nQ: Is there a path between node 5 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1335"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,8) (0,18) (0,6) (0,1) (0,12) (0,3) (0,7) (0,14) (0,10) (0,19) (0,16) (0,13) (1,17) (1,8) (1,18) (1,2) (1,19) (2,8) (2,6) (2,20) (2,14) (3,17) (3,18) (3,6) (3,14) (3,10) (3,19) (4,17) (4,18) (4,6) (4,19) (4,13) (5,15) (6,17) (6,8) (6,18) (6,13) (7,17) (7,14) (7,10) (8,20) (9,15) (9,11) (10,17) (10,18) (11,15) (12,17) (12,18) (12,14) (12,19) (13,17) (13,18) (13,20) (14,17) (14,18) (14,20) (18,20) (19,20)\nQ: Is there a path between node 3 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1336"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,14) (0,20) (0,13) (1,2) (1,8) (1,9) (2,9) (4,10) (4,20) (5,21) (5,17) (5,9) (6,10) (6,14) (6,13) (7,21) (7,22) (8,9) (10,19) (10,18) (10,12) (10,13) (11,16) (11,18) (12,16) (12,19) (12,18) (13,19) (14,19) (16,18) (17,22) (18,19)\nQ: Is there a path between node 20 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1337"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,16) (0,22) (0,4) (0,15) (0,9) (1,8) (1,17) (1,12) (1,3) (1,5) (1,21) (1,6) (1,13) (1,19) (2,20) (2,16) (2,22) (2,4) (2,9) (3,8) (3,17) (3,14) (3,6) (3,10) (3,19) (4,20) (4,16) (4,22) (4,15) (4,9) (5,8) (5,17) (5,12) (5,14) (5,13) (5,10) (5,19) (6,17) (6,12) (6,14) (6,21) (6,13) (6,10) (6,19) (8,17) (8,12) (8,13) (8,19) (9,20) (9,22) (9,15) (10,17) (10,14) (10,21) (11,18) (11,23) (12,17) (12,21) (12,13) (12,19) (13,17) (13,14) (13,21) (15,20) (16,22) (17,21) (18,23)\nQ: Is there a path between node 6 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1338"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,16) (0,9) (0,3) (0,4) (0,8) (0,17) (1,6) (1,12) (1,13) (1,18) (1,2) (1,4) (1,8) (1,17) (2,6) (2,12) (2,15) (2,9) (2,13) (2,18) (2,4) (2,8) (2,17) (3,6) (3,16) (3,12) (3,9) (3,13) (3,18) (3,8) (3,17) (3,5) (4,6) (4,16) (4,12) (4,9) (4,18) (4,17) (4,5) (5,6) (5,12) (5,15) (5,9) (5,17) (6,12) (6,15) (6,9) (6,13) (6,18) (6,8) (7,10) (7,11) (7,19) (8,16) (8,15) (8,9) (8,18) (9,16) (9,12) (9,15) (9,13) (9,18) (9,17) (10,19) (11,14) (11,19) (12,16) (12,15) (12,13) (12,17) (13,18) (14,19) (15,17) (16,17) (17,18)\nQ: Is there a path between node 12 and node 19?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1339"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,19) (1,11) (2,4) (2,13) (3,17) (3,10) (3,11) (5,8) (5,13) (6,10) (6,12) (7,18) (7,9) (10,17) (10,12) (11,12) (12,17) (13,16) (13,15) (14,18)\nQ: Is there a path between node 19 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1340"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,5) (0,2) (0,3) (0,10) (0,6) (0,1) (0,4) (0,9) (0,7) (0,12) (1,8) (1,5) (1,2) (1,3) (1,10) (1,6) (1,4) (1,9) (1,7) (1,12) (2,8) (2,5) (2,3) (2,10) (2,6) (2,4) (2,9) (2,7) (2,12) (3,8) (3,5) (3,10) (3,6) (3,4) (3,9) (3,7) (3,12) (4,8) (4,5) (4,10) (4,6) (4,9) (4,7) (4,12) (5,8) (5,10) (5,6) (5,9) (5,7) (5,12) (6,8) (6,10) (6,9) (6,7) (6,12) (7,8) (7,10) (7,9) (7,12) (8,10) (8,9) (8,12) (9,10) (9,12) (10,12) (11,13)\nQ: Is there a path between node 8 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1341"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,4) (0,9) (0,12) (0,11) (0,5) (1,6) (1,17) (1,8) (1,15) (1,3) (1,2) (1,18) (1,19) (1,13) (1,14) (1,10) (2,6) (2,17) (2,8) (2,15) (2,3) (2,18) (2,19) (2,13) (2,14) (2,10) (3,6) (3,17) (3,8) (3,15) (3,18) (3,19) (3,13) (3,14) (3,10) (4,7) (4,9) (4,12) (4,11) (4,5) (5,7) (5,9) (5,12) (5,11) (6,17) (6,8) (6,15) (6,18) (6,19) (6,13) (6,14) (6,10) (7,9) (7,12) (7,11) (8,17) (8,15) (8,18) (8,19) (8,13) (8,14) (8,10) (9,12) (9,11) (10,17) (10,15) (10,18) (10,19) (10,13) (10,14) (11,12) (13,17) (13,15) (13,18) (13,19) (13,14) (14,17) (14,15) (14,18) (14,19) (15,17) (15,18) (15,19) (17,18) (17,19) (18,19)\nQ: Is there a path between node 19 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1342"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,3) (0,5) (1,2) (1,8) (1,7) (2,8) (2,7) (3,11) (3,9) (3,13) (5,11) (5,12) (10,11) (11,12) (12,13)\nQ: Is there a path between node 6 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1343"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (1,12) (1,19) (2,13) (3,20) (3,11) (4,7) (4,16) (4,18) (5,17) (5,7) (6,15) (6,20) (6,11) (7,20) (7,11) (8,12) (8,13) (8,19) (11,17) (11,15) (12,19) (16,17) (16,20) (17,20) (18,20)\nQ: Is there a path between node 22 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1344"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,10) (0,19) (0,16) (0,7) (0,8) (0,4) (0,3) (0,11) (0,1) (0,18) (0,9) (0,5) (0,2) (0,13) (1,17) (1,10) (1,19) (1,16) (1,7) (1,8) (1,4) (1,3) (1,11) (1,18) (1,9) (1,5) (1,2) (1,13) (2,17) (2,10) (2,19) (2,16) (2,7) (2,8) (2,4) (2,3) (2,11) (2,18) (2,9) (2,5) (2,13) (3,17) (3,10) (3,19) (3,16) (3,7) (3,8) (3,4) (3,11) (3,18) (3,9) (3,5) (3,13) (4,17) (4,10) (4,19) (4,16) (4,7) (4,8) (4,11) (4,18) (4,9) (4,5) (4,13) (5,17) (5,10) (5,19) (5,16) (5,7) (5,8) (5,11) (5,18) (5,9) (5,13) (6,15) (7,17) (7,10) (7,19) (7,16) (7,8) (7,11) (7,18) (7,9) (7,13) (8,17) (8,10) (8,19) (8,16) (8,11) (8,18) (8,9) (8,13) (9,17) (9,10) (9,19) (9,16) (9,11) (9,18) (9,13) (10,17) (10,19) (10,16) (10,11) (10,18) (10,13) (11,17) (11,19) (11,16) (11,18) (11,13) (12,14) (13,17) (13,19) (13,16) (13,18) (16,17) (16,19) (16,18) (17,19) (17,18) (18,19)\nQ: Is there a path between node 2 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1345"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,13) (0,19) (0,11) (0,16) (0,20) (0,8) (0,5) (0,3) (0,2) (0,7) (0,6) (0,17) (0,14) (0,12) (0,1) (0,18) (0,10) (0,23) (0,9) (1,4) (1,13) (1,19) (1,11) (1,16) (1,20) (1,8) (1,5) (1,3) (1,2) (1,7) (1,6) (1,17) (1,14) (1,12) (1,18) (1,10) (1,23) (1,9) (2,4) (2,13) (2,19) (2,11) (2,16) (2,20) (2,8) (2,5) (2,3) (2,7) (2,6) (2,17) (2,14) (2,12) (2,18) (2,10) (2,23) (2,9) (3,4) (3,13) (3,19) (3,11) (3,16) (3,20) (3,8) (3,5) (3,7) (3,6) (3,17) (3,14) (3,12) (3,18) (3,10) (3,23) (3,9) (4,13) (4,19) (4,11) (4,16) (4,20) (4,8) (4,5) (4,7) (4,6) (4,17) (4,14) (4,12) (4,18) (4,10) (4,23) (4,9) (5,13) (5,19) (5,11) (5,16) (5,20) (5,8) (5,7) (5,6) (5,17) (5,14) (5,12) (5,18) (5,10) (5,23) (5,9) (6,13) (6,19) (6,11) (6,16) (6,20) (6,8) (6,7) (6,17) (6,14) (6,12) (6,18) (6,10) (6,23) (6,9) (7,13) (7,19) (7,11) (7,16) (7,20) (7,8) (7,17) (7,14) (7,12) (7,18) (7,10) (7,23) (7,9) (8,13) (8,19) (8,11) (8,16) (8,20) (8,17) (8,14) (8,12) (8,18) (8,10) (8,23) (8,9) (9,13) (9,19) (9,11) (9,16) (9,20) (9,17) (9,14) (9,12) (9,18) (9,10) (9,23) (10,13) (10,19) (10,11) (10,16) (10,20) (10,17) (10,14) (10,12) (10,18) (10,23) (11,13) (11,19) (11,16) (11,20) (11,17) (11,14) (11,12) (11,18) (11,23) (12,13) (12,19) (12,16) (12,20) (12,17) (12,14) (12,18) (12,23) (13,19) (13,16) (13,20) (13,17) (13,14) (13,18) (13,23) (14,19) (14,16) (14,20) (14,17) (14,18) (14,23) (15,21) (15,22) (16,19) (16,20) (16,17) (16,18) (16,23) (17,19) (17,20) (17,18) (17,23) (18,19) (18,20) (18,23) (19,20) (19,23) (20,23) (21,22)\nQ: Is there a path between node 3 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1346"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,15) (1,3) (1,20) (2,11) (3,12) (3,6) (3,16) (3,20) (5,14) (5,7) (6,20) (6,21) (7,13) (7,18) (8,14) (8,13) (9,12) (9,16) (9,21) (10,21) (11,17) (12,16) (14,18) (15,16) (15,21) (16,20) (20,21)\nQ: Is there a path between node 10 and node 18?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1347"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,1) (0,12) (0,4) (1,13) (1,3) (1,6) (1,9) (2,15) (2,14) (2,11) (4,7) (5,16) (5,6) (5,9) (6,13) (6,8) (10,13) (10,12) (11,15) (11,14)\nQ: Is there a path between node 6 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1348"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (1,2)\nQ: Is there a path between node 3 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1349"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (1,8) (1,4) (1,5) (1,7) (1,2) (1,9) (1,6) (2,8) (2,4) (2,5) (2,7) (2,9) (2,6) (4,8) (4,5) (4,7) (4,9) (4,6) (5,8) (5,7) (5,9) (5,6) (6,8) (6,7) (6,9) (7,8) (7,9) (8,9)\nQ: Is there a path between node 1 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1350"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,13) (0,17) (0,10) (0,5) (0,4) (0,16) (0,19) (0,20) (0,7) (0,8) (0,15) (0,1) (0,18) (0,9) (0,12) (1,13) (1,17) (1,10) (1,5) (1,4) (1,16) (1,19) (1,20) (1,7) (1,8) (1,15) (1,18) (1,9) (1,12) (2,11) (2,21) (2,3) (2,14) (3,11) (3,21) (3,14) (4,13) (4,17) (4,10) (4,5) (4,16) (4,19) (4,20) (4,7) (4,8) (4,15) (4,18) (4,9) (4,12) (5,13) (5,17) (5,10) (5,16) (5,19) (5,20) (5,7) (5,8) (5,15) (5,18) (5,9) (5,12) (7,13) (7,17) (7,10) (7,16) (7,19) (7,20) (7,8) (7,15) (7,18) (7,9) (7,12) (8,13) (8,17) (8,10) (8,16) (8,19) (8,20) (8,15) (8,18) (8,9) (8,12) (9,13) (9,17) (9,10) (9,16) (9,19) (9,20) (9,15) (9,18) (9,12) (10,13) (10,17) (10,16) (10,19) (10,20) (10,15) (10,18) (10,12) (11,21) (11,14) (12,13) (12,17) (12,16) (12,19) (12,20) (12,15) (12,18) (13,17) (13,16) (13,19) (13,20) (13,15) (13,18) (14,21) (15,17) (15,16) (15,19) (15,20) (15,18) (16,17) (16,19) (16,20) (16,18) (17,19) (17,20) (17,18) (18,19) (18,20) (19,20)\nQ: Is there a path between node 2 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1351"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,18) (0,24) (0,5) (0,12) (0,26) (0,14) (0,16) (0,21) (0,9) (0,1) (0,28) (0,25) (1,3) (1,18) (1,24) (1,5) (1,12) (1,26) (1,14) (1,16) (1,21) (1,2) (1,23) (1,20) (1,28) (1,25) (2,3) (2,18) (2,10) (2,24) (2,5) (2,12) (2,26) (2,14) (2,16) (2,9) (2,23) (2,20) (2,28) (2,7) (2,25) (2,22) (2,13) (3,18) (3,24) (3,12) (3,26) (3,16) (3,9) (3,19) (3,7) (3,25) (3,22) (4,11) (4,27) (4,17) (4,15) (4,8) (5,18) (5,24) (5,12) (5,26) (5,14) (5,16) (5,21) (5,9) (5,23) (5,19) (5,20) (5,7) (5,13) (6,11) (6,27) (6,29) (6,15) (6,8) (7,18) (7,10) (7,12) (7,26) (7,14) (7,16) (7,21) (7,9) (7,20) (7,25) (7,22) (7,13) (8,11) (8,27) (8,29) (8,17) (8,15) (9,18) (9,10) (9,24) (9,16) (9,21) (9,19) (9,20) (9,28) (9,25) (9,13) (10,18) (10,24) (10,12) (10,26) (10,14) (10,16) (10,23) (10,20) (10,28) (10,25) (10,22) (10,13) (11,27) (11,29) (12,18) (12,24) (12,16) (12,21) (12,23) (12,20) (12,28) (12,22) (12,13) (13,18) (13,24) (13,26) (13,14) (13,16) (13,21) (13,23) (13,20) (13,28) (13,25) (13,22) (14,26) (14,16) (14,21) (14,23) (14,19) (14,20) (14,28) (14,25) (15,27) (15,17) (16,18) (16,24) (16,26) (16,20) (16,25) (16,22) (17,29) (18,24) (18,26) (18,23) (18,19) (18,20) (18,25) (18,22) (19,21) (19,23) (19,28) (19,25) (20,26) (20,23) (20,28) (20,25) (20,22) (21,26) (21,23) (21,28) (21,22) (22,26) (22,23) (22,25) (23,24) (23,26) (24,26) (24,28) (25,26)\nQ: Is there a path between node 15 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1352"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,13) (0,8) (0,18) (0,25) (0,14) (0,17) (0,21) (1,13) (1,26) (1,14) (1,20) (1,17) (1,24) (1,6) (2,8) (2,18) (2,9) (2,26) (2,14) (2,10) (2,15) (3,16) (3,12) (4,13) (4,8) (4,18) (4,25) (4,6) (5,19) (5,13) (5,10) (5,20) (5,22) (5,17) (5,6) (6,8) (6,18) (6,9) (6,26) (6,14) (6,17) (6,21) (6,15) (6,23) (7,25) (7,14) (7,22) (7,24) (7,15) (7,23) (8,13) (8,25) (8,24) (8,23) (9,25) (9,27) (9,26) (9,14) (9,17) (9,24) (9,23) (10,19) (10,13) (10,25) (10,22) (11,12) (12,16) (13,19) (13,18) (13,21) (14,19) (14,18) (14,22) (15,19) (15,25) (15,23) (17,25) (17,22) (17,21) (17,24) (18,21) (18,24) (19,26) (19,22) (19,24) (19,23) (20,25) (20,26) (20,24) (20,23) (21,27) (21,23) (22,25) (22,26) (22,23) (25,27) (25,26)\nQ: Is there a path between node 11 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1353"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (1,12) (1,19) (2,13) (3,20) (3,11) (4,7) (4,16) (4,18) (5,17) (5,7) (6,15) (6,20) (6,11) (7,20) (7,11) (8,12) (8,13) (8,19) (11,17) (11,15) (12,19) (16,17) (16,20) (17,20) (18,20)\nQ: Is there a path between node 1 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1354"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (1,2) (1,5) (5,6)\nQ: Is there a path between node 1 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1355"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,3) (0,2) (0,9) (0,8) (1,6) (1,4) (2,7) (2,10) (2,3) (2,8) (2,5) (3,10) (3,9) (3,8) (4,6) (5,7) (5,10) (5,9) (7,8) (8,9)\nQ: Is there a path between node 7 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1356"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,8) (0,10) (0,4) (0,16) (0,5) (0,2) (0,7) (0,9) (0,15) (0,13) (0,1) (0,12) (0,14) (0,3) (1,11) (1,8) (1,10) (1,4) (1,16) (1,5) (1,2) (1,7) (1,9) (1,15) (1,13) (1,12) (1,14) (1,3) (2,11) (2,8) (2,10) (2,4) (2,16) (2,5) (2,7) (2,9) (2,15) (2,13) (2,12) (2,14) (2,3) (3,11) (3,8) (3,10) (3,4) (3,16) (3,5) (3,7) (3,9) (3,15) (3,13) (3,12) (3,14) (4,11) (4,8) (4,10) (4,16) (4,5) (4,7) (4,9) (4,15) (4,13) (4,12) (4,14) (5,11) (5,8) (5,10) (5,16) (5,7) (5,9) (5,15) (5,13) (5,12) (5,14) (7,11) (7,8) (7,10) (7,16) (7,9) (7,15) (7,13) (7,12) (7,14) (8,11) (8,10) (8,16) (8,9) (8,15) (8,13) (8,12) (8,14) (9,11) (9,10) (9,16) (9,15) (9,13) (9,12) (9,14) (10,11) (10,16) (10,15) (10,13) (10,12) (10,14) (11,16) (11,15) (11,13) (11,12) (11,14) (12,16) (12,15) (12,13) (12,14) (13,16) (13,15) (13,14) (14,16) (14,15) (15,16)\nQ: Is there a path between node 16 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1357"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,10) (0,13) (0,12) (0,9) (0,18) (0,24) (0,5) (0,20) (0,21) (0,7) (0,3) (0,23) (1,2) (1,13) (1,16) (1,12) (1,18) (1,24) (1,20) (1,4) (1,7) (1,3) (1,19) (1,23) (2,13) (2,16) (2,12) (2,9) (2,11) (2,18) (2,24) (2,5) (2,20) (2,4) (2,21) (2,7) (2,3) (2,23) (3,13) (3,16) (3,12) (3,9) (3,11) (3,24) (3,5) (3,20) (3,21) (3,7) (3,19) (3,23) (4,10) (4,16) (4,12) (4,11) (4,18) (4,24) (4,5) (4,20) (4,21) (4,7) (4,19) (4,23) (5,13) (5,12) (5,11) (5,18) (5,24) (5,20) (5,21) (5,7) (5,23) (6,15) (6,25) (6,22) (6,8) (7,13) (7,12) (7,9) (7,11) (7,18) (7,20) (7,21) (7,19) (8,17) (8,15) (8,22) (8,14) (9,10) (9,13) (9,16) (9,11) (9,18) (9,21) (9,19) (9,23) (10,13) (10,12) (10,11) (10,24) (10,20) (10,21) (10,19) (10,23) (11,13) (11,16) (11,24) (11,20) (11,21) (11,19) (11,23) (12,13) (12,16) (12,18) (12,24) (12,20) (12,21) (12,19) (12,23) (13,16) (13,24) (13,21) (13,23) (14,17) (14,15) (14,22) (15,17) (15,25) (15,22) (16,18) (16,24) (16,21) (16,23) (17,25) (17,22) (18,20) (18,21) (18,19) (18,23) (19,20) (19,23) (20,24) (20,21) (21,23) (22,25) (23,24)\nQ: Is there a path between node 15 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1358"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,4) (0,11) (0,13) (1,8) (1,21) (1,10) (1,7) (1,2) (2,24) (2,8) (2,9) (2,10) (2,22) (3,5) (3,11) (3,13) (4,15) (4,6) (4,16) (4,11) (5,12) (5,15) (5,19) (5,18) (5,27) (6,19) (6,11) (7,26) (7,23) (7,9) (8,23) (8,9) (8,10) (8,22) (9,25) (9,14) (10,25) (10,17) (10,23) (11,20) (11,27) (12,15) (12,16) (12,18) (14,22) (15,19) (15,27) (16,19) (17,26) (17,24) (17,28) (17,23) (17,22) (19,20) (19,27) (21,26) (21,25) (21,29) (21,22) (22,29) (23,24) (23,29) (26,28)\nQ: Is there a path between node 8 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1359"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,13) (0,2) (0,14) (0,23) (0,8) (0,1) (0,25) (0,27) (0,10) (1,29) (1,13) (1,19) (1,28) (1,23) (1,30) (1,25) (1,24) (2,12) (2,5) (2,14) (2,17) (2,23) (3,7) (3,12) (3,19) (3,23) (3,8) (3,30) (3,25) (3,24) (4,33) (5,20) (5,23) (5,30) (6,15) (6,11) (7,32) (7,17) (7,23) (7,8) (7,10) (8,29) (8,12) (8,32) (8,20) (8,19) (8,17) (8,30) (9,29) (9,28) (9,30) (9,24) (10,13) (10,20) (10,14) (10,22) (11,31) (12,13) (12,23) (12,27) (12,26) (13,29) (13,32) (13,14) (13,28) (13,30) (13,24) (14,17) (14,30) (14,22) (14,27) (15,16) (15,31) (15,33) (17,32) (17,20) (17,19) (17,27) (17,24) (17,26) (18,21) (20,28) (20,30) (20,25) (21,31) (22,32) (22,28) (22,30) (23,28) (23,25) (23,27) (24,29) (24,28) (24,26) (25,32) (26,29) (26,27) (27,32) (27,30) (28,32) (28,30)\nQ: Is there a path between node 9 and node 22?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1360"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,4) (0,3) (0,6) (0,2) (0,8) (0,5) (0,11) (1,4) (1,3) (1,6) (1,2) (1,8) (1,5) (1,11) (2,4) (2,3) (2,6) (2,8) (2,5) (2,11) (3,4) (3,6) (3,8) (3,5) (3,11) (4,6) (4,8) (4,5) (4,11) (5,6) (5,8) (5,11) (6,8) (6,11) (7,9) (7,10) (8,11) (9,10)\nQ: Is there a path between node 0 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1361"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,21) (0,14) (0,1) (0,22) (0,16) (0,19) (0,5) (0,10) (0,20) (0,11) (0,24) (0,13) (1,21) (1,9) (1,3) (1,14) (1,22) (1,10) (1,20) (1,12) (1,11) (1,24) (1,13) (1,23) (2,8) (2,4) (2,18) (2,15) (3,9) (3,14) (3,16) (3,19) (3,7) (3,6) (3,5) (3,10) (3,11) (4,8) (4,17) (4,18) (4,15) (5,9) (5,14) (5,22) (5,7) (5,6) (5,10) (5,20) (5,12) (5,11) (5,13) (5,23) (6,21) (6,9) (6,22) (6,19) (6,7) (6,20) (6,12) (6,11) (6,13) (6,23) (7,21) (7,9) (7,14) (7,16) (7,19) (7,10) (7,20) (7,12) (7,11) (7,24) (7,13) (7,23) (8,17) (8,18) (8,15) (9,21) (9,16) (9,10) (9,20) (9,12) (9,11) (9,24) (9,13) (9,23) (10,22) (10,19) (10,12) (10,11) (10,13) (10,23) (11,21) (11,22) (11,19) (11,20) (11,12) (11,24) (11,13) (11,23) (12,21) (12,14) (12,22) (12,20) (12,24) (12,13) (12,23) (13,21) (13,14) (13,22) (13,16) (13,20) (13,23) (14,21) (14,16) (14,20) (14,24) (14,23) (15,18) (16,21) (16,22) (16,19) (16,20) (16,24) (16,23) (17,18) (19,21) (19,20) (19,24) (19,23) (20,21) (20,24) (20,23) (21,24) (21,23) (22,23) (23,24)\nQ: Is there a path between node 4 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1362"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,18) (0,1) (0,8) (0,10) (0,11) (0,7) (0,4) (0,2) (0,6) (0,17) (0,14) (1,19) (1,18) (1,8) (1,10) (1,11) (1,7) (1,4) (1,2) (1,6) (1,17) (1,14) (2,19) (2,18) (2,8) (2,10) (2,11) (2,7) (2,4) (2,6) (2,17) (2,14) (3,13) (3,9) (3,15) (4,19) (4,18) (4,8) (4,10) (4,11) (4,7) (4,6) (4,17) (4,14) (5,12) (5,16) (6,19) (6,18) (6,8) (6,10) (6,11) (6,7) (6,17) (6,14) (7,19) (7,18) (7,8) (7,10) (7,11) (7,17) (7,14) (8,19) (8,18) (8,10) (8,11) (8,17) (8,14) (9,13) (9,15) (10,19) (10,18) (10,11) (10,17) (10,14) (11,19) (11,18) (11,17) (11,14) (12,16) (13,15) (14,19) (14,18) (14,17) (17,19) (17,18) (18,19)\nQ: Is there a path between node 13 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1363"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (0,11) (0,8) (0,17) (0,13) (0,6) (0,3) (0,15) (0,7) (1,14) (1,19) (1,9) (1,21) (1,12) (1,22) (1,4) (1,18) (1,5) (1,10) (1,20) (2,16) (3,23) (3,11) (3,8) (3,17) (3,13) (3,6) (3,15) (3,7) (4,14) (4,19) (4,9) (4,21) (4,12) (4,22) (4,18) (4,5) (4,10) (4,20) (5,14) (5,19) (5,9) (5,21) (5,12) (5,22) (5,18) (5,10) (5,20) (6,23) (6,11) (6,8) (6,17) (6,13) (6,15) (6,7) (7,23) (7,11) (7,8) (7,17) (7,13) (7,15) (8,23) (8,11) (8,17) (8,13) (8,15) (9,14) (9,19) (9,21) (9,12) (9,22) (9,18) (9,10) (9,20) (10,14) (10,19) (10,21) (10,12) (10,22) (10,18) (10,20) (11,23) (11,17) (11,13) (11,15) (12,14) (12,19) (12,21) (12,22) (12,18) (12,20) (13,23) (13,17) (13,15) (14,19) (14,21) (14,22) (14,18) (14,20) (15,23) (15,17) (17,23) (18,19) (18,21) (18,22) (18,20) (19,21) (19,22) (19,20) (20,21) (20,22) (21,22)\nQ: Is there a path between node 6 and node 23?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1364"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (0,13) (0,22) (1,12) (1,6) (2,20) (2,14) (2,11) (3,5) (3,23) (3,6) (5,17) (6,19) (7,23) (8,13) (8,15) (9,21) (9,18) (12,24) (12,17) (12,19) (13,21) (13,18) (13,25) (13,15) (13,16) (15,16) (16,21) (16,25) (17,23) (17,19) (19,26) (21,22) (22,25)\nQ: Is there a path between node 9 and node 26?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1365"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,10) (0,1) (1,8) (1,3) (1,14) (3,5) (3,6) (3,9) (3,12) (4,9) (4,16) (6,7) (6,12) (7,14) (8,16) (8,14) (10,11) (10,14) (10,12) (11,14) (12,14)\nQ: Is there a path between node 7 and node 15?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1366"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,5) (0,7) (0,6) (0,2) (0,4) (0,8) (0,9) (1,10) (2,3) (2,5) (2,7) (2,6) (2,4) (2,8) (2,9) (2,11) (3,5) (3,4) (3,8) (3,11) (4,5) (4,6) (4,9) (4,11) (5,6) (5,8) (5,9) (6,7) (6,8) (6,9) (6,11) (7,8) (7,11) (8,9) (9,11)\nQ: Is there a path between node 3 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1367"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,1) (0,14) (0,18) (1,17) (1,14) (1,18) (2,19) (2,7) (2,10) (2,3) (2,12) (2,16) (2,11) (2,5) (2,9) (2,15) (2,6) (2,20) (2,8) (2,4) (2,13) (3,19) (3,7) (3,10) (3,12) (3,16) (3,11) (3,5) (3,9) (3,15) (3,6) (3,20) (3,8) (3,4) (3,13) (4,19) (4,7) (4,10) (4,12) (4,16) (4,11) (4,5) (4,9) (4,15) (4,6) (4,20) (4,8) (4,13) (5,19) (5,7) (5,10) (5,12) (5,16) (5,11) (5,9) (5,15) (5,6) (5,20) (5,8) (5,13) (6,19) (6,7) (6,10) (6,12) (6,16) (6,11) (6,9) (6,15) (6,20) (6,8) (6,13) (7,19) (7,10) (7,12) (7,16) (7,11) (7,9) (7,15) (7,20) (7,8) (7,13) (8,19) (8,10) (8,12) (8,16) (8,11) (8,9) (8,15) (8,20) (8,13) (9,19) (9,10) (9,12) (9,16) (9,11) (9,15) (9,20) (9,13) (10,19) (10,12) (10,16) (10,11) (10,15) (10,20) (10,13) (11,19) (11,12) (11,16) (11,15) (11,20) (11,13) (12,19) (12,16) (12,15) (12,20) (12,13) (13,19) (13,16) (13,15) (13,20) (14,17) (14,18) (15,19) (15,16) (15,20) (16,19) (16,20) (17,18) (19,20)\nQ: Is there a path between node 12 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1368"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,8) (0,11) (0,17) (0,1) (0,2) (0,12) (0,6) (0,18) (0,7) (0,15) (1,19) (1,8) (1,9) (1,11) (1,2) (1,12) (1,6) (1,7) (1,15) (2,19) (2,4) (2,9) (2,11) (2,17) (2,12) (2,6) (2,18) (2,15) (3,5) (3,13) (3,10) (4,19) (4,8) (4,9) (4,11) (4,17) (4,12) (4,6) (4,7) (4,15) (5,13) (5,10) (6,9) (6,11) (6,12) (6,18) (7,19) (7,8) (7,9) (7,11) (7,17) (7,15) (8,19) (8,11) (8,17) (8,12) (9,17) (9,12) (9,18) (10,13) (11,17) (11,15) (12,19) (12,17) (12,18) (12,15) (14,20) (14,21) (15,17) (15,18) (17,19) (17,18) (18,19) (20,21)\nQ: Is there a path between node 5 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1369"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,3) (1,20) (1,21) (1,8) (1,5) (1,16) (1,17) (1,19) (1,6) (1,12) (1,14) (1,9) (1,13) (1,18) (1,7) (1,11) (1,15) (1,2) (1,10) (2,20) (2,21) (2,8) (2,5) (2,16) (2,17) (2,19) (2,6) (2,12) (2,14) (2,9) (2,13) (2,18) (2,7) (2,11) (2,15) (2,10) (3,4) (5,20) (5,21) (5,8) (5,16) (5,17) (5,19) (5,6) (5,12) (5,14) (5,9) (5,13) (5,18) (5,7) (5,11) (5,15) (5,10) (6,20) (6,21) (6,8) (6,16) (6,17) (6,19) (6,12) (6,14) (6,9) (6,13) (6,18) (6,7) (6,11) (6,15) (6,10) (7,20) (7,21) (7,8) (7,16) (7,17) (7,19) (7,12) (7,14) (7,9) (7,13) (7,18) (7,11) (7,15) (7,10) (8,20) (8,21) (8,16) (8,17) (8,19) (8,12) (8,14) (8,9) (8,13) (8,18) (8,11) (8,15) (8,10) (9,20) (9,21) (9,16) (9,17) (9,19) (9,12) (9,14) (9,13) (9,18) (9,11) (9,15) (9,10) (10,20) (10,21) (10,16) (10,17) (10,19) (10,12) (10,14) (10,13) (10,18) (10,11) (10,15) (11,20) (11,21) (11,16) (11,17) (11,19) (11,12) (11,14) (11,13) (11,18) (11,15) (12,20) (12,21) (12,16) (12,17) (12,19) (12,14) (12,13) (12,18) (12,15) (13,20) (13,21) (13,16) (13,17) (13,19) (13,14) (13,18) (13,15) (14,20) (14,21) (14,16) (14,17) (14,19) (14,18) (14,15) (15,20) (15,21) (15,16) (15,17) (15,19) (15,18) (16,20) (16,21) (16,17) (16,19) (16,18) (17,20) (17,21) (17,19) (17,18) (18,20) (18,21) (18,19) (19,20) (19,21) (20,21)\nQ: Is there a path between node 19 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1370"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,1) (0,13) (0,15) (0,16) (0,9) (0,14) (0,3) (0,12) (0,17) (0,2) (0,18) (1,11) (1,13) (1,15) (1,16) (1,9) (1,8) (1,14) (1,3) (1,4) (1,17) (1,18) (2,11) (2,13) (2,15) (2,9) (2,8) (2,14) (2,3) (2,12) (2,17) (2,18) (3,11) (3,13) (3,15) (3,16) (3,9) (3,8) (3,14) (3,12) (3,17) (3,18) (4,13) (4,15) (4,16) (4,8) (4,14) (4,12) (4,18) (5,6) (5,7) (5,10) (6,7) (6,10) (7,10) (8,11) (8,15) (8,16) (8,18) (9,11) (9,13) (9,15) (9,16) (9,14) (9,12) (9,17) (9,18) (11,13) (11,16) (11,17) (11,18) (12,15) (12,16) (12,17) (12,18) (13,15) (13,18) (14,15) (14,17) (15,16) (16,17) (16,18) (17,18)\nQ: Is there a path between node 15 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1371"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,8) (0,4) (0,5) (0,13) (0,2) (0,17) (1,15) (1,8) (1,3) (1,4) (1,5) (1,13) (1,17) (2,15) (2,8) (2,3) (2,4) (2,5) (2,13) (3,8) (3,5) (3,17) (4,15) (4,13) (4,17) (5,15) (5,8) (5,17) (6,14) (6,7) (6,10) (6,16) (6,9) (6,12) (7,14) (7,16) (7,9) (8,13) (9,14) (9,10) (9,11) (9,16) (9,12) (10,14) (10,12) (11,14) (11,12) (12,14) (12,16) (13,17) (15,17)\nQ: Is there a path between node 8 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1372"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,16) (0,22) (0,4) (0,15) (0,9) (1,8) (1,17) (1,12) (1,3) (1,5) (1,21) (1,6) (1,13) (1,19) (2,20) (2,16) (2,22) (2,4) (2,9) (3,8) (3,17) (3,14) (3,6) (3,10) (3,19) (4,20) (4,16) (4,22) (4,15) (4,9) (5,8) (5,17) (5,12) (5,14) (5,13) (5,10) (5,19) (6,17) (6,12) (6,14) (6,21) (6,13) (6,10) (6,19) (8,17) (8,12) (8,13) (8,19) (9,20) (9,22) (9,15) (10,17) (10,14) (10,21) (11,18) (11,23) (12,17) (12,21) (12,13) (12,19) (13,17) (13,14) (13,21) (15,20) (16,22) (17,21) (18,23)\nQ: Is there a path between node 22 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1373"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,3) (0,11) (0,8) (0,2) (0,12) (0,9) (0,1) (1,4) (1,3) (1,6) (1,11) (1,8) (1,7) (1,10) (1,2) (1,12) (2,3) (2,6) (2,11) (2,8) (2,9) (3,6) (3,11) (3,8) (3,7) (3,10) (3,9) (4,6) (4,11) (4,8) (4,7) (4,10) (4,12) (4,9) (6,8) (6,10) (7,10) (7,12) (7,9) (8,11) (8,10) (8,12) (9,10) (10,12)\nQ: Is there a path between node 6 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1374"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,14) (0,12) (1,20) (1,12) (2,13) (2,18) (3,17) (4,20) (7,21) (8,18) (9,20) (9,15) (10,13) (10,19) (13,18) (14,16) (14,15) (15,20)\nQ: Is there a path between node 10 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1375"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,11) (1,9) (1,19) (1,31) (1,20) (2,15) (2,11) (2,27) (2,29) (2,16) (2,31) (3,8) (3,4) (3,12) (3,18) (3,17) (3,10) (3,25) (3,31) (3,20) (4,30) (4,24) (4,19) (5,26) (5,23) (6,13) (7,15) (7,9) (7,30) (7,12) (7,16) (7,19) (7,10) (7,25) (8,15) (8,11) (8,30) (8,24) (8,10) (8,31) (9,11) (9,30) (9,27) (9,29) (9,10) (10,15) (10,30) (10,12) (10,18) (10,19) (10,17) (10,14) (11,30) (11,29) (11,19) (12,15) (12,19) (12,14) (12,20) (13,28) (14,27) (14,24) (14,20) (15,27) (15,18) (15,25) (15,20) (16,29) (16,24) (16,19) (17,29) (17,19) (17,31) (18,30) (18,24) (18,19) (18,31) (19,30) (19,25) (21,28) (21,23) (22,23) (25,27) (25,31) (26,28) (29,31)\nQ: Is there a path between node 2 and node 20?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1376"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (1,20) (2,11) (2,23) (2,14) (2,8) (3,17) (3,14) (3,16) (4,7) (4,16) (4,8) (4,24) (5,6) (5,10) (5,20) (6,20) (7,12) (7,16) (7,8) (7,24) (8,12) (8,23) (8,21) (9,18) (10,18) (10,20) (11,17) (11,19) (11,24) (12,22) (12,17) (12,14) (13,24) (14,23) (14,24) (15,17) (15,19) (15,24) (16,22) (16,19) (17,19) (17,24) (19,24) (23,24)\nQ: Is there a path between node 4 and node 22?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1377"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,17) (0,13) (0,12) (0,4) (0,1) (1,3) (1,17) (1,16) (1,14) (1,4) (2,5) (2,7) (2,9) (2,11) (2,8) (3,15) (3,13) (3,16) (3,12) (3,14) (3,6) (4,15) (4,13) (4,16) (4,12) (4,6) (5,9) (5,11) (5,10) (6,17) (6,13) (6,12) (7,11) (7,10) (7,8) (8,9) (8,11) (9,10) (10,11) (12,15) (12,17) (12,16) (12,14) (13,17) (13,16) (14,15) (14,17) (15,17) (15,16) (16,17)\nQ: Is there a path between node 17 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1378"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,3) (0,5) (1,2) (1,8) (1,7) (2,8) (2,7) (3,11) (3,9) (3,13) (5,11) (5,12) (10,11) (11,12) (12,13)\nQ: Is there a path between node 1 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1379"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,12) (0,1) (0,13) (0,14) (0,11) (0,20) (0,7) (0,21) (1,4) (1,13) (1,14) (1,16) (1,7) (1,21) (2,5) (2,22) (2,8) (2,15) (2,25) (2,9) (2,17) (2,26) (3,11) (3,20) (3,7) (4,13) (4,14) (4,11) (4,20) (4,21) (5,22) (5,18) (5,15) (5,23) (5,25) (5,17) (5,26) (5,24) (6,19) (7,12) (7,13) (7,14) (7,11) (7,20) (7,21) (8,22) (8,15) (8,23) (8,9) (8,17) (8,24) (9,18) (9,15) (9,23) (9,25) (9,17) (11,13) (11,14) (11,16) (11,20) (12,13) (12,14) (12,16) (12,20) (12,21) (13,16) (13,20) (14,16) (14,20) (14,21) (15,22) (15,18) (15,23) (15,25) (15,26) (15,24) (16,21) (17,22) (17,18) (17,23) (17,25) (18,25) (18,24) (20,21) (22,23) (22,25) (22,26) (22,24) (23,26) (23,24) (24,25) (25,26)\nQ: Is there a path between node 4 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1380"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,3) (0,2) (0,9) (0,8) (1,6) (1,4) (2,7) (2,10) (2,3) (2,8) (2,5) (3,10) (3,9) (3,8) (4,6) (5,7) (5,10) (5,9) (7,8) (8,9)\nQ: Is there a path between node 10 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1381"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,13) (0,19) (0,11) (0,16) (0,20) (0,8) (0,5) (0,3) (0,2) (0,7) (0,6) (0,17) (0,14) (0,12) (0,1) (0,18) (0,10) (0,23) (0,9) (1,4) (1,13) (1,19) (1,11) (1,16) (1,20) (1,8) (1,5) (1,3) (1,2) (1,7) (1,6) (1,17) (1,14) (1,12) (1,18) (1,10) (1,23) (1,9) (2,4) (2,13) (2,19) (2,11) (2,16) (2,20) (2,8) (2,5) (2,3) (2,7) (2,6) (2,17) (2,14) (2,12) (2,18) (2,10) (2,23) (2,9) (3,4) (3,13) (3,19) (3,11) (3,16) (3,20) (3,8) (3,5) (3,7) (3,6) (3,17) (3,14) (3,12) (3,18) (3,10) (3,23) (3,9) (4,13) (4,19) (4,11) (4,16) (4,20) (4,8) (4,5) (4,7) (4,6) (4,17) (4,14) (4,12) (4,18) (4,10) (4,23) (4,9) (5,13) (5,19) (5,11) (5,16) (5,20) (5,8) (5,7) (5,6) (5,17) (5,14) (5,12) (5,18) (5,10) (5,23) (5,9) (6,13) (6,19) (6,11) (6,16) (6,20) (6,8) (6,7) (6,17) (6,14) (6,12) (6,18) (6,10) (6,23) (6,9) (7,13) (7,19) (7,11) (7,16) (7,20) (7,8) (7,17) (7,14) (7,12) (7,18) (7,10) (7,23) (7,9) (8,13) (8,19) (8,11) (8,16) (8,20) (8,17) (8,14) (8,12) (8,18) (8,10) (8,23) (8,9) (9,13) (9,19) (9,11) (9,16) (9,20) (9,17) (9,14) (9,12) (9,18) (9,10) (9,23) (10,13) (10,19) (10,11) (10,16) (10,20) (10,17) (10,14) (10,12) (10,18) (10,23) (11,13) (11,19) (11,16) (11,20) (11,17) (11,14) (11,12) (11,18) (11,23) (12,13) (12,19) (12,16) (12,20) (12,17) (12,14) (12,18) (12,23) (13,19) (13,16) (13,20) (13,17) (13,14) (13,18) (13,23) (14,19) (14,16) (14,20) (14,17) (14,18) (14,23) (15,21) (15,22) (16,19) (16,20) (16,17) (16,18) (16,23) (17,19) (17,20) (17,18) (17,23) (18,19) (18,20) (18,23) (19,20) (19,23) (20,23) (21,22)\nQ: Is there a path between node 21 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1382"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,4) (1,2) (3,4)\nQ: Is there a path between node 1 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1383"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,1) (1,11) (1,5) (1,8) (2,14) (2,10) (2,6) (2,3) (2,13) (2,4) (3,7) (3,14) (3,6) (3,12) (3,13) (3,4) (4,9) (4,7) (4,10) (4,12) (4,13) (5,11) (5,8) (6,7) (6,10) (6,12) (6,13) (7,9) (7,14) (7,10) (7,13) (8,11) (10,14) (10,12) (10,13) (12,14) (12,13) (13,14)\nQ: Is there a path between node 7 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1384"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,11) (0,22) (0,30) (0,25) (0,19) (0,12) (0,13) (0,10) (0,29) (1,17) (1,4) (1,18) (1,7) (1,27) (1,2) (1,3) (1,9) (1,23) (1,28) (2,4) (2,21) (2,26) (2,7) (2,27) (2,9) (2,23) (2,28) (3,17) (3,4) (3,21) (3,26) (3,18) (3,7) (3,27) (3,14) (3,9) (3,23) (3,28) (3,24) (4,17) (4,21) (4,26) (4,18) (4,14) (4,9) (4,28) (4,24) (5,11) (5,22) (5,20) (5,25) (5,29) (6,8) (7,21) (7,26) (7,18) (7,27) (7,23) (7,28) (7,24) (9,21) (9,26) (9,18) (9,27) (9,14) (9,23) (9,28) (9,24) (10,11) (10,22) (10,20) (10,30) (10,25) (10,16) (10,19) (10,15) (10,13) (10,29) (11,22) (11,20) (11,30) (11,25) (11,16) (11,19) (11,12) (11,15) (11,13) (11,29) (12,22) (12,20) (12,30) (12,16) (12,15) (12,13) (13,22) (13,20) (13,30) (13,25) (13,16) (13,19) (13,15) (13,29) (14,26) (14,18) (14,23) (14,28) (14,24) (15,22) (15,30) (15,16) (15,19) (15,29) (16,22) (16,30) (16,25) (16,19) (16,29) (17,26) (17,18) (17,27) (17,23) (17,28) (18,21) (18,26) (18,27) (18,24) (19,20) (19,30) (19,25) (19,29) (20,22) (20,25) (20,29) (21,26) (21,27) (21,28) (21,24) (22,30) (22,29) (23,26) (23,27) (23,28) (23,24) (24,27) (24,28) (25,29) (26,27) (27,28) (29,30)\nQ: Is there a path between node 8 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1385"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,30) (0,27) (0,33) (0,11) (0,5) (0,12) (0,20) (0,7) (0,28) (0,17) (0,6) (0,4) (0,32) (0,13) (0,3) (0,22) (0,31) (1,25) (1,29) (1,30) (1,27) (1,33) (1,2) (1,5) (1,12) (1,20) (1,28) (1,18) (1,16) (1,24) (1,6) (1,13) (1,3) (1,22) (1,31) (2,25) (2,23) (2,29) (2,30) (2,27) (2,33) (2,11) (2,5) (2,12) (2,7) (2,18) (2,16) (2,17) (2,24) (2,13) (2,22) (2,15) (3,25) (3,23) (3,29) (3,30) (3,12) (3,7) (3,18) (3,16) (3,24) (3,4) (3,13) (3,22) (3,31) (4,23) (4,29) (4,27) (4,33) (4,11) (4,5) (4,7) (4,18) (4,24) (4,32) (4,15) (4,31) (5,25) (5,23) (5,30) (5,27) (5,33) (5,11) (5,12) (5,20) (5,7) (5,28) (5,24) (5,6) (5,32) (5,13) (5,22) (5,15) (5,31) (6,25) (6,23) (6,30) (6,27) (6,33) (6,12) (6,20) (6,7) (6,18) (6,24) (6,32) (6,13) (7,25) (7,30) (7,27) (7,33) (7,20) (7,28) (7,18) (7,24) (7,32) (7,13) (7,22) (7,15) (7,31) (8,14) (8,26) (8,19) (9,14) (9,26) (9,19) (9,21) (9,10) (10,14) (10,26) (10,19) (11,23) (11,29) (11,30) (11,27) (11,33) (11,20) (11,18) (11,16) (11,17) (11,32) (11,13) (11,22) (11,15) (11,31) (12,25) (12,23) (12,29) (12,27) (12,33) (12,28) (12,16) (12,24) (12,13) (12,22) (12,15) (12,31) (13,25) (13,23) (13,29) (13,27) (13,33) (13,20) (13,28) (13,18) (13,16) (13,17) (13,24) (13,32) (13,15) (13,31) (14,26) (15,25) (15,23) (15,29) (15,30) (15,33) (15,16) (15,17) (15,24) (15,22) (15,31) (16,25) (16,23) (16,29) (16,30) (16,27) (16,28) (16,17) (16,24) (16,32) (16,22) (17,25) (17,23) (17,29) (17,33) (17,20) (17,18) (17,24) (17,31) (18,25) (18,29) (18,30) (18,33) (18,28) (18,24) (18,31) (20,25) (20,23) (20,30) (20,24) (20,32) (20,22) (20,31) (21,26) (22,25) (22,29) (22,30) (22,28) (22,24) (23,25) (23,29) (23,27) (23,28) (23,24) (23,32) (24,25) (24,29) (24,27) (24,33) (24,28) (24,31) (25,29) (25,30) (25,27) (25,28) (25,32) (25,31) (27,29) (27,30) (27,33) (27,28) (28,29) (28,30) (28,33) (28,32) (28,31) (29,30) (29,33) (29,32) (29,31) (30,33) (30,32) (30,31) (31,33) (31,32) (32,33)\nQ: Is there a path between node 24 and node 28?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1386"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,9) (0,8) (0,19) (0,13) (0,11) (1,15) (1,6) (1,3) (1,12) (1,4) (1,2) (1,23) (1,5) (1,16) (1,22) (1,17) (1,18) (1,21) (1,24) (1,25) (2,15) (2,3) (2,4) (2,20) (2,23) (2,22) (2,27) (2,18) (2,21) (2,24) (3,15) (3,4) (3,26) (3,20) (3,23) (3,5) (3,16) (3,14) (3,22) (3,27) (3,18) (3,21) (3,24) (3,25) (4,15) (4,6) (4,12) (4,26) (4,20) (4,5) (4,22) (4,27) (4,17) (4,21) (4,25) (5,15) (5,6) (5,12) (5,20) (5,16) (5,14) (5,22) (5,27) (5,18) (5,21) (5,25) (6,15) (6,12) (6,27) (6,17) (6,21) (6,24) (6,25) (7,19) (7,13) (8,9) (8,19) (8,13) (9,19) (9,10) (10,19) (10,13) (10,11) (11,13) (12,15) (12,26) (12,20) (12,14) (12,22) (12,21) (12,24) (13,19) (14,15) (14,26) (14,20) (14,16) (14,22) (14,17) (14,21) (14,24) (14,25) (15,26) (15,20) (15,23) (15,16) (15,22) (15,17) (15,18) (15,24) (16,26) (16,27) (16,18) (16,25) (17,26) (17,23) (17,18) (17,21) (17,24) (17,25) (18,26) (18,20) (18,22) (18,27) (18,24) (18,25) (20,26) (20,23) (20,22) (20,27) (20,24) (20,25) (21,22) (21,27) (21,24) (21,25) (22,23) (22,27) (22,24) (22,25) (23,27) (23,25) (24,26) (24,27) (25,26) (25,27) (26,27)\nQ: Is there a path between node 4 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1387"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,20) (0,8) (0,31) (0,22) (1,4) (1,24) (1,19) (1,16) (1,5) (1,2) (1,8) (1,18) (1,27) (2,4) (2,19) (2,12) (2,17) (2,21) (2,31) (2,22) (3,25) (3,20) (3,14) (3,31) (3,22) (3,27) (4,7) (4,21) (4,26) (4,27) (5,11) (5,24) (5,20) (5,19) (5,12) (5,16) (5,17) (5,21) (5,9) (5,22) (6,15) (7,24) (7,20) (7,19) (7,16) (7,29) (7,17) (7,21) (7,14) (7,9) (7,8) (7,18) (7,22) (7,30) (8,20) (8,12) (8,14) (9,20) (9,16) (9,14) (9,18) (9,26) (9,23) (10,15) (11,25) (11,28) (11,20) (11,21) (11,26) (12,28) (12,24) (12,20) (12,29) (12,14) (12,18) (12,26) (12,22) (12,27) (12,23) (14,24) (14,16) (14,18) (14,31) (16,25) (16,26) (16,31) (16,23) (17,31) (17,27) (18,25) (18,28) (18,24) (18,21) (18,26) (18,27) (19,29) (19,21) (19,22) (20,25) (20,21) (20,26) (21,24) (21,29) (21,31) (21,23) (22,29) (22,26) (22,23) (23,25) (23,26) (24,25) (24,26) (24,30) (25,29) (25,31) (26,29) (26,31) (27,28) (27,31) (28,29) (29,31) (29,30) (30,31)\nQ: Is there a path between node 2 and node 25?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1388"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,1) (0,14) (0,18) (1,17) (1,14) (1,18) (2,19) (2,7) (2,10) (2,3) (2,12) (2,16) (2,11) (2,5) (2,9) (2,15) (2,6) (2,20) (2,8) (2,4) (2,13) (3,19) (3,7) (3,10) (3,12) (3,16) (3,11) (3,5) (3,9) (3,15) (3,6) (3,20) (3,8) (3,4) (3,13) (4,19) (4,7) (4,10) (4,12) (4,16) (4,11) (4,5) (4,9) (4,15) (4,6) (4,20) (4,8) (4,13) (5,19) (5,7) (5,10) (5,12) (5,16) (5,11) (5,9) (5,15) (5,6) (5,20) (5,8) (5,13) (6,19) (6,7) (6,10) (6,12) (6,16) (6,11) (6,9) (6,15) (6,20) (6,8) (6,13) (7,19) (7,10) (7,12) (7,16) (7,11) (7,9) (7,15) (7,20) (7,8) (7,13) (8,19) (8,10) (8,12) (8,16) (8,11) (8,9) (8,15) (8,20) (8,13) (9,19) (9,10) (9,12) (9,16) (9,11) (9,15) (9,20) (9,13) (10,19) (10,12) (10,16) (10,11) (10,15) (10,20) (10,13) (11,19) (11,12) (11,16) (11,15) (11,20) (11,13) (12,19) (12,16) (12,15) (12,20) (12,13) (13,19) (13,16) (13,15) (13,20) (14,17) (14,18) (15,19) (15,16) (15,20) (16,19) (16,20) (17,18) (19,20)\nQ: Is there a path between node 18 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1389"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,9) (0,2) (0,5) (0,10) (0,1) (1,4) (1,9) (1,2) (1,5) (1,10) (2,4) (2,9) (2,5) (2,10) (3,11) (3,8) (3,12) (3,7) (3,6) (4,9) (4,5) (4,10) (5,9) (5,10) (6,11) (6,8) (6,12) (6,7) (7,11) (7,8) (7,12) (8,11) (8,12) (9,10) (11,12)\nQ: Is there a path between node 9 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1390"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,9) (0,2) (0,5) (0,10) (0,1) (1,4) (1,9) (1,2) (1,5) (1,10) (2,4) (2,9) (2,5) (2,10) (3,11) (3,8) (3,12) (3,7) (3,6) (4,9) (4,5) (4,10) (5,9) (5,10) (6,11) (6,8) (6,12) (6,7) (7,11) (7,8) (7,12) (8,11) (8,12) (9,10) (11,12)\nQ: Is there a path between node 5 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1391"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,21) (0,8) (0,11) (0,16) (0,13) (0,10) (0,20) (0,6) (0,4) (1,14) (1,17) (1,18) (1,5) (1,19) (1,2) (2,22) (2,14) (2,5) (3,8) (3,11) (3,10) (3,12) (3,6) (4,11) (4,13) (4,20) (4,12) (5,22) (5,14) (5,17) (5,18) (5,9) (5,19) (6,8) (6,11) (6,16) (6,13) (6,10) (6,20) (6,12) (7,15) (8,11) (8,13) (8,10) (8,20) (8,12) (9,22) (9,14) (9,17) (9,18) (9,19) (10,21) (10,13) (11,16) (11,13) (11,20) (11,12) (12,21) (12,16) (12,13) (12,20) (13,21) (13,16) (13,20) (14,22) (14,18) (16,21) (16,20) (17,22) (17,18) (17,19) (18,19) (20,21)\nQ: Is there a path between node 0 and node 12?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1392"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,30) (0,27) (0,33) (0,11) (0,5) (0,12) (0,20) (0,7) (0,28) (0,17) (0,6) (0,4) (0,32) (0,13) (0,3) (0,22) (0,31) (1,25) (1,29) (1,30) (1,27) (1,33) (1,2) (1,5) (1,12) (1,20) (1,28) (1,18) (1,16) (1,24) (1,6) (1,13) (1,3) (1,22) (1,31) (2,25) (2,23) (2,29) (2,30) (2,27) (2,33) (2,11) (2,5) (2,12) (2,7) (2,18) (2,16) (2,17) (2,24) (2,13) (2,22) (2,15) (3,25) (3,23) (3,29) (3,30) (3,12) (3,7) (3,18) (3,16) (3,24) (3,4) (3,13) (3,22) (3,31) (4,23) (4,29) (4,27) (4,33) (4,11) (4,5) (4,7) (4,18) (4,24) (4,32) (4,15) (4,31) (5,25) (5,23) (5,30) (5,27) (5,33) (5,11) (5,12) (5,20) (5,7) (5,28) (5,24) (5,6) (5,32) (5,13) (5,22) (5,15) (5,31) (6,25) (6,23) (6,30) (6,27) (6,33) (6,12) (6,20) (6,7) (6,18) (6,24) (6,32) (6,13) (7,25) (7,30) (7,27) (7,33) (7,20) (7,28) (7,18) (7,24) (7,32) (7,13) (7,22) (7,15) (7,31) (8,14) (8,26) (8,19) (9,14) (9,26) (9,19) (9,21) (9,10) (10,14) (10,26) (10,19) (11,23) (11,29) (11,30) (11,27) (11,33) (11,20) (11,18) (11,16) (11,17) (11,32) (11,13) (11,22) (11,15) (11,31) (12,25) (12,23) (12,29) (12,27) (12,33) (12,28) (12,16) (12,24) (12,13) (12,22) (12,15) (12,31) (13,25) (13,23) (13,29) (13,27) (13,33) (13,20) (13,28) (13,18) (13,16) (13,17) (13,24) (13,32) (13,15) (13,31) (14,26) (15,25) (15,23) (15,29) (15,30) (15,33) (15,16) (15,17) (15,24) (15,22) (15,31) (16,25) (16,23) (16,29) (16,30) (16,27) (16,28) (16,17) (16,24) (16,32) (16,22) (17,25) (17,23) (17,29) (17,33) (17,20) (17,18) (17,24) (17,31) (18,25) (18,29) (18,30) (18,33) (18,28) (18,24) (18,31) (20,25) (20,23) (20,30) (20,24) (20,32) (20,22) (20,31) (21,26) (22,25) (22,29) (22,30) (22,28) (22,24) (23,25) (23,29) (23,27) (23,28) (23,24) (23,32) (24,25) (24,29) (24,27) (24,33) (24,28) (24,31) (25,29) (25,30) (25,27) (25,28) (25,32) (25,31) (27,29) (27,30) (27,33) (27,28) (28,29) (28,30) (28,33) (28,32) (28,31) (29,30) (29,33) (29,32) (29,31) (30,33) (30,32) (30,31) (31,33) (31,32) (32,33)\nQ: Is there a path between node 3 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1393"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,4) (0,3) (0,6) (0,2) (0,8) (0,5) (0,11) (1,4) (1,3) (1,6) (1,2) (1,8) (1,5) (1,11) (2,4) (2,3) (2,6) (2,8) (2,5) (2,11) (3,4) (3,6) (3,8) (3,5) (3,11) (4,6) (4,8) (4,5) (4,11) (5,6) (5,8) (5,11) (6,8) (6,11) (7,9) (7,10) (8,11) (9,10)\nQ: Is there a path between node 10 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1394"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,6) (2,7) (2,6) (2,4) (5,7) (6,8)\nQ: Is there a path between node 4 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1395"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,11) (3,15) (3,8) (5,18) (5,7) (6,17) (6,7) (7,13) (7,8) (7,14) (8,18) (8,12) (9,11) (9,15) (9,13) (9,17) (10,18) (11,13) (11,17) (12,18) (12,17) (12,14) (13,17) (14,17) (17,18)\nQ: Is there a path between node 14 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1396"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,23) (1,6) (1,19) (1,7) (2,17) (2,24) (2,10) (2,20) (3,22) (3,27) (4,17) (4,15) (5,19) (5,12) (5,25) (6,19) (6,7) (7,18) (7,23) (8,16) (8,13) (9,27) (9,13) (10,21) (10,15) (10,11) (11,17) (11,26) (11,24) (11,14) (12,25) (12,23) (14,17) (14,26) (15,21) (17,26) (17,21) (17,24) (20,21) (20,24) (21,26) (21,24) (23,25)\nQ: Is there a path between node 16 and node 15?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1397"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,21) (0,7) (0,6) (0,3) (0,17) (0,20) (0,22) (0,16) (0,23) (0,25) (0,27) (1,5) (1,21) (1,4) (1,7) (1,15) (1,18) (1,2) (1,24) (1,20) (1,11) (1,16) (1,25) (1,27) (2,14) (2,5) (2,21) (2,4) (2,15) (2,24) (2,22) (2,11) (2,23) (2,25) (2,27) (3,14) (3,13) (3,21) (3,7) (3,15) (3,6) (3,17) (3,24) (3,22) (3,11) (3,16) (3,23) (4,14) (4,13) (4,5) (4,19) (4,7) (4,18) (4,17) (4,22) (4,11) (4,23) (4,25) (4,27) (5,13) (5,19) (5,15) (5,18) (5,24) (5,20) (5,22) (5,11) (5,23) (5,27) (6,14) (6,21) (6,19) (6,7) (6,15) (6,18) (6,17) (6,24) (6,20) (6,11) (6,16) (6,25) (6,27) (7,14) (7,13) (7,21) (7,19) (7,15) (7,18) (7,17) (7,20) (7,22) (7,11) (7,23) (7,27) (8,30) (8,28) (9,31) (9,10) (9,26) (9,29) (10,31) (10,26) (10,29) (11,13) (11,21) (11,19) (11,15) (11,24) (11,22) (11,25) (11,27) (12,28) (13,14) (13,21) (13,15) (13,18) (13,17) (13,24) (13,20) (13,16) (13,23) (13,25) (13,27) (14,21) (14,19) (14,24) (14,20) (14,22) (14,16) (14,23) (14,25) (15,21) (15,18) (15,17) (15,24) (15,20) (15,22) (15,16) (15,25) (15,27) (16,21) (16,18) (16,17) (16,24) (16,20) (16,22) (16,25) (17,21) (17,19) (17,18) (17,24) (17,20) (17,22) (17,23) (17,25) (17,27) (18,21) (18,24) (18,20) (18,25) (18,27) (19,21) (19,20) (19,22) (19,27) (20,21) (20,24) (20,22) (20,23) (20,27) (21,24) (21,22) (21,25) (21,27) (22,25) (23,25) (23,27) (25,27) (26,31) (26,29) (29,31)\nQ: Is there a path between node 30 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1398"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,7) (0,12) (0,32) (0,22) (0,9) (0,20) (0,2) (0,5) (0,14) (0,4) (0,26) (0,21) (1,11) (1,8) (1,24) (1,3) (1,31) (1,28) (1,6) (2,16) (2,7) (2,32) (2,22) (2,9) (2,20) (2,14) (2,4) (2,21) (3,11) (3,8) (3,24) (3,31) (3,28) (4,16) (4,32) (4,22) (4,9) (4,20) (4,5) (4,14) (4,26) (5,16) (5,7) (5,12) (5,32) (5,22) (5,9) (5,20) (5,14) (5,26) (5,21) (6,8) (6,24) (6,31) (6,28) (7,12) (7,32) (7,22) (7,9) (7,14) (7,26) (7,21) (8,24) (8,31) (8,28) (9,16) (9,12) (9,32) (9,20) (9,26) (9,21) (10,23) (10,13) (10,29) (10,19) (10,25) (10,18) (12,32) (12,22) (12,20) (12,26) (12,21) (13,30) (13,27) (13,29) (13,19) (13,25) (13,18) (14,16) (14,32) (14,22) (14,20) (14,26) (15,30) (15,29) (15,25) (15,18) (16,32) (16,22) (16,20) (16,26) (16,21) (17,30) (17,27) (18,30) (18,29) (19,30) (19,23) (19,27) (19,25) (20,32) (20,22) (20,26) (21,32) (21,26) (22,32) (22,26) (23,30) (23,29) (23,25) (24,28) (26,32) (27,30) (27,29) (28,31) (29,30)\nQ: Is there a path between node 0 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1399"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,31) (1,4) (1,27) (1,25) (2,31) (2,24) (2,13) (2,10) (3,30) (3,32) (3,27) (3,15) (4,30) (4,6) (4,28) (4,8) (5,22) (6,27) (7,20) (7,11) (7,12) (8,15) (9,14) (10,17) (10,23) (10,13) (11,14) (12,18) (13,23) (14,22) (15,30) (15,27) (15,25) (15,16) (15,28) (17,23) (17,21) (18,22) (18,33) (20,22) (21,31) (23,24) (25,30) (25,27) (25,28) (26,31) (27,30) (27,32) (28,32)\nQ: Is there a path between node 4 and node 25?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1400"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,10) (0,2) (2,15) (2,20) (2,23) (2,14) (2,17) (2,24) (2,18) (3,21) (4,27) (5,9) (5,22) (6,29) (6,8) (7,29) (7,25) (7,20) (7,17) (7,18) (7,8) (8,23) (8,24) (10,23) (10,18) (11,27) (12,13) (13,21) (14,25) (14,23) (14,17) (14,24) (15,29) (15,25) (15,23) (15,16) (16,29) (16,17) (17,25) (17,23) (17,24) (17,18) (18,29) (20,25) (22,26) (23,25) (24,29) (26,27)\nQ: Is there a path between node 25 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1401"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,28) (0,1) (0,22) (0,20) (0,15) (0,18) (0,2) (0,5) (0,10) (0,8) (0,14) (0,6) (1,27) (1,12) (1,19) (1,28) (1,25) (1,29) (1,22) (1,4) (1,7) (1,15) (1,18) (1,3) (1,2) (1,24) (1,5) (1,11) (1,14) (1,13) (1,6) (2,12) (2,19) (2,28) (2,29) (2,4) (2,15) (2,16) (2,18) (2,3) (2,10) (2,13) (2,21) (2,6) (3,27) (3,19) (3,28) (3,20) (3,4) (3,7) (3,16) (3,18) (3,9) (3,24) (3,5) (3,11) (3,10) (3,8) (3,14) (3,23) (3,21) (3,6) (4,27) (4,12) (4,19) (4,28) (4,25) (4,20) (4,7) (4,15) (4,16) (4,5) (4,8) (4,14) (4,13) (4,21) (4,6) (5,27) (5,12) (5,19) (5,28) (5,25) (5,29) (5,22) (5,20) (5,7) (5,15) (5,16) (5,24) (5,11) (5,10) (5,8) (5,14) (5,23) (5,13) (5,21) (5,6) (6,27) (6,12) (6,28) (6,25) (6,29) (6,22) (6,20) (6,7) (6,16) (6,18) (6,9) (6,24) (6,8) (6,14) (6,21) (7,19) (7,25) (7,29) (7,22) (7,20) (7,15) (7,16) (7,24) (7,11) (7,10) (7,14) (7,23) (7,21) (8,27) (8,12) (8,19) (8,29) (8,22) (8,20) (8,15) (8,16) (8,9) (8,24) (8,11) (8,10) (8,14) (8,13) (9,12) (9,19) (9,25) (9,22) (9,20) (9,18) (9,24) (9,11) (9,10) (9,14) (9,23) (9,13) (9,21) (10,27) (10,12) (10,19) (10,28) (10,25) (10,29) (10,16) (10,18) (10,24) (10,14) (10,23) (10,13) (10,21) (11,27) (11,12) (11,25) (11,22) (11,20) (11,18) (11,24) (12,19) (12,28) (12,29) (12,22) (12,15) (12,16) (12,18) (12,14) (12,23) (12,13) (12,21) (13,27) (13,28) (13,25) (13,29) (13,22) (13,20) (13,15) (13,18) (13,24) (14,19) (14,28) (14,25) (14,29) (14,15) (14,16) (14,18) (14,24) (14,23) (15,27) (15,28) (15,25) (15,29) (15,20) (15,18) (15,23) (15,21) (16,27) (16,19) (16,28) (16,25) (16,29) (16,22) (16,20) (16,18) (16,24) (16,21) (18,19) (18,28) (18,29) (18,22) (18,20) (18,24) (18,23) (18,21) (19,27) (19,28) (19,25) (19,29) (19,22) (19,20) (19,24) (19,23) (19,21) (20,27) (20,28) (20,29) (20,22) (20,23) (20,21) (21,27) (21,28) (21,24) (21,23) (22,27) (22,28) (22,29) (22,23) (23,27) (23,28) (23,25) (23,29) (24,27) (24,28) (24,25) (24,29) (25,27) (25,29) (27,28) (27,29)\nQ: Is there a path between node 17 and node 29?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1402"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,4) (0,12) (0,11) (0,10) (0,3) (0,17) (0,21) (0,27) (0,15) (0,23) (0,31) (0,29) (0,2) (0,8) (0,9) (0,14) (0,18) (1,5) (1,26) (1,13) (1,20) (1,32) (1,7) (2,19) (2,4) (2,28) (2,22) (2,16) (2,12) (2,10) (2,3) (2,17) (2,21) (2,27) (2,15) (2,23) (2,31) (2,29) (2,8) (2,9) (2,14) (2,18) (3,4) (3,22) (3,16) (3,12) (3,10) (3,17) (3,21) (3,27) (3,23) (3,31) (3,29) (3,6) (3,9) (3,14) (3,18) (4,16) (4,12) (4,11) (4,17) (4,21) (4,15) (4,30) (4,23) (4,29) (4,6) (4,8) (4,9) (4,18) (5,26) (5,13) (5,25) (5,24) (5,32) (5,7) (6,19) (6,22) (6,12) (6,11) (6,10) (6,17) (6,21) (6,27) (6,15) (6,30) (6,23) (6,31) (6,29) (6,9) (6,14) (7,26) (7,25) (7,32) (8,19) (8,28) (8,10) (8,17) (8,27) (8,15) (8,30) (8,23) (9,19) (9,28) (9,22) (9,16) (9,12) (9,10) (9,17) (9,21) (9,15) (9,30) (9,23) (9,29) (9,18) (10,19) (10,28) (10,22) (10,12) (10,11) (10,17) (10,21) (10,27) (10,15) (10,30) (10,23) (10,31) (10,29) (10,14) (10,18) (11,16) (11,12) (11,17) (11,21) (11,27) (11,15) (11,30) (11,31) (11,29) (11,14) (11,18) (12,19) (12,28) (12,22) (12,17) (12,27) (12,15) (12,30) (12,23) (12,31) (12,29) (12,14) (12,18) (13,26) (13,25) (13,20) (13,32) (14,28) (14,16) (14,17) (14,21) (14,27) (14,15) (14,31) (14,29) (14,18) (15,19) (15,22) (15,16) (15,17) (15,21) (15,27) (15,30) (15,23) (15,31) (15,29) (15,18) (16,19) (16,28) (16,22) (16,17) (16,21) (16,27) (16,30) (16,31) (16,18) (17,22) (17,21) (17,30) (17,31) (17,29) (17,18) (18,19) (18,28) (18,22) (18,21) (18,27) (18,29) (19,28) (19,22) (19,21) (19,30) (19,31) (19,29) (20,32) (21,28) (21,22) (21,27) (21,29) (22,28) (22,30) (22,23) (22,31) (22,29) (23,28) (23,27) (23,30) (23,31) (23,29) (24,26) (24,25) (25,26) (25,32) (26,32) (27,28) (27,30) (27,29) (28,30) (28,31) (28,29) (29,30) (29,31)\nQ: Is there a path between node 21 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1403"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,4) (0,16) (0,21) (0,1) (0,25) (0,14) (0,9) (0,5) (0,6) (0,12) (0,17) (0,24) (0,23) (1,29) (1,4) (1,27) (1,16) (1,21) (1,14) (1,9) (1,6) (1,24) (1,23) (2,26) (2,10) (2,22) (2,15) (2,28) (2,8) (2,30) (2,19) (3,26) (3,10) (3,11) (3,22) (3,15) (3,28) (3,8) (3,30) (3,19) (3,20) (4,29) (4,27) (4,16) (4,21) (4,14) (4,9) (4,5) (4,6) (4,12) (4,24) (5,29) (5,27) (5,21) (5,7) (5,14) (5,12) (5,17) (5,24) (5,23) (6,29) (6,27) (6,7) (6,25) (6,14) (6,9) (6,12) (6,24) (6,23) (7,25) (7,14) (7,9) (7,12) (7,17) (7,23) (8,26) (8,10) (8,11) (8,13) (8,30) (8,19) (9,29) (9,27) (9,16) (9,14) (9,12) (9,24) (9,23) (10,26) (10,13) (10,15) (10,28) (10,19) (10,20) (11,26) (11,13) (11,15) (11,28) (11,30) (11,19) (11,20) (12,29) (12,27) (12,16) (12,21) (12,25) (12,17) (12,24) (12,23) (13,26) (13,28) (13,30) (14,29) (14,16) (14,21) (14,25) (14,17) (14,24) (14,23) (15,26) (15,28) (15,30) (15,20) (16,27) (16,21) (16,17) (16,24) (16,23) (17,29) (17,27) (17,21) (17,25) (17,24) (19,26) (19,22) (19,30) (19,20) (20,26) (20,22) (20,28) (21,29) (21,27) (21,25) (21,24) (21,23) (22,26) (22,28) (22,30) (23,29) (23,27) (23,25) (24,29) (24,27) (24,25) (25,29) (26,28) (28,30)\nQ: Is there a path between node 13 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1404"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,13) (0,1) (0,9) (0,5) (0,7) (0,3) (0,10) (0,23) (0,26) (0,27) (0,8) (0,14) (0,22) (0,20) (0,15) (0,4) (0,2) (1,25) (1,11) (1,21) (1,13) (1,9) (1,3) (1,10) (1,23) (1,26) (1,27) (1,14) (1,20) (1,15) (1,2) (1,28) (2,25) (2,11) (2,16) (2,21) (2,6) (2,13) (2,9) (2,7) (2,23) (2,26) (2,8) (2,20) (2,15) (3,25) (3,6) (3,13) (3,9) (3,10) (3,27) (3,20) (3,15) (3,4) (3,28) (4,11) (4,16) (4,6) (4,13) (4,10) (4,23) (4,26) (4,27) (4,8) (4,14) (4,22) (4,15) (4,28) (5,25) (5,16) (5,21) (5,6) (5,13) (5,9) (5,7) (5,26) (5,8) (5,22) (5,15) (5,28) (6,11) (6,16) (6,21) (6,13) (6,9) (6,7) (6,10) (6,27) (6,22) (6,20) (6,15) (7,25) (7,16) (7,21) (7,9) (7,10) (7,27) (7,8) (7,14) (7,22) (7,20) (7,15) (7,28) (8,25) (8,13) (8,23) (8,26) (8,27) (8,14) (8,20) (8,28) (9,25) (9,11) (9,16) (9,21) (9,10) (9,23) (9,26) (9,27) (9,22) (9,20) (9,28) (10,11) (10,16) (10,21) (10,13) (10,23) (10,26) (10,27) (10,14) (10,22) (10,20) (10,15) (10,28) (11,25) (11,16) (11,21) (11,13) (11,23) (11,26) (11,27) (11,14) (11,22) (11,20) (12,24) (12,19) (13,25) (13,16) (13,14) (13,22) (13,15) (13,28) (14,25) (14,21) (14,23) (14,26) (14,20) (14,15) (15,16) (15,21) (15,26) (15,27) (15,22) (15,28) (16,21) (16,23) (16,26) (16,27) (16,28) (17,18) (20,25) (20,23) (20,26) (20,27) (20,22) (20,28) (21,25) (21,23) (21,26) (21,22) (22,25) (22,23) (22,27) (23,25) (23,26) (23,27) (23,28) (25,26) (25,27) (26,27) (27,28)\nQ: Is there a path between node 16 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1405"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,10) (0,17) (0,15) (0,4) (0,12) (0,24) (0,9) (0,3) (0,13) (0,23) (0,7) (0,19) (0,16) (0,6) (0,25) (0,8) (1,10) (1,17) (1,4) (1,12) (1,24) (1,3) (1,13) (1,23) (1,26) (1,22) (1,19) (1,6) (1,14) (1,25) (1,8) (1,20) (2,10) (2,17) (2,11) (2,4) (2,24) (2,9) (2,3) (2,13) (2,23) (2,26) (2,7) (2,22) (2,19) (2,6) (2,14) (2,25) (2,8) (3,10) (3,17) (3,11) (3,15) (3,4) (3,12) (3,24) (3,9) (3,13) (3,26) (3,7) (3,19) (3,16) (3,14) (3,25) (3,8) (3,20) (4,10) (4,17) (4,11) (4,15) (4,12) (4,24) (4,9) (4,7) (4,19) (4,16) (4,6) (4,25) (4,20) (5,18) (6,10) (6,17) (6,15) (6,12) (6,24) (6,9) (6,23) (6,7) (6,16) (6,25) (6,8) (7,10) (7,11) (7,15) (7,12) (7,13) (7,22) (7,19) (7,16) (7,25) (7,8) (7,20) (8,10) (8,17) (8,11) (8,15) (8,12) (8,24) (8,9) (8,23) (8,22) (8,19) (8,16) (8,14) (8,25) (8,20) (9,10) (9,17) (9,11) (9,12) (9,24) (9,13) (9,23) (9,26) (9,22) (9,19) (9,16) (9,20) (10,17) (10,11) (10,15) (10,12) (10,24) (10,13) (10,23) (10,26) (10,19) (10,14) (10,20) (11,15) (11,12) (11,24) (11,13) (11,23) (11,26) (11,19) (11,16) (11,14) (11,20) (12,15) (12,24) (12,23) (12,22) (12,19) (12,16) (12,14) (12,25) (12,20) (13,15) (13,24) (13,23) (13,19) (13,16) (13,14) (13,25) (13,20) (14,17) (14,15) (14,24) (14,23) (14,26) (14,22) (14,19) (14,16) (14,25) (14,20) (15,17) (15,24) (15,23) (15,26) (15,16) (15,20) (16,24) (16,23) (16,26) (16,19) (16,25) (16,20) (17,23) (17,20) (18,21) (19,23) (19,22) (19,25) (19,20) (20,24) (20,23) (20,22) (20,25) (22,26) (22,25) (23,24) (23,26) (23,25) (24,26) (24,25) (25,26)\nQ: Is there a path between node 5 and node 19?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1406"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,6) (1,2) (3,7) (3,5)\nQ: Is there a path between node 6 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1407"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,9) (0,14) (0,18) (0,3) (0,1) (0,17) (0,4) (0,8) (0,7) (0,15) (0,11) (0,10) (0,13) (1,5) (1,9) (1,14) (1,18) (1,3) (1,17) (1,4) (1,8) (1,7) (1,15) (1,11) (1,10) (1,13) (3,5) (3,9) (3,14) (3,18) (3,17) (3,4) (3,8) (3,7) (3,15) (3,11) (3,10) (3,13) (4,5) (4,9) (4,14) (4,18) (4,17) (4,8) (4,7) (4,15) (4,11) (4,10) (4,13) (5,9) (5,14) (5,18) (5,17) (5,8) (5,7) (5,15) (5,11) (5,10) (5,13) (6,12) (6,16) (7,9) (7,14) (7,18) (7,17) (7,8) (7,15) (7,11) (7,10) (7,13) (8,9) (8,14) (8,18) (8,17) (8,15) (8,11) (8,10) (8,13) (9,14) (9,18) (9,17) (9,15) (9,11) (9,10) (9,13) (10,14) (10,18) (10,17) (10,15) (10,11) (10,13) (11,14) (11,18) (11,17) (11,15) (11,13) (12,16) (13,14) (13,18) (13,17) (13,15) (14,18) (14,17) (14,15) (15,18) (15,17) (17,18)\nQ: Is there a path between node 12 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1408"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,2) (0,3) (1,5) (2,4) (2,3) (3,4)\nQ: Is there a path between node 5 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1409"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,12) (0,1) (0,7) (0,16) (0,13) (0,9) (0,2) (0,10) (0,21) (0,19) (0,3) (0,20) (0,8) (0,23) (0,5) (0,4) (0,6) (0,22) (1,15) (1,12) (1,7) (1,16) (1,13) (1,9) (1,2) (1,10) (1,21) (1,19) (1,3) (1,20) (1,8) (1,23) (1,5) (1,4) (1,6) (1,22) (2,15) (2,12) (2,7) (2,16) (2,13) (2,9) (2,10) (2,21) (2,19) (2,3) (2,20) (2,8) (2,23) (2,5) (2,4) (2,6) (2,22) (3,15) (3,12) (3,7) (3,16) (3,13) (3,9) (3,10) (3,21) (3,19) (3,20) (3,8) (3,23) (3,5) (3,4) (3,6) (3,22) (4,15) (4,12) (4,7) (4,16) (4,13) (4,9) (4,10) (4,21) (4,19) (4,20) (4,8) (4,23) (4,5) (4,6) (4,22) (5,15) (5,12) (5,7) (5,16) (5,13) (5,9) (5,10) (5,21) (5,19) (5,20) (5,8) (5,23) (5,6) (5,22) (6,15) (6,12) (6,7) (6,16) (6,13) (6,9) (6,10) (6,21) (6,19) (6,20) (6,8) (6,23) (6,22) (7,15) (7,12) (7,16) (7,13) (7,9) (7,10) (7,21) (7,19) (7,20) (7,8) (7,23) (7,22) (8,15) (8,12) (8,16) (8,13) (8,9) (8,10) (8,21) (8,19) (8,20) (8,23) (8,22) (9,15) (9,12) (9,16) (9,13) (9,10) (9,21) (9,19) (9,20) (9,23) (9,22) (10,15) (10,12) (10,16) (10,13) (10,21) (10,19) (10,20) (10,23) (10,22) (11,17) (11,14) (11,18) (12,15) (12,16) (12,13) (12,21) (12,19) (12,20) (12,23) (12,22) (13,15) (13,16) (13,21) (13,19) (13,20) (13,23) (13,22) (14,17) (14,18) (15,16) (15,21) (15,19) (15,20) (15,23) (15,22) (16,21) (16,19) (16,20) (16,23) (16,22) (17,18) (19,21) (19,20) (19,23) (19,22) (20,21) (20,23) (20,22) (21,23) (21,22) (22,23)\nQ: Is there a path between node 18 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1410"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,1) (1,12) (1,15) (2,9) (2,6) (3,10) (3,17) (3,15) (5,7) (6,10) (6,9) (6,11) (7,13) (8,17) (8,16) (10,15) (11,12) (15,17)\nQ: Is there a path between node 8 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1411"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (0,1) (0,19) (0,15) (0,20) (0,9) (0,21) (0,3) (0,22) (0,32) (0,24) (0,14) (0,11) (0,17) (0,5) (0,34) (0,4) (0,26) (0,10) (0,8) (1,27) (1,23) (1,30) (1,6) (1,19) (1,20) (1,2) (1,9) (1,21) (1,3) (1,22) (1,24) (1,14) (1,11) (1,17) (1,5) (1,4) (1,26) (1,8) (2,27) (2,30) (2,6) (2,19) (2,20) (2,9) (2,21) (2,3) (2,22) (2,32) (2,7) (2,11) (2,17) (2,5) (2,34) (2,4) (2,26) (2,12) (2,10) (3,27) (3,23) (3,30) (3,6) (3,19) (3,15) (3,20) (3,9) (3,22) (3,24) (3,14) (3,34) (3,4) (3,12) (3,10) (3,8) (3,28) (4,27) (4,23) (4,30) (4,19) (4,15) (4,20) (4,9) (4,21) (4,32) (4,24) (4,14) (4,7) (4,11) (4,17) (4,5) (4,26) (4,12) (4,8) (4,28) (5,30) (5,19) (5,9) (5,21) (5,24) (5,7) (5,11) (5,17) (5,34) (5,12) (6,27) (6,23) (6,30) (6,19) (6,20) (6,9) (6,21) (6,22) (6,32) (6,24) (6,14) (6,7) (6,11) (6,17) (6,34) (6,26) (6,8) (6,28) (7,23) (7,30) (7,19) (7,15) (7,20) (7,21) (7,32) (7,24) (7,11) (7,17) (7,34) (7,12) (7,10) (7,8) (7,28) (8,23) (8,15) (8,20) (8,24) (8,14) (8,11) (8,17) (8,34) (8,26) (8,12) (8,10) (8,28) (9,30) (9,19) (9,15) (9,20) (9,22) (9,32) (9,24) (9,11) (9,34) (9,12) (9,10) (9,28) (10,27) (10,23) (10,30) (10,19) (10,21) (10,32) (10,24) (10,26) (10,12) (11,27) (11,30) (11,19) (11,20) (11,21) (11,22) (11,32) (11,24) (11,14) (11,17) (11,34) (11,12) (12,27) (12,30) (12,19) (12,20) (12,22) (12,32) (12,24) (12,14) (12,17) (12,34) (12,28) (14,27) (14,23) (14,30) (14,19) (14,15) (14,21) (14,22) (14,32) (14,17) (14,34) (14,28) (15,19) (15,20) (15,21) (15,22) (15,32) (15,24) (15,34) (15,26) (15,28) (16,33) (16,29) (16,18) (16,31) (17,27) (17,23) (17,30) (17,19) (17,20) (17,21) (17,22) (17,32) (17,24) (17,34) (17,28) (18,33) (18,31) (18,25) (19,27) (19,23) (19,30) (19,20) (19,22) (19,32) (19,34) (19,26) (19,28) (20,23) (20,30) (20,21) (20,22) (20,32) (20,24) (20,34) (20,26) (21,27) (21,23) (21,30) (21,22) (21,32) (21,24) (21,34) (21,26) (21,28) (22,27) (22,23) (22,24) (22,34) (22,26) (22,28) (23,32) (23,26) (23,28) (24,27) (24,32) (24,34) (24,26) (25,33) (26,30) (26,32) (26,34) (27,30) (27,32) (27,28) (28,30) (28,32) (28,34) (29,33) (29,31) (31,33) (32,34)\nQ: Is there a path between node 17 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1412"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,4) (1,23) (1,7) (1,18) (1,24) (1,32) (1,31) (1,21) (1,27) (1,11) (1,6) (1,29) (1,17) (1,20) (2,23) (2,7) (2,18) (2,33) (2,24) (2,31) (2,21) (2,8) (2,27) (2,11) (2,29) (2,17) (2,26) (3,9) (3,22) (3,13) (3,5) (3,30) (3,28) (3,16) (3,14) (3,15) (4,19) (4,10) (5,9) (5,22) (5,13) (5,28) (5,16) (5,14) (6,18) (6,32) (6,25) (6,21) (6,8) (6,11) (6,17) (6,20) (6,26) (7,18) (7,33) (7,24) (7,32) (7,25) (7,31) (7,21) (7,17) (7,20) (7,26) (8,18) (8,33) (8,32) (8,25) (8,31) (8,27) (8,11) (8,29) (8,20) (8,26) (9,22) (9,13) (9,30) (9,28) (9,14) (9,15) (10,19) (10,12) (11,18) (11,33) (11,24) (11,25) (11,31) (11,27) (11,29) (11,26) (12,19) (13,28) (13,15) (14,30) (14,28) (14,16) (14,15) (15,22) (15,30) (15,16) (16,22) (17,23) (17,18) (17,33) (17,25) (17,31) (17,21) (17,27) (17,29) (17,20) (17,26) (18,23) (18,32) (18,25) (18,21) (18,29) (18,20) (18,26) (20,23) (20,33) (20,32) (20,25) (20,31) (20,21) (20,27) (20,29) (20,26) (21,23) (21,33) (21,24) (21,25) (21,29) (23,33) (23,24) (23,25) (23,31) (23,27) (23,29) (23,26) (24,33) (24,32) (24,25) (24,27) (24,29) (24,26) (25,32) (25,31) (25,27) (25,29) (25,26) (26,33) (26,31) (26,27) (27,31) (27,29) (28,30) (31,32) (32,33)\nQ: Is there a path between node 23 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1413"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (1,2) (1,5) (5,6)\nQ: Is there a path between node 1 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1414"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,3) (0,13) (0,15) (0,7) (1,4) (1,6) (2,9) (2,18) (2,13) (3,12) (4,11) (6,8) (6,17) (7,16) (7,12) (7,13) (7,14) (8,11) (8,17) (8,20) (9,18) (9,21) (9,14) (9,15) (10,12) (12,16) (12,15) (13,18) (13,15) (14,16) (14,21) (15,16) (15,18) (16,18)\nQ: Is there a path between node 10 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1415"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,1) (0,14) (0,18) (1,17) (1,14) (1,18) (2,19) (2,7) (2,10) (2,3) (2,12) (2,16) (2,11) (2,5) (2,9) (2,15) (2,6) (2,20) (2,8) (2,4) (2,13) (3,19) (3,7) (3,10) (3,12) (3,16) (3,11) (3,5) (3,9) (3,15) (3,6) (3,20) (3,8) (3,4) (3,13) (4,19) (4,7) (4,10) (4,12) (4,16) (4,11) (4,5) (4,9) (4,15) (4,6) (4,20) (4,8) (4,13) (5,19) (5,7) (5,10) (5,12) (5,16) (5,11) (5,9) (5,15) (5,6) (5,20) (5,8) (5,13) (6,19) (6,7) (6,10) (6,12) (6,16) (6,11) (6,9) (6,15) (6,20) (6,8) (6,13) (7,19) (7,10) (7,12) (7,16) (7,11) (7,9) (7,15) (7,20) (7,8) (7,13) (8,19) (8,10) (8,12) (8,16) (8,11) (8,9) (8,15) (8,20) (8,13) (9,19) (9,10) (9,12) (9,16) (9,11) (9,15) (9,20) (9,13) (10,19) (10,12) (10,16) (10,11) (10,15) (10,20) (10,13) (11,19) (11,12) (11,16) (11,15) (11,20) (11,13) (12,19) (12,16) (12,15) (12,20) (12,13) (13,19) (13,16) (13,15) (13,20) (14,17) (14,18) (15,19) (15,16) (15,20) (16,19) (16,20) (17,18) (19,20)\nQ: Is there a path between node 11 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1416"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,1) (0,13) (0,15) (0,16) (0,9) (0,14) (0,3) (0,12) (0,17) (0,2) (0,18) (1,11) (1,13) (1,15) (1,16) (1,9) (1,8) (1,14) (1,3) (1,4) (1,17) (1,18) (2,11) (2,13) (2,15) (2,9) (2,8) (2,14) (2,3) (2,12) (2,17) (2,18) (3,11) (3,13) (3,15) (3,16) (3,9) (3,8) (3,14) (3,12) (3,17) (3,18) (4,13) (4,15) (4,16) (4,8) (4,14) (4,12) (4,18) (5,6) (5,7) (5,10) (6,7) (6,10) (7,10) (8,11) (8,15) (8,16) (8,18) (9,11) (9,13) (9,15) (9,16) (9,14) (9,12) (9,17) (9,18) (11,13) (11,16) (11,17) (11,18) (12,15) (12,16) (12,17) (12,18) (13,15) (13,18) (14,15) (14,17) (15,16) (16,17) (16,18) (17,18)\nQ: Is there a path between node 9 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1417"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (1,20) (2,11) (2,23) (2,14) (2,8) (3,17) (3,14) (3,16) (4,7) (4,16) (4,8) (4,24) (5,6) (5,10) (5,20) (6,20) (7,12) (7,16) (7,8) (7,24) (8,12) (8,23) (8,21) (9,18) (10,18) (10,20) (11,17) (11,19) (11,24) (12,22) (12,17) (12,14) (13,24) (14,23) (14,24) (15,17) (15,19) (15,24) (16,22) (16,19) (17,19) (17,24) (19,24) (23,24)\nQ: Is there a path between node 6 and node 15?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1418"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,6) (3,4) (4,5) (5,10) (6,8) (8,9)\nQ: Is there a path between node 6 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1419"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,12) (0,11) (0,4) (2,10) (2,8) (2,4) (4,6) (4,11) (5,9) (6,7) (6,10) (6,11) (7,8) (8,10) (8,9) (9,12) (10,11)\nQ: Is there a path between node 5 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1420"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,27) (0,23) (0,4) (0,20) (0,17) (0,6) (1,5) (1,22) (1,11) (1,19) (1,24) (1,2) (1,15) (1,8) (1,30) (1,9) (1,28) (1,18) (2,5) (2,22) (2,24) (2,15) (2,8) (2,30) (2,9) (2,28) (2,18) (3,26) (3,13) (4,21) (4,29) (4,23) (4,20) (4,17) (4,6) (5,22) (5,19) (5,24) (5,14) (5,30) (5,28) (5,18) (6,21) (6,29) (6,27) (6,23) (6,20) (6,17) (7,26) (7,10) (7,13) (7,16) (7,12) (8,11) (8,24) (8,14) (8,30) (8,9) (8,28) (8,18) (9,22) (9,11) (9,19) (9,15) (9,28) (10,16) (10,12) (11,15) (11,30) (11,28) (11,18) (12,13) (12,16) (13,26) (13,16) (13,25) (14,22) (14,19) (14,15) (14,30) (15,19) (15,30) (15,28) (15,18) (16,26) (16,25) (17,29) (17,23) (18,19) (18,24) (18,28) (19,30) (19,28) (20,21) (20,27) (21,29) (21,27) (21,23) (22,24) (22,28) (23,27) (24,30) (24,28) (25,26) (28,30)\nQ: Is there a path between node 16 and node 20?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1421"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (1,2)\nQ: Is there a path between node 0 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1422"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,4) (1,5)\nQ: Is there a path between node 1 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1423"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,16) (0,22) (0,4) (0,15) (0,9) (1,8) (1,17) (1,12) (1,3) (1,5) (1,21) (1,6) (1,13) (1,19) (2,20) (2,16) (2,22) (2,4) (2,9) (3,8) (3,17) (3,14) (3,6) (3,10) (3,19) (4,20) (4,16) (4,22) (4,15) (4,9) (5,8) (5,17) (5,12) (5,14) (5,13) (5,10) (5,19) (6,17) (6,12) (6,14) (6,21) (6,13) (6,10) (6,19) (8,17) (8,12) (8,13) (8,19) (9,20) (9,22) (9,15) (10,17) (10,14) (10,21) (11,18) (11,23) (12,17) (12,21) (12,13) (12,19) (13,17) (13,14) (13,21) (15,20) (16,22) (17,21) (18,23)\nQ: Is there a path between node 22 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1424"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,4) (0,16) (0,21) (0,1) (0,25) (0,14) (0,9) (0,5) (0,6) (0,12) (0,17) (0,24) (0,23) (1,29) (1,4) (1,27) (1,16) (1,21) (1,14) (1,9) (1,6) (1,24) (1,23) (2,26) (2,10) (2,22) (2,15) (2,28) (2,8) (2,30) (2,19) (3,26) (3,10) (3,11) (3,22) (3,15) (3,28) (3,8) (3,30) (3,19) (3,20) (4,29) (4,27) (4,16) (4,21) (4,14) (4,9) (4,5) (4,6) (4,12) (4,24) (5,29) (5,27) (5,21) (5,7) (5,14) (5,12) (5,17) (5,24) (5,23) (6,29) (6,27) (6,7) (6,25) (6,14) (6,9) (6,12) (6,24) (6,23) (7,25) (7,14) (7,9) (7,12) (7,17) (7,23) (8,26) (8,10) (8,11) (8,13) (8,30) (8,19) (9,29) (9,27) (9,16) (9,14) (9,12) (9,24) (9,23) (10,26) (10,13) (10,15) (10,28) (10,19) (10,20) (11,26) (11,13) (11,15) (11,28) (11,30) (11,19) (11,20) (12,29) (12,27) (12,16) (12,21) (12,25) (12,17) (12,24) (12,23) (13,26) (13,28) (13,30) (14,29) (14,16) (14,21) (14,25) (14,17) (14,24) (14,23) (15,26) (15,28) (15,30) (15,20) (16,27) (16,21) (16,17) (16,24) (16,23) (17,29) (17,27) (17,21) (17,25) (17,24) (19,26) (19,22) (19,30) (19,20) (20,26) (20,22) (20,28) (21,29) (21,27) (21,25) (21,24) (21,23) (22,26) (22,28) (22,30) (23,29) (23,27) (23,25) (24,29) (24,27) (24,25) (25,29) (26,28) (28,30)\nQ: Is there a path between node 11 and node 17?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1425"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (1,27) (1,24) (1,21) (1,3) (2,10) (2,22) (2,6) (2,18) (2,25) (2,12) (3,19) (3,27) (3,24) (4,10) (4,6) (4,18) (4,25) (5,28) (5,16) (6,10) (6,13) (6,25) (6,12) (6,9) (7,28) (8,10) (8,14) (8,18) (8,29) (8,25) (8,23) (9,13) (9,14) (10,29) (10,25) (12,22) (12,18) (12,17) (13,29) (13,26) (14,20) (14,17) (15,19) (17,25) (18,20) (18,25) (20,29) (20,26) (20,23) (21,27) (21,24) (23,26) (23,25) (24,27) (26,29)\nQ: Is there a path between node 18 and node 17?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1426"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,5) (0,11) (0,8) (0,6) (0,1) (1,10) (1,3) (1,5) (1,9) (1,6) (1,2) (2,10) (2,3) (2,5) (2,9) (2,8) (2,7) (2,6) (2,13) (3,9) (3,11) (3,8) (3,7) (4,12) (5,10) (5,9) (5,8) (5,7) (5,6) (6,10) (6,9) (6,11) (6,8) (7,10) (7,11) (7,8) (7,13) (8,10) (8,11) (8,13) (9,10) (9,11) (9,13) (10,11) (10,13)\nQ: Is there a path between node 6 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1427"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,2) (0,4) (0,5) (0,15) (0,7) (1,9) (1,13) (1,12) (1,3) (2,14) (2,10) (2,4) (2,8) (2,15) (2,7) (3,9) (3,13) (3,12) (3,11) (4,14) (4,6) (4,10) (4,8) (4,15) (5,6) (5,8) (5,7) (6,14) (6,8) (6,15) (7,14) (7,10) (7,8) (7,15) (8,14) (8,10) (8,15) (9,13) (9,12) (9,11) (10,14) (10,15) (11,13) (11,12) (12,13) (14,15)\nQ: Is there a path between node 1 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1428"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,3) (0,14) (1,8) (1,6) (1,14) (2,6) (2,12) (2,18) (3,8) (3,6) (3,12) (3,18) (4,12) (4,9) (4,14) (5,15) (5,16) (5,7) (6,8) (6,12) (6,14) (7,10) (9,11) (9,18) (15,17) (15,16)\nQ: Is there a path between node 5 and node 16?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1429"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,4) (0,12) (0,11) (0,10) (0,3) (0,17) (0,21) (0,27) (0,15) (0,23) (0,31) (0,29) (0,2) (0,8) (0,9) (0,14) (0,18) (1,5) (1,26) (1,13) (1,20) (1,32) (1,7) (2,19) (2,4) (2,28) (2,22) (2,16) (2,12) (2,10) (2,3) (2,17) (2,21) (2,27) (2,15) (2,23) (2,31) (2,29) (2,8) (2,9) (2,14) (2,18) (3,4) (3,22) (3,16) (3,12) (3,10) (3,17) (3,21) (3,27) (3,23) (3,31) (3,29) (3,6) (3,9) (3,14) (3,18) (4,16) (4,12) (4,11) (4,17) (4,21) (4,15) (4,30) (4,23) (4,29) (4,6) (4,8) (4,9) (4,18) (5,26) (5,13) (5,25) (5,24) (5,32) (5,7) (6,19) (6,22) (6,12) (6,11) (6,10) (6,17) (6,21) (6,27) (6,15) (6,30) (6,23) (6,31) (6,29) (6,9) (6,14) (7,26) (7,25) (7,32) (8,19) (8,28) (8,10) (8,17) (8,27) (8,15) (8,30) (8,23) (9,19) (9,28) (9,22) (9,16) (9,12) (9,10) (9,17) (9,21) (9,15) (9,30) (9,23) (9,29) (9,18) (10,19) (10,28) (10,22) (10,12) (10,11) (10,17) (10,21) (10,27) (10,15) (10,30) (10,23) (10,31) (10,29) (10,14) (10,18) (11,16) (11,12) (11,17) (11,21) (11,27) (11,15) (11,30) (11,31) (11,29) (11,14) (11,18) (12,19) (12,28) (12,22) (12,17) (12,27) (12,15) (12,30) (12,23) (12,31) (12,29) (12,14) (12,18) (13,26) (13,25) (13,20) (13,32) (14,28) (14,16) (14,17) (14,21) (14,27) (14,15) (14,31) (14,29) (14,18) (15,19) (15,22) (15,16) (15,17) (15,21) (15,27) (15,30) (15,23) (15,31) (15,29) (15,18) (16,19) (16,28) (16,22) (16,17) (16,21) (16,27) (16,30) (16,31) (16,18) (17,22) (17,21) (17,30) (17,31) (17,29) (17,18) (18,19) (18,28) (18,22) (18,21) (18,27) (18,29) (19,28) (19,22) (19,21) (19,30) (19,31) (19,29) (20,32) (21,28) (21,22) (21,27) (21,29) (22,28) (22,30) (22,23) (22,31) (22,29) (23,28) (23,27) (23,30) (23,31) (23,29) (24,26) (24,25) (25,26) (25,32) (26,32) (27,28) (27,30) (27,29) (28,30) (28,31) (28,29) (29,30) (29,31)\nQ: Is there a path between node 10 and node 21?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1430"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,6) (0,11) (0,19) (0,20) (0,1) (0,15) (0,12) (0,7) (0,22) (0,5) (0,21) (0,3) (0,4) (0,18) (0,17) (1,14) (1,6) (1,11) (1,19) (1,20) (1,15) (1,12) (1,7) (1,22) (1,5) (1,21) (1,3) (1,4) (1,18) (1,17) (2,13) (2,10) (2,8) (2,16) (2,9) (3,14) (3,6) (3,11) (3,19) (3,20) (3,15) (3,12) (3,7) (3,22) (3,5) (3,21) (3,4) (3,18) (3,17) (4,14) (4,6) (4,11) (4,19) (4,20) (4,15) (4,12) (4,7) (4,22) (4,5) (4,21) (4,18) (4,17) (5,14) (5,6) (5,11) (5,19) (5,20) (5,15) (5,12) (5,7) (5,22) (5,21) (5,18) (5,17) (6,14) (6,11) (6,19) (6,20) (6,15) (6,12) (6,7) (6,22) (6,21) (6,18) (6,17) (7,14) (7,11) (7,19) (7,20) (7,15) (7,12) (7,22) (7,21) (7,18) (7,17) (8,13) (8,10) (8,16) (8,9) (9,13) (9,10) (9,16) (10,13) (10,16) (11,14) (11,19) (11,20) (11,15) (11,12) (11,22) (11,21) (11,18) (11,17) (12,14) (12,19) (12,20) (12,15) (12,22) (12,21) (12,18) (12,17) (13,16) (14,19) (14,20) (14,15) (14,22) (14,21) (14,18) (14,17) (15,19) (15,20) (15,22) (15,21) (15,18) (15,17) (17,19) (17,20) (17,22) (17,21) (17,18) (18,19) (18,20) (18,22) (18,21) (19,20) (19,22) (19,21) (20,22) (20,21) (21,22)\nQ: Is there a path between node 0 and node 21?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1431"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,4) (0,9) (0,12) (0,11) (0,5) (1,6) (1,17) (1,8) (1,15) (1,3) (1,2) (1,18) (1,19) (1,13) (1,14) (1,10) (2,6) (2,17) (2,8) (2,15) (2,3) (2,18) (2,19) (2,13) (2,14) (2,10) (3,6) (3,17) (3,8) (3,15) (3,18) (3,19) (3,13) (3,14) (3,10) (4,7) (4,9) (4,12) (4,11) (4,5) (5,7) (5,9) (5,12) (5,11) (6,17) (6,8) (6,15) (6,18) (6,19) (6,13) (6,14) (6,10) (7,9) (7,12) (7,11) (8,17) (8,15) (8,18) (8,19) (8,13) (8,14) (8,10) (9,12) (9,11) (10,17) (10,15) (10,18) (10,19) (10,13) (10,14) (11,12) (13,17) (13,15) (13,18) (13,19) (13,14) (14,17) (14,15) (14,18) (14,19) (15,17) (15,18) (15,19) (17,18) (17,19) (18,19)\nQ: Is there a path between node 12 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1432"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,2) (1,5) (1,2) (2,5) (2,10) (3,10) (3,4) (3,8) (4,5) (5,10) (5,8) (7,11) (8,10) (9,11)\nQ: Is there a path between node 10 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1433"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,15) (0,22) (0,18) (1,5) (1,14) (1,21) (1,16) (1,19) (1,3) (1,17) (1,13) (1,11) (1,2) (1,20) (1,8) (1,6) (1,12) (1,9) (1,7) (2,5) (2,14) (2,21) (2,16) (2,19) (2,3) (2,17) (2,13) (2,11) (2,20) (2,8) (2,6) (2,12) (2,9) (2,7) (3,5) (3,14) (3,21) (3,16) (3,19) (3,17) (3,13) (3,11) (3,20) (3,8) (3,6) (3,12) (3,9) (3,7) (5,14) (5,21) (5,16) (5,19) (5,17) (5,13) (5,11) (5,20) (5,8) (5,6) (5,12) (5,9) (5,7) (6,14) (6,21) (6,16) (6,19) (6,17) (6,13) (6,11) (6,20) (6,8) (6,12) (6,9) (6,7) (7,14) (7,21) (7,16) (7,19) (7,17) (7,13) (7,11) (7,20) (7,8) (7,12) (7,9) (8,14) (8,21) (8,16) (8,19) (8,17) (8,13) (8,11) (8,20) (8,12) (8,9) (9,14) (9,21) (9,16) (9,19) (9,17) (9,13) (9,11) (9,20) (9,12) (10,15) (10,22) (10,18) (11,14) (11,21) (11,16) (11,19) (11,17) (11,13) (11,20) (11,12) (12,14) (12,21) (12,16) (12,19) (12,17) (12,13) (12,20) (13,14) (13,21) (13,16) (13,19) (13,17) (13,20) (14,21) (14,16) (14,19) (14,17) (14,20) (15,22) (15,18) (16,21) (16,19) (16,17) (16,20) (17,21) (17,19) (17,20) (18,22) (19,21) (19,20) (20,21)\nQ: Is there a path between node 22 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1434"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,31) (1,4) (1,27) (1,25) (2,31) (2,24) (2,13) (2,10) (3,30) (3,32) (3,27) (3,15) (4,30) (4,6) (4,28) (4,8) (5,22) (6,27) (7,20) (7,11) (7,12) (8,15) (9,14) (10,17) (10,23) (10,13) (11,14) (12,18) (13,23) (14,22) (15,30) (15,27) (15,25) (15,16) (15,28) (17,23) (17,21) (18,22) (18,33) (20,22) (21,31) (23,24) (25,30) (25,27) (25,28) (26,31) (27,30) (27,32) (28,32)\nQ: Is there a path between node 18 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1435"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,1) (1,11) (1,5) (1,8) (2,14) (2,10) (2,6) (2,3) (2,13) (2,4) (3,7) (3,14) (3,6) (3,12) (3,13) (3,4) (4,9) (4,7) (4,10) (4,12) (4,13) (5,11) (5,8) (6,7) (6,10) (6,12) (6,13) (7,9) (7,14) (7,10) (7,13) (8,11) (10,14) (10,12) (10,13) (12,14) (12,13) (13,14)\nQ: Is there a path between node 0 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1436"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (1,8) (1,4) (1,5) (1,7) (1,2) (1,9) (1,6) (2,8) (2,4) (2,5) (2,7) (2,9) (2,6) (4,8) (4,5) (4,7) (4,9) (4,6) (5,8) (5,7) (5,9) (5,6) (6,8) (6,7) (6,9) (7,8) (7,9) (8,9)\nQ: Is there a path between node 0 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1437"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,10) (0,17) (0,15) (0,4) (0,12) (0,24) (0,9) (0,3) (0,13) (0,23) (0,7) (0,19) (0,16) (0,6) (0,25) (0,8) (1,10) (1,17) (1,4) (1,12) (1,24) (1,3) (1,13) (1,23) (1,26) (1,22) (1,19) (1,6) (1,14) (1,25) (1,8) (1,20) (2,10) (2,17) (2,11) (2,4) (2,24) (2,9) (2,3) (2,13) (2,23) (2,26) (2,7) (2,22) (2,19) (2,6) (2,14) (2,25) (2,8) (3,10) (3,17) (3,11) (3,15) (3,4) (3,12) (3,24) (3,9) (3,13) (3,26) (3,7) (3,19) (3,16) (3,14) (3,25) (3,8) (3,20) (4,10) (4,17) (4,11) (4,15) (4,12) (4,24) (4,9) (4,7) (4,19) (4,16) (4,6) (4,25) (4,20) (5,18) (6,10) (6,17) (6,15) (6,12) (6,24) (6,9) (6,23) (6,7) (6,16) (6,25) (6,8) (7,10) (7,11) (7,15) (7,12) (7,13) (7,22) (7,19) (7,16) (7,25) (7,8) (7,20) (8,10) (8,17) (8,11) (8,15) (8,12) (8,24) (8,9) (8,23) (8,22) (8,19) (8,16) (8,14) (8,25) (8,20) (9,10) (9,17) (9,11) (9,12) (9,24) (9,13) (9,23) (9,26) (9,22) (9,19) (9,16) (9,20) (10,17) (10,11) (10,15) (10,12) (10,24) (10,13) (10,23) (10,26) (10,19) (10,14) (10,20) (11,15) (11,12) (11,24) (11,13) (11,23) (11,26) (11,19) (11,16) (11,14) (11,20) (12,15) (12,24) (12,23) (12,22) (12,19) (12,16) (12,14) (12,25) (12,20) (13,15) (13,24) (13,23) (13,19) (13,16) (13,14) (13,25) (13,20) (14,17) (14,15) (14,24) (14,23) (14,26) (14,22) (14,19) (14,16) (14,25) (14,20) (15,17) (15,24) (15,23) (15,26) (15,16) (15,20) (16,24) (16,23) (16,26) (16,19) (16,25) (16,20) (17,23) (17,20) (18,21) (19,23) (19,22) (19,25) (19,20) (20,24) (20,23) (20,22) (20,25) (22,26) (22,25) (23,24) (23,26) (23,25) (24,26) (24,25) (25,26)\nQ: Is there a path between node 8 and node 19?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1438"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,8) (0,10) (0,4) (0,16) (0,5) (0,2) (0,7) (0,9) (0,15) (0,13) (0,1) (0,12) (0,14) (0,3) (1,11) (1,8) (1,10) (1,4) (1,16) (1,5) (1,2) (1,7) (1,9) (1,15) (1,13) (1,12) (1,14) (1,3) (2,11) (2,8) (2,10) (2,4) (2,16) (2,5) (2,7) (2,9) (2,15) (2,13) (2,12) (2,14) (2,3) (3,11) (3,8) (3,10) (3,4) (3,16) (3,5) (3,7) (3,9) (3,15) (3,13) (3,12) (3,14) (4,11) (4,8) (4,10) (4,16) (4,5) (4,7) (4,9) (4,15) (4,13) (4,12) (4,14) (5,11) (5,8) (5,10) (5,16) (5,7) (5,9) (5,15) (5,13) (5,12) (5,14) (7,11) (7,8) (7,10) (7,16) (7,9) (7,15) (7,13) (7,12) (7,14) (8,11) (8,10) (8,16) (8,9) (8,15) (8,13) (8,12) (8,14) (9,11) (9,10) (9,16) (9,15) (9,13) (9,12) (9,14) (10,11) (10,16) (10,15) (10,13) (10,12) (10,14) (11,16) (11,15) (11,13) (11,12) (11,14) (12,16) (12,15) (12,13) (12,14) (13,16) (13,15) (13,14) (14,16) (14,15) (15,16)\nQ: Is there a path between node 6 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1439"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,3) (0,7) (0,10) (0,13) (0,12) (0,16) (1,14) (1,2) (1,5) (1,9) (1,8) (1,15) (1,4) (1,6) (2,14) (2,5) (2,9) (2,8) (2,15) (2,4) (2,6) (3,11) (3,7) (3,10) (3,13) (3,12) (3,16) (4,14) (4,5) (4,9) (4,8) (4,15) (4,6) (5,14) (5,9) (5,8) (5,15) (5,6) (6,14) (6,9) (6,8) (6,15) (7,11) (7,10) (7,13) (7,12) (7,16) (8,14) (8,9) (8,15) (9,14) (9,15) (10,11) (10,13) (10,12) (10,16) (11,13) (11,12) (11,16) (12,13) (12,16) (13,16) (14,15)\nQ: Is there a path between node 3 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1440"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,16) (0,9) (0,3) (0,4) (0,8) (0,17) (1,6) (1,12) (1,13) (1,18) (1,2) (1,4) (1,8) (1,17) (2,6) (2,12) (2,15) (2,9) (2,13) (2,18) (2,4) (2,8) (2,17) (3,6) (3,16) (3,12) (3,9) (3,13) (3,18) (3,8) (3,17) (3,5) (4,6) (4,16) (4,12) (4,9) (4,18) (4,17) (4,5) (5,6) (5,12) (5,15) (5,9) (5,17) (6,12) (6,15) (6,9) (6,13) (6,18) (6,8) (7,10) (7,11) (7,19) (8,16) (8,15) (8,9) (8,18) (9,16) (9,12) (9,15) (9,13) (9,18) (9,17) (10,19) (11,14) (11,19) (12,16) (12,15) (12,13) (12,17) (13,18) (14,19) (15,17) (16,17) (17,18)\nQ: Is there a path between node 1 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1441"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,6) (3,4) (4,5) (5,10) (6,8) (8,9)\nQ: Is there a path between node 1 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1442"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (0,3) (0,4) (0,1) (1,2) (1,5) (1,6) (1,3) (1,4) (2,5) (2,6) (2,3) (2,4) (3,5) (3,6) (3,4) (4,5) (4,6) (5,6)\nQ: Is there a path between node 6 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1443"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,6) (0,1) (0,5) (1,7) (1,6) (1,8) (1,5) (2,7) (2,8) (2,5) (3,4) (5,7) (5,6) (5,8)\nQ: Is there a path between node 4 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1444"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,6) (2,7) (2,6) (2,4) (5,7) (6,8)\nQ: Is there a path between node 4 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1445"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,19) (0,17) (0,3) (0,10) (0,14) (1,7) (1,8) (1,15) (1,13) (2,9) (2,12) (2,18) (2,4) (3,6) (3,19) (3,17) (3,16) (3,10) (3,14) (4,12) (4,18) (5,9) (5,18) (6,19) (6,17) (6,16) (6,14) (6,20) (7,8) (7,15) (7,13) (9,12) (9,18) (10,16) (10,14) (10,20) (11,15) (12,18) (13,15) (14,19) (14,17) (14,20) (16,19) (16,17) (17,20) (19,20)\nQ: Is there a path between node 10 and node 16?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1446"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,30) (0,27) (0,33) (0,11) (0,5) (0,12) (0,20) (0,7) (0,28) (0,17) (0,6) (0,4) (0,32) (0,13) (0,3) (0,22) (0,31) (1,25) (1,29) (1,30) (1,27) (1,33) (1,2) (1,5) (1,12) (1,20) (1,28) (1,18) (1,16) (1,24) (1,6) (1,13) (1,3) (1,22) (1,31) (2,25) (2,23) (2,29) (2,30) (2,27) (2,33) (2,11) (2,5) (2,12) (2,7) (2,18) (2,16) (2,17) (2,24) (2,13) (2,22) (2,15) (3,25) (3,23) (3,29) (3,30) (3,12) (3,7) (3,18) (3,16) (3,24) (3,4) (3,13) (3,22) (3,31) (4,23) (4,29) (4,27) (4,33) (4,11) (4,5) (4,7) (4,18) (4,24) (4,32) (4,15) (4,31) (5,25) (5,23) (5,30) (5,27) (5,33) (5,11) (5,12) (5,20) (5,7) (5,28) (5,24) (5,6) (5,32) (5,13) (5,22) (5,15) (5,31) (6,25) (6,23) (6,30) (6,27) (6,33) (6,12) (6,20) (6,7) (6,18) (6,24) (6,32) (6,13) (7,25) (7,30) (7,27) (7,33) (7,20) (7,28) (7,18) (7,24) (7,32) (7,13) (7,22) (7,15) (7,31) (8,14) (8,26) (8,19) (9,14) (9,26) (9,19) (9,21) (9,10) (10,14) (10,26) (10,19) (11,23) (11,29) (11,30) (11,27) (11,33) (11,20) (11,18) (11,16) (11,17) (11,32) (11,13) (11,22) (11,15) (11,31) (12,25) (12,23) (12,29) (12,27) (12,33) (12,28) (12,16) (12,24) (12,13) (12,22) (12,15) (12,31) (13,25) (13,23) (13,29) (13,27) (13,33) (13,20) (13,28) (13,18) (13,16) (13,17) (13,24) (13,32) (13,15) (13,31) (14,26) (15,25) (15,23) (15,29) (15,30) (15,33) (15,16) (15,17) (15,24) (15,22) (15,31) (16,25) (16,23) (16,29) (16,30) (16,27) (16,28) (16,17) (16,24) (16,32) (16,22) (17,25) (17,23) (17,29) (17,33) (17,20) (17,18) (17,24) (17,31) (18,25) (18,29) (18,30) (18,33) (18,28) (18,24) (18,31) (20,25) (20,23) (20,30) (20,24) (20,32) (20,22) (20,31) (21,26) (22,25) (22,29) (22,30) (22,28) (22,24) (23,25) (23,29) (23,27) (23,28) (23,24) (23,32) (24,25) (24,29) (24,27) (24,33) (24,28) (24,31) (25,29) (25,30) (25,27) (25,28) (25,32) (25,31) (27,29) (27,30) (27,33) (27,28) (28,29) (28,30) (28,33) (28,32) (28,31) (29,30) (29,33) (29,32) (29,31) (30,33) (30,32) (30,31) (31,33) (31,32) (32,33)\nQ: Is there a path between node 19 and node 20?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1447"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (1,11) (1,9) (1,14) (2,5) (2,6) (3,11) (3,13) (4,11) (4,13) (4,15) (5,7) (5,6) (7,10) (8,11) (8,9) (9,14) (9,12) (11,13) (13,14) (13,15)\nQ: Is there a path between node 4 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1448"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,15) (0,22) (0,18) (1,5) (1,14) (1,21) (1,16) (1,19) (1,3) (1,17) (1,13) (1,11) (1,2) (1,20) (1,8) (1,6) (1,12) (1,9) (1,7) (2,5) (2,14) (2,21) (2,16) (2,19) (2,3) (2,17) (2,13) (2,11) (2,20) (2,8) (2,6) (2,12) (2,9) (2,7) (3,5) (3,14) (3,21) (3,16) (3,19) (3,17) (3,13) (3,11) (3,20) (3,8) (3,6) (3,12) (3,9) (3,7) (5,14) (5,21) (5,16) (5,19) (5,17) (5,13) (5,11) (5,20) (5,8) (5,6) (5,12) (5,9) (5,7) (6,14) (6,21) (6,16) (6,19) (6,17) (6,13) (6,11) (6,20) (6,8) (6,12) (6,9) (6,7) (7,14) (7,21) (7,16) (7,19) (7,17) (7,13) (7,11) (7,20) (7,8) (7,12) (7,9) (8,14) (8,21) (8,16) (8,19) (8,17) (8,13) (8,11) (8,20) (8,12) (8,9) (9,14) (9,21) (9,16) (9,19) (9,17) (9,13) (9,11) (9,20) (9,12) (10,15) (10,22) (10,18) (11,14) (11,21) (11,16) (11,19) (11,17) (11,13) (11,20) (11,12) (12,14) (12,21) (12,16) (12,19) (12,17) (12,13) (12,20) (13,14) (13,21) (13,16) (13,19) (13,17) (13,20) (14,21) (14,16) (14,19) (14,17) (14,20) (15,22) (15,18) (16,21) (16,19) (16,17) (16,20) (17,21) (17,19) (17,20) (18,22) (19,21) (19,20) (20,21)\nQ: Is there a path between node 8 and node 17?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1449"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,3) (0,11) (0,18) (0,7) (0,8) (0,9) (0,1) (0,10) (0,15) (0,17) (0,13) (0,16) (0,19) (0,2) (0,6) (0,5) (0,14) (1,12) (1,3) (1,11) (1,18) (1,7) (1,8) (1,9) (1,10) (1,15) (1,17) (1,13) (1,16) (1,19) (1,2) (1,6) (1,5) (1,14) (2,12) (2,3) (2,11) (2,18) (2,7) (2,8) (2,9) (2,10) (2,15) (2,17) (2,13) (2,16) (2,19) (2,6) (2,5) (2,14) (3,12) (3,11) (3,18) (3,7) (3,8) (3,9) (3,10) (3,15) (3,17) (3,13) (3,16) (3,19) (3,6) (3,5) (3,14) (4,20) (4,21) (5,12) (5,11) (5,18) (5,7) (5,8) (5,9) (5,10) (5,15) (5,17) (5,13) (5,16) (5,19) (5,6) (5,14) (6,12) (6,11) (6,18) (6,7) (6,8) (6,9) (6,10) (6,15) (6,17) (6,13) (6,16) (6,19) (6,14) (7,12) (7,11) (7,18) (7,8) (7,9) (7,10) (7,15) (7,17) (7,13) (7,16) (7,19) (7,14) (8,12) (8,11) (8,18) (8,9) (8,10) (8,15) (8,17) (8,13) (8,16) (8,19) (8,14) (9,12) (9,11) (9,18) (9,10) (9,15) (9,17) (9,13) (9,16) (9,19) (9,14) (10,12) (10,11) (10,18) (10,15) (10,17) (10,13) (10,16) (10,19) (10,14) (11,12) (11,18) (11,15) (11,17) (11,13) (11,16) (11,19) (11,14) (12,18) (12,15) (12,17) (12,13) (12,16) (12,19) (12,14) (13,18) (13,15) (13,17) (13,16) (13,19) (13,14) (14,18) (14,15) (14,17) (14,16) (14,19) (15,18) (15,17) (15,16) (15,19) (16,18) (16,17) (16,19) (17,18) (17,19) (18,19) (20,21)\nQ: Is there a path between node 5 and node 17?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1450"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,6) (3,4) (4,5) (5,10) (6,8) (8,9)\nQ: Is there a path between node 4 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1451"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,10) (0,12) (0,20) (0,14) (0,8) (0,3) (0,6) (0,5) (0,15) (0,19) (0,7) (0,9) (0,22) (0,2) (0,21) (0,18) (1,4) (1,10) (1,12) (1,20) (1,8) (1,5) (1,15) (1,16) (1,19) (1,7) (1,9) (1,22) (1,2) (1,18) (2,4) (2,10) (2,12) (2,14) (2,3) (2,5) (2,15) (2,19) (2,7) (2,22) (2,21) (2,18) (3,4) (3,12) (3,20) (3,14) (3,6) (3,5) (3,15) (3,16) (3,19) (3,7) (3,9) (3,22) (3,21) (3,18) (4,10) (4,12) (4,8) (4,6) (4,5) (4,15) (4,16) (4,19) (4,7) (4,9) (4,21) (4,18) (5,12) (5,14) (5,8) (5,6) (5,15) (5,16) (5,19) (5,7) (5,9) (5,22) (5,18) (6,10) (6,12) (6,20) (6,14) (6,16) (6,19) (6,7) (6,9) (6,22) (6,21) (6,18) (7,10) (7,12) (7,14) (7,8) (7,16) (7,9) (7,22) (7,21) (7,18) (8,10) (8,12) (8,14) (8,15) (8,16) (8,19) (8,9) (8,21) (9,12) (9,20) (9,15) (9,16) (9,22) (9,21) (9,18) (10,12) (10,20) (10,14) (10,15) (10,16) (10,18) (12,16) (12,19) (13,17) (14,20) (14,16) (15,16) (15,22) (15,21) (16,20) (16,21) (16,18) (18,22) (18,21) (19,20) (19,22) (19,21) (21,22)\nQ: Is there a path between node 5 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1452"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,15) (0,22) (0,18) (1,5) (1,14) (1,21) (1,16) (1,19) (1,3) (1,17) (1,13) (1,11) (1,2) (1,20) (1,8) (1,6) (1,12) (1,9) (1,7) (2,5) (2,14) (2,21) (2,16) (2,19) (2,3) (2,17) (2,13) (2,11) (2,20) (2,8) (2,6) (2,12) (2,9) (2,7) (3,5) (3,14) (3,21) (3,16) (3,19) (3,17) (3,13) (3,11) (3,20) (3,8) (3,6) (3,12) (3,9) (3,7) (5,14) (5,21) (5,16) (5,19) (5,17) (5,13) (5,11) (5,20) (5,8) (5,6) (5,12) (5,9) (5,7) (6,14) (6,21) (6,16) (6,19) (6,17) (6,13) (6,11) (6,20) (6,8) (6,12) (6,9) (6,7) (7,14) (7,21) (7,16) (7,19) (7,17) (7,13) (7,11) (7,20) (7,8) (7,12) (7,9) (8,14) (8,21) (8,16) (8,19) (8,17) (8,13) (8,11) (8,20) (8,12) (8,9) (9,14) (9,21) (9,16) (9,19) (9,17) (9,13) (9,11) (9,20) (9,12) (10,15) (10,22) (10,18) (11,14) (11,21) (11,16) (11,19) (11,17) (11,13) (11,20) (11,12) (12,14) (12,21) (12,16) (12,19) (12,17) (12,13) (12,20) (13,14) (13,21) (13,16) (13,19) (13,17) (13,20) (14,21) (14,16) (14,19) (14,17) (14,20) (15,22) (15,18) (16,21) (16,19) (16,17) (16,20) (17,21) (17,19) (17,20) (18,22) (19,21) (19,20) (20,21)\nQ: Is there a path between node 6 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1453"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,14) (0,12) (1,20) (1,12) (2,13) (2,18) (3,17) (4,20) (7,21) (8,18) (9,20) (9,15) (10,13) (10,19) (13,18) (14,16) (14,15) (15,20)\nQ: Is there a path between node 15 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1454"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,21) (0,11) (0,15) (0,4) (0,22) (0,5) (0,3) (0,6) (0,20) (0,13) (0,18) (0,9) (0,1) (0,12) (0,24) (0,16) (0,8) (0,23) (0,2) (1,21) (1,11) (1,15) (1,4) (1,22) (1,5) (1,3) (1,6) (1,20) (1,13) (1,18) (1,9) (1,12) (1,24) (1,16) (1,8) (1,23) (1,2) (2,21) (2,11) (2,15) (2,4) (2,22) (2,5) (2,3) (2,6) (2,20) (2,13) (2,18) (2,9) (2,12) (2,24) (2,16) (2,8) (2,23) (3,21) (3,11) (3,15) (3,4) (3,22) (3,5) (3,6) (3,20) (3,13) (3,18) (3,9) (3,12) (3,24) (3,16) (3,8) (3,23) (4,21) (4,11) (4,15) (4,22) (4,5) (4,6) (4,20) (4,13) (4,18) (4,9) (4,12) (4,24) (4,16) (4,8) (4,23) (5,21) (5,11) (5,15) (5,22) (5,6) (5,20) (5,13) (5,18) (5,9) (5,12) (5,24) (5,16) (5,8) (5,23) (6,21) (6,11) (6,15) (6,22) (6,20) (6,13) (6,18) (6,9) (6,12) (6,24) (6,16) (6,8) (6,23) (7,10) (7,14) (7,17) (7,19) (8,21) (8,11) (8,15) (8,22) (8,20) (8,13) (8,18) (8,9) (8,12) (8,24) (8,16) (8,23) (9,21) (9,11) (9,15) (9,22) (9,20) (9,13) (9,18) (9,12) (9,24) (9,16) (9,23) (10,14) (10,17) (10,19) (11,21) (11,15) (11,22) (11,20) (11,13) (11,18) (11,12) (11,24) (11,16) (11,23) (12,21) (12,15) (12,22) (12,20) (12,13) (12,18) (12,24) (12,16) (12,23) (13,21) (13,15) (13,22) (13,20) (13,18) (13,24) (13,16) (13,23) (14,17) (14,19) (15,21) (15,22) (15,20) (15,18) (15,24) (15,16) (15,23) (16,21) (16,22) (16,20) (16,18) (16,24) (16,23) (17,19) (18,21) (18,22) (18,20) (18,24) (18,23) (20,21) (20,22) (20,24) (20,23) (21,22) (21,24) (21,23) (22,24) (22,23) (23,24)\nQ: Is there a path between node 11 and node 22?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1455"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,13) (0,8) (0,18) (0,25) (0,14) (0,17) (0,21) (1,13) (1,26) (1,14) (1,20) (1,17) (1,24) (1,6) (2,8) (2,18) (2,9) (2,26) (2,14) (2,10) (2,15) (3,16) (3,12) (4,13) (4,8) (4,18) (4,25) (4,6) (5,19) (5,13) (5,10) (5,20) (5,22) (5,17) (5,6) (6,8) (6,18) (6,9) (6,26) (6,14) (6,17) (6,21) (6,15) (6,23) (7,25) (7,14) (7,22) (7,24) (7,15) (7,23) (8,13) (8,25) (8,24) (8,23) (9,25) (9,27) (9,26) (9,14) (9,17) (9,24) (9,23) (10,19) (10,13) (10,25) (10,22) (11,12) (12,16) (13,19) (13,18) (13,21) (14,19) (14,18) (14,22) (15,19) (15,25) (15,23) (17,25) (17,22) (17,21) (17,24) (18,21) (18,24) (19,26) (19,22) (19,24) (19,23) (20,25) (20,26) (20,24) (20,23) (21,27) (21,23) (22,25) (22,26) (22,23) (25,27) (25,26)\nQ: Is there a path between node 12 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1456"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,2) (3,5)\nQ: Is there a path between node 1 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1457"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,3) (0,11) (0,18) (0,7) (0,8) (0,9) (0,1) (0,10) (0,15) (0,17) (0,13) (0,16) (0,19) (0,2) (0,6) (0,5) (0,14) (1,12) (1,3) (1,11) (1,18) (1,7) (1,8) (1,9) (1,10) (1,15) (1,17) (1,13) (1,16) (1,19) (1,2) (1,6) (1,5) (1,14) (2,12) (2,3) (2,11) (2,18) (2,7) (2,8) (2,9) (2,10) (2,15) (2,17) (2,13) (2,16) (2,19) (2,6) (2,5) (2,14) (3,12) (3,11) (3,18) (3,7) (3,8) (3,9) (3,10) (3,15) (3,17) (3,13) (3,16) (3,19) (3,6) (3,5) (3,14) (4,20) (4,21) (5,12) (5,11) (5,18) (5,7) (5,8) (5,9) (5,10) (5,15) (5,17) (5,13) (5,16) (5,19) (5,6) (5,14) (6,12) (6,11) (6,18) (6,7) (6,8) (6,9) (6,10) (6,15) (6,17) (6,13) (6,16) (6,19) (6,14) (7,12) (7,11) (7,18) (7,8) (7,9) (7,10) (7,15) (7,17) (7,13) (7,16) (7,19) (7,14) (8,12) (8,11) (8,18) (8,9) (8,10) (8,15) (8,17) (8,13) (8,16) (8,19) (8,14) (9,12) (9,11) (9,18) (9,10) (9,15) (9,17) (9,13) (9,16) (9,19) (9,14) (10,12) (10,11) (10,18) (10,15) (10,17) (10,13) (10,16) (10,19) (10,14) (11,12) (11,18) (11,15) (11,17) (11,13) (11,16) (11,19) (11,14) (12,18) (12,15) (12,17) (12,13) (12,16) (12,19) (12,14) (13,18) (13,15) (13,17) (13,16) (13,19) (13,14) (14,18) (14,15) (14,17) (14,16) (14,19) (15,18) (15,17) (15,16) (15,19) (16,18) (16,17) (16,19) (17,18) (17,19) (18,19) (20,21)\nQ: Is there a path between node 5 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1458"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,9) (0,8) (0,19) (0,13) (0,11) (1,15) (1,6) (1,3) (1,12) (1,4) (1,2) (1,23) (1,5) (1,16) (1,22) (1,17) (1,18) (1,21) (1,24) (1,25) (2,15) (2,3) (2,4) (2,20) (2,23) (2,22) (2,27) (2,18) (2,21) (2,24) (3,15) (3,4) (3,26) (3,20) (3,23) (3,5) (3,16) (3,14) (3,22) (3,27) (3,18) (3,21) (3,24) (3,25) (4,15) (4,6) (4,12) (4,26) (4,20) (4,5) (4,22) (4,27) (4,17) (4,21) (4,25) (5,15) (5,6) (5,12) (5,20) (5,16) (5,14) (5,22) (5,27) (5,18) (5,21) (5,25) (6,15) (6,12) (6,27) (6,17) (6,21) (6,24) (6,25) (7,19) (7,13) (8,9) (8,19) (8,13) (9,19) (9,10) (10,19) (10,13) (10,11) (11,13) (12,15) (12,26) (12,20) (12,14) (12,22) (12,21) (12,24) (13,19) (14,15) (14,26) (14,20) (14,16) (14,22) (14,17) (14,21) (14,24) (14,25) (15,26) (15,20) (15,23) (15,16) (15,22) (15,17) (15,18) (15,24) (16,26) (16,27) (16,18) (16,25) (17,26) (17,23) (17,18) (17,21) (17,24) (17,25) (18,26) (18,20) (18,22) (18,27) (18,24) (18,25) (20,26) (20,23) (20,22) (20,27) (20,24) (20,25) (21,22) (21,27) (21,24) (21,25) (22,23) (22,27) (22,24) (22,25) (23,27) (23,25) (24,26) (24,27) (25,26) (25,27) (26,27)\nQ: Is there a path between node 21 and node 22?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1459"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,15) (0,25) (0,14) (0,7) (0,2) (0,9) (0,5) (1,26) (1,15) (1,25) (1,7) (1,6) (1,2) (1,20) (1,22) (2,25) (2,19) (2,14) (2,4) (3,12) (3,16) (4,15) (4,7) (4,6) (4,8) (5,26) (5,20) (5,8) (5,9) (5,22) (5,13) (6,19) (6,17) (6,7) (6,20) (6,22) (7,19) (7,17) (7,9) (8,19) (9,26) (9,14) (9,24) (11,12) (12,21) (12,18) (12,16) (13,17) (13,22) (14,26) (14,22) (15,19) (15,20) (16,21) (18,23) (19,20) (19,22) (25,26)\nQ: Is there a path between node 2 and node 13?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1460"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,17) (0,23) (0,22) (0,1) (0,9) (0,11) (0,14) (0,19) (0,12) (0,18) (0,8) (0,4) (0,16) (0,15) (0,10) (0,6) (1,20) (1,17) (1,23) (1,22) (1,9) (1,11) (1,14) (1,19) (1,12) (1,18) (1,8) (1,4) (1,16) (1,15) (1,10) (1,6) (2,13) (2,5) (2,3) (2,21) (2,7) (3,13) (3,5) (3,21) (3,7) (4,20) (4,17) (4,23) (4,22) (4,9) (4,11) (4,14) (4,19) (4,12) (4,18) (4,8) (4,16) (4,15) (4,10) (4,6) (5,13) (5,21) (5,7) (6,20) (6,17) (6,23) (6,22) (6,9) (6,11) (6,14) (6,19) (6,12) (6,18) (6,8) (6,16) (6,15) (6,10) (7,13) (7,21) (8,20) (8,17) (8,23) (8,22) (8,9) (8,11) (8,14) (8,19) (8,12) (8,18) (8,16) (8,15) (8,10) (9,20) (9,17) (9,23) (9,22) (9,11) (9,14) (9,19) (9,12) (9,18) (9,16) (9,15) (9,10) (10,20) (10,17) (10,23) (10,22) (10,11) (10,14) (10,19) (10,12) (10,18) (10,16) (10,15) (11,20) (11,17) (11,23) (11,22) (11,14) (11,19) (11,12) (11,18) (11,16) (11,15) (12,20) (12,17) (12,23) (12,22) (12,14) (12,19) (12,18) (12,16) (12,15) (13,21) (14,20) (14,17) (14,23) (14,22) (14,19) (14,18) (14,16) (14,15) (15,20) (15,17) (15,23) (15,22) (15,19) (15,18) (15,16) (16,20) (16,17) (16,23) (16,22) (16,19) (16,18) (17,20) (17,23) (17,22) (17,19) (17,18) (18,20) (18,23) (18,22) (18,19) (19,20) (19,23) (19,22) (20,23) (20,22) (22,23)\nQ: Is there a path between node 18 and node 17?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1461"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (1,17) (2,9) (3,16) (5,18) (5,11) (5,21) (6,21) (6,15) (7,19) (7,21) (8,10) (8,12) (8,16) (10,16) (14,23) (15,21) (16,19) (17,20) (18,19) (20,23)\nQ: Is there a path between node 13 and node 19?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1462"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,12) (0,11) (0,8) (0,1) (0,13) (0,10) (0,3) (1,2) (1,5) (1,12) (1,11) (1,8) (1,13) (1,10) (1,3) (2,5) (2,12) (2,11) (2,8) (2,13) (2,10) (2,3) (3,5) (3,12) (3,11) (3,8) (3,13) (3,10) (4,9) (4,6) (4,7) (4,14) (5,12) (5,11) (5,8) (5,13) (5,10) (6,9) (6,7) (6,14) (7,9) (7,14) (8,12) (8,11) (8,13) (8,10) (9,14) (10,12) (10,11) (10,13) (11,12) (11,13) (12,13)\nQ: Is there a path between node 14 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1463"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,15) (0,22) (0,18) (1,5) (1,14) (1,21) (1,16) (1,19) (1,3) (1,17) (1,13) (1,11) (1,2) (1,20) (1,8) (1,6) (1,12) (1,9) (1,7) (2,5) (2,14) (2,21) (2,16) (2,19) (2,3) (2,17) (2,13) (2,11) (2,20) (2,8) (2,6) (2,12) (2,9) (2,7) (3,5) (3,14) (3,21) (3,16) (3,19) (3,17) (3,13) (3,11) (3,20) (3,8) (3,6) (3,12) (3,9) (3,7) (5,14) (5,21) (5,16) (5,19) (5,17) (5,13) (5,11) (5,20) (5,8) (5,6) (5,12) (5,9) (5,7) (6,14) (6,21) (6,16) (6,19) (6,17) (6,13) (6,11) (6,20) (6,8) (6,12) (6,9) (6,7) (7,14) (7,21) (7,16) (7,19) (7,17) (7,13) (7,11) (7,20) (7,8) (7,12) (7,9) (8,14) (8,21) (8,16) (8,19) (8,17) (8,13) (8,11) (8,20) (8,12) (8,9) (9,14) (9,21) (9,16) (9,19) (9,17) (9,13) (9,11) (9,20) (9,12) (10,15) (10,22) (10,18) (11,14) (11,21) (11,16) (11,19) (11,17) (11,13) (11,20) (11,12) (12,14) (12,21) (12,16) (12,19) (12,17) (12,13) (12,20) (13,14) (13,21) (13,16) (13,19) (13,17) (13,20) (14,21) (14,16) (14,19) (14,17) (14,20) (15,22) (15,18) (16,21) (16,19) (16,17) (16,20) (17,21) (17,19) (17,20) (18,22) (19,21) (19,20) (20,21)\nQ: Is there a path between node 15 and node 21?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1464"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,1) (0,3) (1,5) (1,3) (2,4) (3,5)\nQ: Is there a path between node 2 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1465"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,1) (0,3) (1,5) (1,3) (2,4) (3,5)\nQ: Is there a path between node 5 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1466"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,5) (3,5)\nQ: Is there a path between node 1 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1467"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,21) (0,17) (0,7) (0,29) (1,20) (2,32) (2,6) (2,13) (3,22) (3,23) (3,8) (4,30) (4,31) (6,23) (6,16) (6,32) (7,19) (8,14) (8,23) (8,16) (8,32) (8,13) (9,24) (9,17) (9,29) (13,14) (13,32) (14,16) (14,32) (16,20) (16,28) (17,24) (20,28) (21,29) (24,29) (27,30) (30,31)\nQ: Is there a path between node 13 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1468"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,7) (0,2) (0,8) (1,6) (2,3) (3,6) (3,7) (4,6) (4,5) (5,8) (7,8)\nQ: Is there a path between node 0 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1469"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (1,14) (1,3) (1,9) (1,10) (1,4) (1,7) (1,6) (1,13) (1,12) (1,11) (2,15) (3,14) (3,8) (3,9) (3,10) (3,4) (3,12) (3,11) (4,8) (4,9) (4,10) (4,7) (4,5) (4,11) (5,9) (5,7) (5,13) (5,12) (5,11) (6,14) (6,8) (6,7) (6,13) (6,11) (7,8) (7,9) (7,10) (7,11) (8,14) (8,10) (8,12) (8,11) (9,14) (9,10) (9,13) (9,12) (10,14) (10,13) (10,12) (11,14) (11,13) (11,12) (12,14)\nQ: Is there a path between node 10 and node 15?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1470"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (1,5) (1,18) (1,7) (1,22) (1,11) (1,20) (1,4) (1,23) (2,14) (2,10) (2,21) (2,15) (2,16) (2,3) (3,14) (3,10) (3,15) (3,16) (3,6) (3,19) (4,18) (4,7) (4,22) (4,11) (4,20) (4,23) (5,13) (5,7) (5,22) (5,11) (5,20) (5,23) (6,10) (6,21) (6,15) (6,16) (6,9) (6,8) (6,19) (7,13) (7,22) (7,20) (7,23) (8,10) (8,9) (8,19) (9,21) (9,15) (9,19) (10,21) (10,16) (10,19) (11,18) (11,13) (11,22) (11,23) (12,17) (13,22) (13,20) (14,15) (14,16) (14,19) (15,16) (15,19) (16,21) (16,19) (18,20) (18,23) (19,21) (20,22) (20,23) (22,23)\nQ: Is there a path between node 21 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1471"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,8) (0,11) (0,17) (0,1) (0,2) (0,12) (0,6) (0,18) (0,7) (0,15) (1,19) (1,8) (1,9) (1,11) (1,2) (1,12) (1,6) (1,7) (1,15) (2,19) (2,4) (2,9) (2,11) (2,17) (2,12) (2,6) (2,18) (2,15) (3,5) (3,13) (3,10) (4,19) (4,8) (4,9) (4,11) (4,17) (4,12) (4,6) (4,7) (4,15) (5,13) (5,10) (6,9) (6,11) (6,12) (6,18) (7,19) (7,8) (7,9) (7,11) (7,17) (7,15) (8,19) (8,11) (8,17) (8,12) (9,17) (9,12) (9,18) (10,13) (11,17) (11,15) (12,19) (12,17) (12,18) (12,15) (14,20) (14,21) (15,17) (15,18) (17,19) (17,18) (18,19) (20,21)\nQ: Is there a path between node 12 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1472"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,12) (0,1) (0,13) (0,14) (0,11) (0,20) (0,7) (0,21) (1,4) (1,13) (1,14) (1,16) (1,7) (1,21) (2,5) (2,22) (2,8) (2,15) (2,25) (2,9) (2,17) (2,26) (3,11) (3,20) (3,7) (4,13) (4,14) (4,11) (4,20) (4,21) (5,22) (5,18) (5,15) (5,23) (5,25) (5,17) (5,26) (5,24) (6,19) (7,12) (7,13) (7,14) (7,11) (7,20) (7,21) (8,22) (8,15) (8,23) (8,9) (8,17) (8,24) (9,18) (9,15) (9,23) (9,25) (9,17) (11,13) (11,14) (11,16) (11,20) (12,13) (12,14) (12,16) (12,20) (12,21) (13,16) (13,20) (14,16) (14,20) (14,21) (15,22) (15,18) (15,23) (15,25) (15,26) (15,24) (16,21) (17,22) (17,18) (17,23) (17,25) (18,25) (18,24) (20,21) (22,23) (22,25) (22,26) (22,24) (23,26) (23,24) (24,25) (25,26)\nQ: Is there a path between node 1 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1473"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,8) (0,10) (0,12) (0,13) (1,10) (2,5) (2,16) (3,13) (4,16) (5,7) (5,14) (6,7) (7,16) (7,14) (9,13) (10,15) (11,12) (12,15)\nQ: Is there a path between node 11 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1474"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,19) (1,11) (2,4) (2,13) (3,17) (3,10) (3,11) (5,8) (5,13) (6,10) (6,12) (7,18) (7,9) (10,17) (10,12) (11,12) (12,17) (13,16) (13,15) (14,18)\nQ: Is there a path between node 7 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1475"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,3) (0,11) (0,8) (0,2) (0,12) (0,9) (0,1) (1,4) (1,3) (1,6) (1,11) (1,8) (1,7) (1,10) (1,2) (1,12) (2,3) (2,6) (2,11) (2,8) (2,9) (3,6) (3,11) (3,8) (3,7) (3,10) (3,9) (4,6) (4,11) (4,8) (4,7) (4,10) (4,12) (4,9) (6,8) (6,10) (7,10) (7,12) (7,9) (8,11) (8,10) (8,12) (9,10) (10,12)\nQ: Is there a path between node 5 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1476"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (0,10) (0,23) (0,3) (0,9) (0,26) (1,8) (1,20) (1,6) (1,4) (1,19) (1,16) (1,13) (1,24) (2,8) (2,20) (2,4) (2,19) (2,16) (2,13) (2,24) (2,12) (3,10) (3,9) (3,21) (3,22) (4,6) (4,19) (4,13) (4,24) (4,12) (5,15) (5,25) (5,11) (5,7) (6,8) (6,20) (6,19) (6,16) (6,13) (6,24) (7,15) (7,25) (7,14) (8,19) (8,13) (8,24) (8,12) (9,18) (9,23) (10,18) (10,23) (10,21) (10,26) (11,15) (11,17) (11,25) (12,20) (12,19) (12,16) (12,24) (13,20) (13,19) (13,16) (13,24) (14,17) (14,25) (15,17) (15,25) (16,20) (16,24) (17,25) (18,21) (18,22) (19,20) (19,24) (20,24) (21,23) (22,23) (22,26) (23,26)\nQ: Is there a path between node 10 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1477"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,18) (1,12) (1,15) (1,7) (2,17) (2,3) (3,17) (4,12) (5,17) (5,19) (6,18) (6,10) (6,9) (6,12) (6,16) (7,18) (7,9) (7,13) (7,8) (8,14) (9,18) (9,14) (9,12) (9,13) (10,12) (10,15) (11,17) (12,16) (14,18)\nQ: Is there a path between node 4 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1478"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (1,4) (2,4)\nQ: Is there a path between node 4 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1479"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,4) (0,9) (0,12) (0,11) (0,5) (1,6) (1,17) (1,8) (1,15) (1,3) (1,2) (1,18) (1,19) (1,13) (1,14) (1,10) (2,6) (2,17) (2,8) (2,15) (2,3) (2,18) (2,19) (2,13) (2,14) (2,10) (3,6) (3,17) (3,8) (3,15) (3,18) (3,19) (3,13) (3,14) (3,10) (4,7) (4,9) (4,12) (4,11) (4,5) (5,7) (5,9) (5,12) (5,11) (6,17) (6,8) (6,15) (6,18) (6,19) (6,13) (6,14) (6,10) (7,9) (7,12) (7,11) (8,17) (8,15) (8,18) (8,19) (8,13) (8,14) (8,10) (9,12) (9,11) (10,17) (10,15) (10,18) (10,19) (10,13) (10,14) (11,12) (13,17) (13,15) (13,18) (13,19) (13,14) (14,17) (14,15) (14,18) (14,19) (15,17) (15,18) (15,19) (17,18) (17,19) (18,19)\nQ: Is there a path between node 6 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1480"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,3) (1,20) (1,21) (1,8) (1,5) (1,16) (1,17) (1,19) (1,6) (1,12) (1,14) (1,9) (1,13) (1,18) (1,7) (1,11) (1,15) (1,2) (1,10) (2,20) (2,21) (2,8) (2,5) (2,16) (2,17) (2,19) (2,6) (2,12) (2,14) (2,9) (2,13) (2,18) (2,7) (2,11) (2,15) (2,10) (3,4) (5,20) (5,21) (5,8) (5,16) (5,17) (5,19) (5,6) (5,12) (5,14) (5,9) (5,13) (5,18) (5,7) (5,11) (5,15) (5,10) (6,20) (6,21) (6,8) (6,16) (6,17) (6,19) (6,12) (6,14) (6,9) (6,13) (6,18) (6,7) (6,11) (6,15) (6,10) (7,20) (7,21) (7,8) (7,16) (7,17) (7,19) (7,12) (7,14) (7,9) (7,13) (7,18) (7,11) (7,15) (7,10) (8,20) (8,21) (8,16) (8,17) (8,19) (8,12) (8,14) (8,9) (8,13) (8,18) (8,11) (8,15) (8,10) (9,20) (9,21) (9,16) (9,17) (9,19) (9,12) (9,14) (9,13) (9,18) (9,11) (9,15) (9,10) (10,20) (10,21) (10,16) (10,17) (10,19) (10,12) (10,14) (10,13) (10,18) (10,11) (10,15) (11,20) (11,21) (11,16) (11,17) (11,19) (11,12) (11,14) (11,13) (11,18) (11,15) (12,20) (12,21) (12,16) (12,17) (12,19) (12,14) (12,13) (12,18) (12,15) (13,20) (13,21) (13,16) (13,17) (13,19) (13,14) (13,18) (13,15) (14,20) (14,21) (14,16) (14,17) (14,19) (14,18) (14,15) (15,20) (15,21) (15,16) (15,17) (15,19) (15,18) (16,20) (16,21) (16,17) (16,19) (16,18) (17,20) (17,21) (17,19) (17,18) (18,20) (18,21) (18,19) (19,20) (19,21) (20,21)\nQ: Is there a path between node 15 and node 21?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1481"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 2 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1482"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,8) (0,5) (0,4) (0,25) (0,22) (0,16) (0,24) (0,21) (2,15) (2,23) (2,26) (2,10) (2,3) (2,11) (2,6) (2,27) (3,15) (3,23) (3,14) (3,26) (3,10) (3,11) (3,27) (4,8) (4,13) (4,5) (4,20) (4,18) (4,7) (4,22) (4,16) (4,24) (5,8) (5,13) (5,20) (5,7) (5,22) (5,24) (5,21) (6,15) (6,23) (6,14) (6,26) (6,10) (6,11) (6,27) (7,12) (7,20) (7,25) (7,16) (7,21) (8,12) (8,20) (8,25) (8,16) (8,24) (10,15) (10,23) (10,14) (10,26) (10,19) (10,11) (10,27) (11,15) (11,23) (11,26) (11,27) (12,16) (12,24) (12,21) (13,20) (13,18) (13,25) (13,22) (13,16) (13,24) (13,21) (14,15) (14,26) (15,26) (15,27) (16,22) (16,24) (16,21) (18,25) (18,22) (18,21) (19,23) (19,26) (19,27) (20,25) (20,24) (21,25) (21,24) (22,25) (22,24) (23,26) (23,27) (24,25) (26,27)\nQ: Is there a path between node 19 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1483"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,3) (0,5) (1,2) (1,10) (1,3) (1,5) (2,6) (2,10) (3,17) (3,14) (3,6) (3,9) (4,14) (4,7) (4,9) (5,17) (5,14) (5,6) (5,10) (5,7) (6,14) (6,16) (6,7) (9,17) (9,16) (9,10) (10,14) (11,15) (12,13) (14,17) (14,16) (14,15) (15,17)\nQ: Is there a path between node 2 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1484"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,11) (0,15) (0,25) (0,31) (0,23) (0,14) (1,28) (1,20) (1,12) (1,21) (1,19) (1,24) (1,27) (1,13) (1,6) (2,20) (2,22) (2,21) (2,19) (2,13) (2,6) (3,15) (3,4) (3,25) (3,23) (4,9) (4,15) (4,14) (5,8) (5,17) (5,10) (5,26) (5,7) (5,16) (6,20) (6,21) (6,19) (6,27) (6,13) (7,17) (7,16) (7,29) (8,17) (9,11) (9,15) (9,31) (9,23) (9,14) (10,17) (11,15) (11,30) (11,23) (11,14) (12,20) (12,22) (12,19) (12,27) (12,13) (12,18) (13,28) (13,22) (13,21) (13,24) (13,27) (13,18) (14,15) (14,25) (14,31) (14,23) (15,25) (15,30) (15,23) (16,26) (17,26) (17,29) (18,28) (18,20) (18,22) (18,21) (18,19) (18,24) (18,27) (19,22) (19,21) (19,24) (19,27) (20,28) (20,22) (20,21) (20,24) (20,27) (21,28) (21,22) (21,24) (22,24) (22,27) (23,30) (23,31) (24,28) (25,31) (27,28) (30,31)\nQ: Is there a path between node 3 and node 31?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1485"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,17) (0,1) (0,4) (0,15) (0,2) (0,13) (0,10) (0,6) (0,18) (0,11) (0,12) (0,5) (1,19) (1,17) (1,4) (1,15) (1,2) (1,13) (1,10) (1,6) (1,18) (1,11) (1,12) (1,5) (2,19) (2,17) (2,4) (2,15) (2,13) (2,10) (2,6) (2,18) (2,11) (2,12) (2,5) (3,20) (3,16) (3,14) (3,8) (4,19) (4,17) (4,15) (4,13) (4,10) (4,6) (4,18) (4,11) (4,12) (4,5) (5,19) (5,17) (5,15) (5,13) (5,10) (5,6) (5,18) (5,11) (5,12) (6,19) (6,17) (6,15) (6,13) (6,10) (6,18) (6,11) (6,12) (7,9) (8,20) (8,16) (8,14) (10,19) (10,17) (10,15) (10,13) (10,18) (10,11) (10,12) (11,19) (11,17) (11,15) (11,13) (11,18) (11,12) (12,19) (12,17) (12,15) (12,13) (12,18) (13,19) (13,17) (13,15) (13,18) (14,20) (14,16) (15,19) (15,17) (15,18) (16,20) (17,19) (17,18) (18,19)\nQ: Is there a path between node 16 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1486"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,19) (0,25) (0,2) (0,13) (0,1) (1,17) (1,24) (1,25) (1,11) (2,17) (2,25) (2,16) (2,13) (3,17) (4,23) (4,7) (4,14) (4,8) (5,18) (5,16) (6,18) (6,16) (6,21) (7,14) (7,15) (7,10) (8,23) (8,10) (9,14) (9,10) (10,23) (10,20) (11,17) (11,18) (11,25) (11,16) (11,13) (12,16) (13,17) (13,24) (13,25) (13,21) (14,15) (16,21) (17,19) (17,18) (17,25) (19,25) (19,21) (21,25)\nQ: Is there a path between node 3 and node 15?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1487"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,9) (0,4) (0,14) (0,6) (0,10) (0,12) (0,2) (1,13) (1,11) (1,3) (1,5) (1,7) (1,16) (1,8) (1,17) (2,15) (2,9) (2,4) (2,14) (2,6) (2,10) (2,12) (3,13) (3,11) (3,5) (3,7) (3,16) (3,8) (3,17) (4,15) (4,9) (4,14) (4,6) (4,10) (4,12) (5,13) (5,11) (5,7) (5,16) (5,8) (5,17) (6,15) (6,9) (6,14) (6,10) (6,12) (7,13) (7,11) (7,16) (7,8) (7,17) (8,13) (8,11) (8,16) (8,17) (9,15) (9,14) (9,10) (9,12) (10,15) (10,14) (10,12) (11,13) (11,16) (11,17) (12,15) (12,14) (13,16) (13,17) (14,15) (16,17)\nQ: Is there a path between node 12 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1488"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,10) (0,19) (0,16) (0,7) (0,8) (0,4) (0,3) (0,11) (0,1) (0,18) (0,9) (0,5) (0,2) (0,13) (1,17) (1,10) (1,19) (1,16) (1,7) (1,8) (1,4) (1,3) (1,11) (1,18) (1,9) (1,5) (1,2) (1,13) (2,17) (2,10) (2,19) (2,16) (2,7) (2,8) (2,4) (2,3) (2,11) (2,18) (2,9) (2,5) (2,13) (3,17) (3,10) (3,19) (3,16) (3,7) (3,8) (3,4) (3,11) (3,18) (3,9) (3,5) (3,13) (4,17) (4,10) (4,19) (4,16) (4,7) (4,8) (4,11) (4,18) (4,9) (4,5) (4,13) (5,17) (5,10) (5,19) (5,16) (5,7) (5,8) (5,11) (5,18) (5,9) (5,13) (6,15) (7,17) (7,10) (7,19) (7,16) (7,8) (7,11) (7,18) (7,9) (7,13) (8,17) (8,10) (8,19) (8,16) (8,11) (8,18) (8,9) (8,13) (9,17) (9,10) (9,19) (9,16) (9,11) (9,18) (9,13) (10,17) (10,19) (10,16) (10,11) (10,18) (10,13) (11,17) (11,19) (11,16) (11,18) (11,13) (12,14) (13,17) (13,19) (13,16) (13,18) (16,17) (16,19) (16,18) (17,19) (17,18) (18,19)\nQ: Is there a path between node 7 and node 16?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1489"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,30) (0,6) (0,12) (1,15) (2,17) (2,4) (3,25) (3,30) (3,12) (4,18) (4,16) (4,20) (4,22) (4,28) (4,8) (4,17) (5,12) (5,11) (6,19) (7,9) (7,10) (8,22) (8,28) (8,21) (9,23) (10,12) (10,11) (11,30) (11,19) (11,12) (12,25) (12,19) (13,27) (13,26) (15,26) (16,18) (16,29) (16,20) (16,24) (16,22) (16,28) (16,17) (17,22) (17,28) (17,21) (18,29) (18,20) (18,24) (18,22) (19,30) (20,22) (20,28) (21,24) (24,28) (25,30)\nQ: Is there a path between node 1 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1490"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,19) (0,17) (0,3) (0,10) (0,14) (1,7) (1,8) (1,15) (1,13) (2,9) (2,12) (2,18) (2,4) (3,6) (3,19) (3,17) (3,16) (3,10) (3,14) (4,12) (4,18) (5,9) (5,18) (6,19) (6,17) (6,16) (6,14) (6,20) (7,8) (7,15) (7,13) (9,12) (9,18) (10,16) (10,14) (10,20) (11,15) (12,18) (13,15) (14,19) (14,17) (14,20) (16,19) (16,17) (17,20) (19,20)\nQ: Is there a path between node 3 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1491"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,34) (0,4) (0,7) (0,28) (0,8) (0,15) (0,23) (0,13) (0,22) (0,32) (0,11) (0,18) (1,7) (1,2) (1,13) (1,27) (1,26) (1,9) (2,14) (2,31) (2,15) (2,23) (2,13) (2,9) (2,22) (2,17) (2,32) (2,18) (3,24) (4,7) (4,27) (4,17) (5,16) (5,12) (5,29) (5,20) (6,34) (6,7) (6,14) (6,31) (6,10) (6,23) (6,26) (6,21) (6,17) (6,18) (7,33) (7,14) (7,28) (7,15) (7,26) (7,19) (8,14) (8,28) (8,31) (8,10) (8,13) (8,25) (8,30) (8,18) (9,14) (9,21) (9,25) (9,22) (9,11) (10,31) (10,15) (10,27) (10,25) (10,17) (10,32) (11,28) (11,31) (11,15) (11,13) (11,27) (11,21) (11,25) (11,22) (12,16) (13,33) (13,14) (13,28) (13,26) (13,21) (13,17) (13,32) (13,18) (14,33) (14,31) (14,23) (14,27) (14,25) (15,34) (15,30) (15,17) (15,19) (16,24) (17,23) (17,26) (17,19) (18,34) (18,21) (18,30) (19,33) (19,21) (19,25) (19,30) (21,33) (21,28) (21,25) (21,30) (22,33) (22,23) (22,26) (22,25) (23,34) (23,25) (25,33) (25,32) (26,33) (26,28) (26,31) (26,32) (27,33) (27,32) (32,33)\nQ: Is there a path between node 4 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1492"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,8) (0,4) (0,5) (0,13) (0,2) (0,17) (1,15) (1,8) (1,3) (1,4) (1,5) (1,13) (1,17) (2,15) (2,8) (2,3) (2,4) (2,5) (2,13) (3,8) (3,5) (3,17) (4,15) (4,13) (4,17) (5,15) (5,8) (5,17) (6,14) (6,7) (6,10) (6,16) (6,9) (6,12) (7,14) (7,16) (7,9) (8,13) (9,14) (9,10) (9,11) (9,16) (9,12) (10,14) (10,12) (11,14) (11,12) (12,14) (12,16) (13,17) (15,17)\nQ: Is there a path between node 10 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1493"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,3) (0,4) (1,3) (1,4) (3,4)\nQ: Is there a path between node 3 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1494"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,3) (0,12) (0,6) (0,11) (1,16) (1,3) (1,12) (1,6) (1,11) (1,14) (1,10) (2,15) (2,7) (2,13) (2,5) (2,9) (2,4) (2,18) (3,17) (3,12) (3,11) (3,14) (4,15) (4,7) (4,5) (4,9) (4,8) (5,15) (5,13) (5,9) (5,8) (5,18) (6,16) (6,17) (6,12) (6,14) (6,10) (7,15) (7,13) (7,9) (7,18) (8,15) (8,9) (8,18) (9,13) (9,18) (10,16) (10,17) (10,12) (10,11) (11,16) (11,17) (11,12) (12,16) (12,17) (12,14) (13,15) (13,18) (14,16) (14,17) (15,18) (16,17)\nQ: Is there a path between node 2 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1495"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,2) (0,1) (0,4) (1,3) (1,2) (1,4) (1,6) (2,3) (2,4) (2,5) (3,4) (3,6) (4,6) (5,6)\nQ: Is there a path between node 7 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1496"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,21) (0,14) (0,1) (0,22) (0,16) (0,19) (0,5) (0,10) (0,20) (0,11) (0,24) (0,13) (1,21) (1,9) (1,3) (1,14) (1,22) (1,10) (1,20) (1,12) (1,11) (1,24) (1,13) (1,23) (2,8) (2,4) (2,18) (2,15) (3,9) (3,14) (3,16) (3,19) (3,7) (3,6) (3,5) (3,10) (3,11) (4,8) (4,17) (4,18) (4,15) (5,9) (5,14) (5,22) (5,7) (5,6) (5,10) (5,20) (5,12) (5,11) (5,13) (5,23) (6,21) (6,9) (6,22) (6,19) (6,7) (6,20) (6,12) (6,11) (6,13) (6,23) (7,21) (7,9) (7,14) (7,16) (7,19) (7,10) (7,20) (7,12) (7,11) (7,24) (7,13) (7,23) (8,17) (8,18) (8,15) (9,21) (9,16) (9,10) (9,20) (9,12) (9,11) (9,24) (9,13) (9,23) (10,22) (10,19) (10,12) (10,11) (10,13) (10,23) (11,21) (11,22) (11,19) (11,20) (11,12) (11,24) (11,13) (11,23) (12,21) (12,14) (12,22) (12,20) (12,24) (12,13) (12,23) (13,21) (13,14) (13,22) (13,16) (13,20) (13,23) (14,21) (14,16) (14,20) (14,24) (14,23) (15,18) (16,21) (16,22) (16,19) (16,20) (16,24) (16,23) (17,18) (19,21) (19,20) (19,24) (19,23) (20,21) (20,24) (20,23) (21,24) (21,23) (22,23) (23,24)\nQ: Is there a path between node 11 and node 17?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1497"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,11) (0,17) (0,3) (0,19) (0,9) (0,16) (0,15) (0,7) (0,12) (0,2) (1,11) (1,10) (1,3) (1,4) (1,8) (1,19) (1,13) (1,9) (1,16) (1,15) (1,7) (1,12) (1,2) (2,17) (2,5) (2,16) (2,15) (3,17) (3,10) (3,5) (3,6) (3,8) (3,13) (3,9) (3,16) (3,15) (3,7) (3,12) (4,11) (4,5) (4,8) (4,19) (4,13) (4,9) (4,7) (4,12) (5,11) (5,10) (5,6) (5,8) (5,19) (5,13) (5,7) (6,11) (6,17) (6,10) (6,8) (6,19) (6,13) (6,16) (6,15) (6,7) (6,12) (7,11) (7,17) (7,10) (7,19) (7,9) (7,16) (7,15) (8,11) (8,17) (8,10) (8,19) (8,13) (8,15) (8,12) (9,11) (9,17) (9,10) (9,13) (9,16) (9,15) (10,11) (10,17) (10,19) (10,13) (10,15) (10,12) (11,19) (11,15) (11,12) (12,17) (12,19) (12,13) (13,19) (13,16) (13,15) (14,18) (15,19) (15,16) (16,17) (17,19)\nQ: Is there a path between node 3 and node 17?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1498"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,13) (0,11) (0,21) (0,8) (0,18) (0,3) (0,7) (0,15) (0,20) (0,17) (0,10) (0,22) (0,1) (0,9) (0,6) (0,19) (1,23) (1,14) (1,5) (1,13) (1,11) (1,12) (1,21) (1,8) (1,18) (1,3) (1,25) (1,7) (1,28) (1,15) (1,20) (1,17) (1,10) (1,22) (1,9) (1,6) (1,16) (1,19) (3,27) (3,14) (3,5) (3,13) (3,4) (3,21) (3,18) (3,25) (3,28) (3,15) (3,20) (3,17) (3,22) (3,6) (3,16) (3,19) (4,27) (4,23) (4,5) (4,13) (4,11) (4,12) (4,8) (4,28) (4,15) (4,20) (4,17) (4,10) (4,24) (4,6) (5,27) (5,23) (5,14) (5,13) (5,11) (5,12) (5,21) (5,8) (5,18) (5,25) (5,7) (5,15) (5,10) (5,22) (5,24) (5,9) (5,6) (5,16) (5,19) (6,27) (6,14) (6,11) (6,12) (6,18) (6,25) (6,7) (6,20) (6,17) (6,10) (6,22) (6,24) (6,9) (6,16) (6,19) (7,23) (7,14) (7,13) (7,12) (7,21) (7,8) (7,25) (7,28) (7,20) (7,10) (7,22) (7,16) (7,19) (8,27) (8,13) (8,18) (8,25) (8,15) (8,17) (8,10) (8,22) (8,24) (8,9) (8,16) (8,19) (9,27) (9,23) (9,11) (9,21) (9,25) (9,28) (9,15) (9,20) (9,17) (9,10) (9,22) (9,24) (9,16) (9,19) (10,27) (10,14) (10,11) (10,12) (10,25) (10,28) (10,15) (10,20) (10,17) (10,24) (10,16) (10,19) (11,23) (11,21) (11,18) (11,25) (11,28) (11,15) (11,17) (11,22) (11,24) (11,19) (12,27) (12,23) (12,13) (12,21) (12,18) (12,25) (12,28) (12,15) (12,17) (12,22) (12,24) (12,16) (13,27) (13,14) (13,21) (13,18) (13,28) (13,15) (13,17) (13,24) (13,16) (13,19) (14,27) (14,25) (14,28) (14,15) (14,17) (14,22) (14,24) (14,16) (15,23) (15,21) (15,18) (15,25) (15,20) (15,24) (16,27) (16,23) (16,17) (16,24) (16,19) (17,27) (17,23) (17,18) (17,25) (17,28) (17,20) (17,22) (17,24) (17,19) (18,23) (18,21) (18,25) (18,28) (18,20) (18,22) (18,24) (18,19) (19,27) (19,23) (19,21) (19,25) (19,24) (20,27) (20,23) (20,21) (20,25) (20,24) (21,23) (21,22) (23,27) (23,24) (25,27) (25,28) (27,28)\nQ: Is there a path between node 2 and node 24?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1499"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,24) (0,1) (0,6) (0,14) (1,10) (2,25) (2,5) (2,20) (2,18) (3,22) (3,6) (3,19) (3,23) (4,9) (4,18) (5,15) (5,25) (5,17) (5,20) (6,11) (6,24) (6,14) (6,7) (6,21) (7,24) (8,25) (8,17) (8,20) (8,18) (9,25) (10,24) (10,22) (10,21) (11,22) (11,19) (11,23) (12,15) (12,16) (12,17) (13,19) (13,14) (14,22) (14,19) (15,16) (15,18) (16,17) (17,20) (18,25) (19,24) (19,22) (20,25) (21,23) (22,24) (22,23)\nQ: Is there a path between node 11 and node 23?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1500"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,17) (0,24) (1,11) (1,9) (1,3) (2,19) (2,29) (2,27) (3,7) (3,20) (4,23) (4,25) (5,17) (6,22) (7,29) (7,27) (7,9) (8,16) (8,30) (8,26) (8,18) (8,31) (9,11) (9,27) (10,13) (10,12) (11,19) (11,27) (12,26) (12,18) (14,28) (15,27) (16,30) (17,23) (18,26) (19,28) (20,29) (21,22) (23,24) (24,25) (27,28) (30,31)\nQ: Is there a path between node 27 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1501"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,13) (0,6) (0,5) (0,15) (0,14) (0,1) (0,10) (0,8) (0,7) (0,2) (0,11) (0,3) (1,12) (1,13) (1,6) (1,5) (1,15) (1,14) (1,10) (1,8) (1,7) (1,2) (1,11) (1,3) (2,12) (2,13) (2,6) (2,5) (2,15) (2,14) (2,10) (2,8) (2,7) (2,11) (2,3) (3,12) (3,13) (3,6) (3,5) (3,15) (3,14) (3,10) (3,8) (3,7) (3,11) (4,9) (5,12) (5,13) (5,6) (5,15) (5,14) (5,10) (5,8) (5,7) (5,11) (6,12) (6,13) (6,15) (6,14) (6,10) (6,8) (6,7) (6,11) (7,12) (7,13) (7,15) (7,14) (7,10) (7,8) (7,11) (8,12) (8,13) (8,15) (8,14) (8,10) (8,11) (10,12) (10,13) (10,15) (10,14) (10,11) (11,12) (11,13) (11,15) (11,14) (12,13) (12,15) (12,14) (13,15) (13,14) (14,15)\nQ: Is there a path between node 3 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1502"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,10) (0,17) (0,15) (0,4) (0,12) (0,24) (0,9) (0,3) (0,13) (0,23) (0,7) (0,19) (0,16) (0,6) (0,25) (0,8) (1,10) (1,17) (1,4) (1,12) (1,24) (1,3) (1,13) (1,23) (1,26) (1,22) (1,19) (1,6) (1,14) (1,25) (1,8) (1,20) (2,10) (2,17) (2,11) (2,4) (2,24) (2,9) (2,3) (2,13) (2,23) (2,26) (2,7) (2,22) (2,19) (2,6) (2,14) (2,25) (2,8) (3,10) (3,17) (3,11) (3,15) (3,4) (3,12) (3,24) (3,9) (3,13) (3,26) (3,7) (3,19) (3,16) (3,14) (3,25) (3,8) (3,20) (4,10) (4,17) (4,11) (4,15) (4,12) (4,24) (4,9) (4,7) (4,19) (4,16) (4,6) (4,25) (4,20) (5,18) (6,10) (6,17) (6,15) (6,12) (6,24) (6,9) (6,23) (6,7) (6,16) (6,25) (6,8) (7,10) (7,11) (7,15) (7,12) (7,13) (7,22) (7,19) (7,16) (7,25) (7,8) (7,20) (8,10) (8,17) (8,11) (8,15) (8,12) (8,24) (8,9) (8,23) (8,22) (8,19) (8,16) (8,14) (8,25) (8,20) (9,10) (9,17) (9,11) (9,12) (9,24) (9,13) (9,23) (9,26) (9,22) (9,19) (9,16) (9,20) (10,17) (10,11) (10,15) (10,12) (10,24) (10,13) (10,23) (10,26) (10,19) (10,14) (10,20) (11,15) (11,12) (11,24) (11,13) (11,23) (11,26) (11,19) (11,16) (11,14) (11,20) (12,15) (12,24) (12,23) (12,22) (12,19) (12,16) (12,14) (12,25) (12,20) (13,15) (13,24) (13,23) (13,19) (13,16) (13,14) (13,25) (13,20) (14,17) (14,15) (14,24) (14,23) (14,26) (14,22) (14,19) (14,16) (14,25) (14,20) (15,17) (15,24) (15,23) (15,26) (15,16) (15,20) (16,24) (16,23) (16,26) (16,19) (16,25) (16,20) (17,23) (17,20) (18,21) (19,23) (19,22) (19,25) (19,20) (20,24) (20,23) (20,22) (20,25) (22,26) (22,25) (23,24) (23,26) (23,25) (24,26) (24,25) (25,26)\nQ: Is there a path between node 21 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1503"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,16) (0,22) (0,4) (0,15) (0,9) (1,8) (1,17) (1,12) (1,3) (1,5) (1,21) (1,6) (1,13) (1,19) (2,20) (2,16) (2,22) (2,4) (2,9) (3,8) (3,17) (3,14) (3,6) (3,10) (3,19) (4,20) (4,16) (4,22) (4,15) (4,9) (5,8) (5,17) (5,12) (5,14) (5,13) (5,10) (5,19) (6,17) (6,12) (6,14) (6,21) (6,13) (6,10) (6,19) (8,17) (8,12) (8,13) (8,19) (9,20) (9,22) (9,15) (10,17) (10,14) (10,21) (11,18) (11,23) (12,17) (12,21) (12,13) (12,19) (13,17) (13,14) (13,21) (15,20) (16,22) (17,21) (18,23)\nQ: Is there a path between node 4 and node 16?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1504"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,1) (0,13) (0,15) (0,16) (0,9) (0,14) (0,3) (0,12) (0,17) (0,2) (0,18) (1,11) (1,13) (1,15) (1,16) (1,9) (1,8) (1,14) (1,3) (1,4) (1,17) (1,18) (2,11) (2,13) (2,15) (2,9) (2,8) (2,14) (2,3) (2,12) (2,17) (2,18) (3,11) (3,13) (3,15) (3,16) (3,9) (3,8) (3,14) (3,12) (3,17) (3,18) (4,13) (4,15) (4,16) (4,8) (4,14) (4,12) (4,18) (5,6) (5,7) (5,10) (6,7) (6,10) (7,10) (8,11) (8,15) (8,16) (8,18) (9,11) (9,13) (9,15) (9,16) (9,14) (9,12) (9,17) (9,18) (11,13) (11,16) (11,17) (11,18) (12,15) (12,16) (12,17) (12,18) (13,15) (13,18) (14,15) (14,17) (15,16) (16,17) (16,18) (17,18)\nQ: Is there a path between node 18 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1505"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,15) (0,22) (0,18) (1,5) (1,14) (1,21) (1,16) (1,19) (1,3) (1,17) (1,13) (1,11) (1,2) (1,20) (1,8) (1,6) (1,12) (1,9) (1,7) (2,5) (2,14) (2,21) (2,16) (2,19) (2,3) (2,17) (2,13) (2,11) (2,20) (2,8) (2,6) (2,12) (2,9) (2,7) (3,5) (3,14) (3,21) (3,16) (3,19) (3,17) (3,13) (3,11) (3,20) (3,8) (3,6) (3,12) (3,9) (3,7) (5,14) (5,21) (5,16) (5,19) (5,17) (5,13) (5,11) (5,20) (5,8) (5,6) (5,12) (5,9) (5,7) (6,14) (6,21) (6,16) (6,19) (6,17) (6,13) (6,11) (6,20) (6,8) (6,12) (6,9) (6,7) (7,14) (7,21) (7,16) (7,19) (7,17) (7,13) (7,11) (7,20) (7,8) (7,12) (7,9) (8,14) (8,21) (8,16) (8,19) (8,17) (8,13) (8,11) (8,20) (8,12) (8,9) (9,14) (9,21) (9,16) (9,19) (9,17) (9,13) (9,11) (9,20) (9,12) (10,15) (10,22) (10,18) (11,14) (11,21) (11,16) (11,19) (11,17) (11,13) (11,20) (11,12) (12,14) (12,21) (12,16) (12,19) (12,17) (12,13) (12,20) (13,14) (13,21) (13,16) (13,19) (13,17) (13,20) (14,21) (14,16) (14,19) (14,17) (14,20) (15,22) (15,18) (16,21) (16,19) (16,17) (16,20) (17,21) (17,19) (17,20) (18,22) (19,21) (19,20) (20,21)\nQ: Is there a path between node 8 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1506"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,13) (0,2) (0,15) (0,6) (0,17) (0,8) (0,16) (0,18) (0,9) (0,12) (0,11) (1,10) (1,14) (1,7) (1,5) (1,4) (2,3) (2,13) (2,15) (2,6) (2,17) (2,8) (2,16) (2,18) (2,9) (2,12) (2,11) (3,13) (3,15) (3,6) (3,17) (3,8) (3,16) (3,18) (3,9) (3,12) (3,11) (4,10) (4,14) (4,7) (4,5) (5,10) (5,14) (5,7) (6,13) (6,15) (6,17) (6,8) (6,16) (6,18) (6,9) (6,12) (6,11) (7,10) (7,14) (8,13) (8,15) (8,17) (8,16) (8,18) (8,9) (8,12) (8,11) (9,13) (9,15) (9,17) (9,16) (9,18) (9,12) (9,11) (10,14) (11,13) (11,15) (11,17) (11,16) (11,18) (11,12) (12,13) (12,15) (12,17) (12,16) (12,18) (13,15) (13,17) (13,16) (13,18) (15,17) (15,16) (15,18) (16,17) (16,18) (17,18)\nQ: Is there a path between node 8 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1507"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,11) (0,6) (1,5) (1,8) (1,10) (1,15) (1,17) (1,13) (1,16) (2,5) (2,4) (2,8) (2,10) (2,14) (2,17) (2,13) (2,16) (3,9) (3,6) (3,12) (4,8) (4,15) (4,14) (4,17) (4,13) (5,8) (5,15) (5,17) (6,7) (6,9) (7,11) (7,9) (8,15) (8,17) (8,13) (8,16) (9,11) (10,15) (10,14) (10,17) (11,12) (13,15) (13,14) (13,16) (14,15) (14,17) (14,16) (15,17) (15,16) (16,17)\nQ: Is there a path between node 9 and node 15?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1508"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,18) (0,19) (0,20) (0,23) (0,9) (0,10) (0,22) (0,13) (0,1) (0,12) (0,5) (0,7) (0,15) (0,4) (1,11) (1,18) (1,19) (1,20) (1,23) (1,9) (1,10) (1,22) (1,13) (1,12) (1,5) (1,7) (1,15) (1,4) (2,8) (2,6) (2,3) (2,24) (2,16) (2,21) (2,17) (2,14) (3,8) (3,6) (3,24) (3,16) (3,21) (3,17) (3,14) (4,11) (4,18) (4,19) (4,20) (4,23) (4,9) (4,10) (4,22) (4,13) (4,12) (4,5) (4,7) (4,15) (5,11) (5,18) (5,19) (5,20) (5,23) (5,9) (5,10) (5,22) (5,13) (5,12) (5,7) (5,15) (6,8) (6,24) (6,16) (6,21) (6,17) (6,14) (7,11) (7,18) (7,19) (7,20) (7,23) (7,9) (7,10) (7,22) (7,13) (7,12) (7,15) (8,24) (8,16) (8,21) (8,17) (8,14) (9,11) (9,18) (9,19) (9,20) (9,23) (9,10) (9,22) (9,13) (9,12) (9,15) (10,11) (10,18) (10,19) (10,20) (10,23) (10,22) (10,13) (10,12) (10,15) (11,18) (11,19) (11,20) (11,23) (11,22) (11,13) (11,12) (11,15) (12,18) (12,19) (12,20) (12,23) (12,22) (12,13) (12,15) (13,18) (13,19) (13,20) (13,23) (13,22) (13,15) (14,24) (14,16) (14,21) (14,17) (15,18) (15,19) (15,20) (15,23) (15,22) (16,24) (16,21) (16,17) (17,24) (17,21) (18,19) (18,20) (18,23) (18,22) (19,20) (19,23) (19,22) (20,23) (20,22) (21,24) (22,23)\nQ: Is there a path between node 18 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1509"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,12) (0,11) (0,8) (0,1) (0,13) (0,10) (0,3) (1,2) (1,5) (1,12) (1,11) (1,8) (1,13) (1,10) (1,3) (2,5) (2,12) (2,11) (2,8) (2,13) (2,10) (2,3) (3,5) (3,12) (3,11) (3,8) (3,13) (3,10) (4,9) (4,6) (4,7) (4,14) (5,12) (5,11) (5,8) (5,13) (5,10) (6,9) (6,7) (6,14) (7,9) (7,14) (8,12) (8,11) (8,13) (8,10) (9,14) (10,12) (10,11) (10,13) (11,12) (11,13) (12,13)\nQ: Is there a path between node 4 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1510"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,10) (0,1) (1,8) (1,3) (1,14) (3,5) (3,6) (3,9) (3,12) (4,9) (4,16) (6,7) (6,12) (7,14) (8,16) (8,14) (10,11) (10,14) (10,12) (11,14) (12,14)\nQ: Is there a path between node 13 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1511"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,11) (1,9) (1,19) (1,31) (1,20) (2,15) (2,11) (2,27) (2,29) (2,16) (2,31) (3,8) (3,4) (3,12) (3,18) (3,17) (3,10) (3,25) (3,31) (3,20) (4,30) (4,24) (4,19) (5,26) (5,23) (6,13) (7,15) (7,9) (7,30) (7,12) (7,16) (7,19) (7,10) (7,25) (8,15) (8,11) (8,30) (8,24) (8,10) (8,31) (9,11) (9,30) (9,27) (9,29) (9,10) (10,15) (10,30) (10,12) (10,18) (10,19) (10,17) (10,14) (11,30) (11,29) (11,19) (12,15) (12,19) (12,14) (12,20) (13,28) (14,27) (14,24) (14,20) (15,27) (15,18) (15,25) (15,20) (16,29) (16,24) (16,19) (17,29) (17,19) (17,31) (18,30) (18,24) (18,19) (18,31) (19,30) (19,25) (21,28) (21,23) (22,23) (25,27) (25,31) (26,28) (29,31)\nQ: Is there a path between node 8 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1512"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,12) (0,11) (0,4) (2,10) (2,8) (2,4) (4,6) (4,11) (5,9) (6,7) (6,10) (6,11) (7,8) (8,10) (8,9) (9,12) (10,11)\nQ: Is there a path between node 5 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1513"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,15) (0,6) (0,17) (0,4) (0,12) (0,16) (0,9) (1,14) (1,23) (1,18) (1,19) (1,3) (1,21) (2,14) (2,5) (2,11) (2,23) (2,22) (2,8) (2,18) (2,19) (2,3) (2,20) (3,14) (3,5) (3,23) (3,22) (3,8) (3,18) (3,19) (3,20) (3,21) (4,7) (4,15) (4,6) (4,17) (4,13) (4,10) (4,16) (5,14) (5,8) (5,18) (5,19) (5,21) (6,13) (6,10) (6,16) (6,9) (7,15) (7,13) (7,9) (8,14) (8,11) (8,23) (8,22) (8,18) (8,19) (8,20) (8,21) (9,15) (9,13) (9,12) (9,16) (10,15) (10,17) (10,13) (10,12) (11,14) (11,23) (11,22) (11,18) (11,19) (12,17) (12,16) (13,17) (13,16) (14,23) (14,19) (15,17) (16,17) (18,23) (18,22) (18,19) (18,21) (19,23) (19,22) (19,20) (20,23) (20,21) (21,23) (22,23)\nQ: Is there a path between node 22 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1514"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,29) (0,1) (0,9) (0,20) (0,34) (0,7) (0,19) (0,22) (0,31) (1,11) (1,30) (1,6) (1,21) (1,14) (1,28) (1,19) (1,31) (1,4) (2,3) (2,11) (2,18) (2,21) (2,20) (2,14) (2,7) (2,17) (3,11) (3,33) (3,15) (3,30) (3,18) (3,21) (3,14) (3,5) (4,10) (4,26) (4,27) (4,21) (4,34) (5,9) (5,27) (5,30) (5,6) (5,24) (5,14) (5,34) (5,28) (5,17) (6,11) (6,25) (6,10) (6,26) (6,29) (6,15) (6,16) (6,14) (6,7) (6,12) (6,22) (7,10) (7,26) (7,27) (7,18) (7,24) (7,8) (7,31) (8,11) (8,33) (8,9) (8,30) (8,24) (8,20) (8,16) (8,22) (8,17) (9,10) (9,20) (9,16) (9,14) (10,25) (10,33) (10,30) (10,18) (10,24) (10,20) (10,31) (11,15) (11,12) (11,19) (11,17) (12,25) (12,29) (12,27) (12,30) (12,34) (12,28) (12,17) (14,25) (14,33) (14,26) (14,29) (14,30) (14,21) (14,17) (15,20) (15,17) (16,21) (16,28) (16,19) (16,22) (17,27) (17,30) (17,24) (17,19) (18,26) (18,21) (18,28) (19,33) (19,27) (19,34) (19,22) (20,25) (20,26) (20,27) (20,21) (20,28) (20,31) (21,22) (22,24) (22,31) (24,34) (24,28) (25,26) (25,29) (25,27) (26,33) (26,27) (26,30) (27,30) (27,28) (28,31) (29,30) (29,34) (29,31) (30,33) (30,34) (31,33) (31,34)\nQ: Is there a path between node 11 and node 17?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1515"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,11) (0,13) (0,3) (0,15) (0,4) (0,2) (1,7) (1,8) (2,14) (2,23) (2,21) (2,6) (2,10) (3,9) (3,17) (3,13) (3,5) (3,19) (3,4) (3,16) (3,10) (4,9) (4,22) (4,6) (5,11) (5,18) (5,23) (6,9) (6,14) (6,17) (6,20) (6,15) (6,21) (7,8) (9,17) (9,15) (9,21) (10,18) (10,12) (10,16) (11,17) (11,15) (11,22) (11,16) (12,15) (12,22) (13,23) (13,16) (14,17) (14,18) (14,20) (14,21) (14,22) (14,16) (15,20) (17,20) (17,19) (17,23) (18,19) (18,23) (19,20) (19,23) (21,23) (21,22)\nQ: Is there a path between node 20 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1516"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (1,3) (1,2) (1,6) (2,5) (2,6) (3,5) (5,6)\nQ: Is there a path between node 5 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1517"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (1,4) (2,4)\nQ: Is there a path between node 0 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1518"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,6) (0,1) (0,5) (1,7) (1,6) (1,8) (1,5) (2,7) (2,8) (2,5) (3,4) (5,7) (5,6) (5,8)\nQ: Is there a path between node 4 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1519"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,13) (0,6) (0,5) (0,15) (0,14) (0,1) (0,10) (0,8) (0,7) (0,2) (0,11) (0,3) (1,12) (1,13) (1,6) (1,5) (1,15) (1,14) (1,10) (1,8) (1,7) (1,2) (1,11) (1,3) (2,12) (2,13) (2,6) (2,5) (2,15) (2,14) (2,10) (2,8) (2,7) (2,11) (2,3) (3,12) (3,13) (3,6) (3,5) (3,15) (3,14) (3,10) (3,8) (3,7) (3,11) (4,9) (5,12) (5,13) (5,6) (5,15) (5,14) (5,10) (5,8) (5,7) (5,11) (6,12) (6,13) (6,15) (6,14) (6,10) (6,8) (6,7) (6,11) (7,12) (7,13) (7,15) (7,14) (7,10) (7,8) (7,11) (8,12) (8,13) (8,15) (8,14) (8,10) (8,11) (10,12) (10,13) (10,15) (10,14) (10,11) (11,12) (11,13) (11,15) (11,14) (12,13) (12,15) (12,14) (13,15) (13,14) (14,15)\nQ: Is there a path between node 10 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1520"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,18) (0,25) (0,19) (0,16) (0,22) (0,8) (0,10) (0,31) (0,13) (0,5) (0,14) (0,24) (0,27) (0,1) (0,15) (0,23) (1,9) (1,30) (1,25) (1,19) (1,16) (1,17) (1,22) (1,8) (1,21) (1,4) (1,31) (1,13) (1,14) (1,24) (1,12) (1,27) (1,15) (2,11) (2,28) (2,29) (2,7) (3,9) (3,18) (3,25) (3,19) (3,16) (3,22) (3,10) (3,4) (3,31) (3,13) (3,5) (3,14) (3,24) (3,12) (3,20) (3,27) (3,15) (3,23) (4,18) (4,30) (4,19) (4,22) (4,8) (4,21) (4,31) (4,5) (4,24) (4,12) (4,27) (4,23) (5,18) (5,30) (5,25) (5,19) (5,17) (5,10) (5,21) (5,31) (5,12) (5,20) (5,15) (5,23) (6,28) (6,29) (6,7) (6,26) (7,28) (8,9) (8,25) (8,19) (8,16) (8,22) (8,10) (8,13) (8,14) (8,24) (8,12) (8,27) (8,15) (8,23) (9,18) (9,30) (9,19) (9,16) (9,17) (9,22) (9,10) (9,31) (9,13) (9,27) (9,15) (9,23) (10,18) (10,30) (10,25) (10,16) (10,22) (10,21) (10,31) (10,14) (10,24) (10,12) (10,20) (10,15) (11,28) (11,26) (12,19) (12,22) (12,21) (12,13) (12,24) (12,15) (12,23) (13,25) (13,19) (13,16) (13,17) (13,22) (13,31) (13,14) (13,27) (14,30) (14,25) (14,16) (14,17) (14,22) (14,31) (14,24) (14,20) (14,15) (14,23) (15,18) (15,30) (15,25) (15,19) (15,16) (15,22) (15,31) (15,24) (16,18) (16,30) (16,22) (16,21) (16,31) (16,20) (16,27) (17,18) (17,30) (17,25) (17,19) (17,22) (17,21) (17,31) (17,24) (17,27) (17,23) (18,30) (18,25) (18,19) (18,22) (18,21) (18,31) (18,24) (18,27) (18,23) (19,30) (19,25) (19,21) (19,24) (19,20) (19,27) (19,23) (20,21) (20,31) (20,24) (20,27) (20,23) (21,25) (21,22) (21,31) (21,24) (21,27) (21,23) (22,30) (22,31) (22,24) (22,23) (23,30) (23,25) (23,24) (23,27) (24,30) (24,25) (24,31) (24,27) (25,30) (25,27) (26,28) (27,30) (27,31) (28,29) (30,31)\nQ: Is there a path between node 12 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1521"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,10) (0,1) (1,8) (1,3) (1,14) (3,5) (3,6) (3,9) (3,12) (4,9) (4,16) (6,7) (6,12) (7,14) (8,16) (8,14) (10,11) (10,14) (10,12) (11,14) (12,14)\nQ: Is there a path between node 3 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1522"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,14) (0,5) (0,9) (0,8) (0,6) (0,21) (1,4) (1,15) (1,18) (1,11) (1,10) (1,12) (2,20) (2,14) (2,5) (2,9) (2,22) (2,6) (2,16) (3,9) (3,23) (3,22) (3,6) (3,21) (4,15) (4,11) (4,19) (4,13) (5,20) (5,14) (5,9) (5,8) (5,6) (5,21) (6,20) (6,14) (6,9) (6,23) (6,8) (6,16) (7,18) (7,11) (7,10) (7,12) (7,19) (7,13) (8,20) (8,14) (8,23) (8,21) (9,20) (9,23) (9,22) (9,21) (10,15) (10,18) (10,11) (10,12) (10,19) (10,13) (11,15) (11,13) (12,18) (12,19) (13,18) (13,19) (14,23) (14,22) (14,21) (15,19) (16,23) (16,22) (20,21) (22,23)\nQ: Is there a path between node 17 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1523"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,13) (0,2) (0,14) (0,23) (0,8) (0,1) (0,25) (0,27) (0,10) (1,29) (1,13) (1,19) (1,28) (1,23) (1,30) (1,25) (1,24) (2,12) (2,5) (2,14) (2,17) (2,23) (3,7) (3,12) (3,19) (3,23) (3,8) (3,30) (3,25) (3,24) (4,33) (5,20) (5,23) (5,30) (6,15) (6,11) (7,32) (7,17) (7,23) (7,8) (7,10) (8,29) (8,12) (8,32) (8,20) (8,19) (8,17) (8,30) (9,29) (9,28) (9,30) (9,24) (10,13) (10,20) (10,14) (10,22) (11,31) (12,13) (12,23) (12,27) (12,26) (13,29) (13,32) (13,14) (13,28) (13,30) (13,24) (14,17) (14,30) (14,22) (14,27) (15,16) (15,31) (15,33) (17,32) (17,20) (17,19) (17,27) (17,24) (17,26) (18,21) (20,28) (20,30) (20,25) (21,31) (22,32) (22,28) (22,30) (23,28) (23,25) (23,27) (24,29) (24,28) (24,26) (25,32) (26,29) (26,27) (27,32) (27,30) (28,32) (28,30)\nQ: Is there a path between node 7 and node 23?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1524"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,6) (3,4) (4,5) (5,10) (6,8) (8,9)\nQ: Is there a path between node 5 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1525"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,1) (0,2) (0,7) (0,6) (1,2) (1,8) (1,7) (1,4) (1,6) (2,7) (2,4) (2,6) (3,5) (4,9) (4,8) (4,7) (6,9) (6,7) (7,8)\nQ: Is there a path between node 3 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1526"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,6) (3,4) (4,5) (5,10) (6,8) (8,9)\nQ: Is there a path between node 4 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1527"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,18) (0,19) (0,20) (0,23) (0,9) (0,10) (0,22) (0,13) (0,1) (0,12) (0,5) (0,7) (0,15) (0,4) (1,11) (1,18) (1,19) (1,20) (1,23) (1,9) (1,10) (1,22) (1,13) (1,12) (1,5) (1,7) (1,15) (1,4) (2,8) (2,6) (2,3) (2,24) (2,16) (2,21) (2,17) (2,14) (3,8) (3,6) (3,24) (3,16) (3,21) (3,17) (3,14) (4,11) (4,18) (4,19) (4,20) (4,23) (4,9) (4,10) (4,22) (4,13) (4,12) (4,5) (4,7) (4,15) (5,11) (5,18) (5,19) (5,20) (5,23) (5,9) (5,10) (5,22) (5,13) (5,12) (5,7) (5,15) (6,8) (6,24) (6,16) (6,21) (6,17) (6,14) (7,11) (7,18) (7,19) (7,20) (7,23) (7,9) (7,10) (7,22) (7,13) (7,12) (7,15) (8,24) (8,16) (8,21) (8,17) (8,14) (9,11) (9,18) (9,19) (9,20) (9,23) (9,10) (9,22) (9,13) (9,12) (9,15) (10,11) (10,18) (10,19) (10,20) (10,23) (10,22) (10,13) (10,12) (10,15) (11,18) (11,19) (11,20) (11,23) (11,22) (11,13) (11,12) (11,15) (12,18) (12,19) (12,20) (12,23) (12,22) (12,13) (12,15) (13,18) (13,19) (13,20) (13,23) (13,22) (13,15) (14,24) (14,16) (14,21) (14,17) (15,18) (15,19) (15,20) (15,23) (15,22) (16,24) (16,21) (16,17) (17,24) (17,21) (18,19) (18,20) (18,23) (18,22) (19,20) (19,23) (19,22) (20,23) (20,22) (21,24) (22,23)\nQ: Is there a path between node 22 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1528"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,14) (0,12) (1,20) (1,12) (2,13) (2,18) (3,17) (4,20) (7,21) (8,18) (9,20) (9,15) (10,13) (10,19) (13,18) (14,16) (14,15) (15,20)\nQ: Is there a path between node 1 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1529"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,11) (0,2) (0,7) (0,8) (0,16) (0,15) (1,11) (1,2) (1,7) (1,8) (1,16) (1,15) (1,14) (2,4) (2,11) (2,5) (2,7) (2,12) (2,16) (2,15) (3,13) (3,10) (4,6) (4,5) (4,7) (4,8) (4,12) (4,16) (4,15) (4,14) (5,6) (5,7) (5,8) (5,12) (5,16) (5,14) (6,11) (6,7) (6,8) (6,12) (6,16) (6,15) (6,14) (7,11) (7,8) (7,16) (7,14) (8,11) (8,12) (8,16) (11,12) (11,16) (11,15) (11,14) (12,14) (14,16) (14,15)\nQ: Is there a path between node 11 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1530"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,21) (0,17) (0,7) (0,29) (1,20) (2,32) (2,6) (2,13) (3,22) (3,23) (3,8) (4,30) (4,31) (6,23) (6,16) (6,32) (7,19) (8,14) (8,23) (8,16) (8,32) (8,13) (9,24) (9,17) (9,29) (13,14) (13,32) (14,16) (14,32) (16,20) (16,28) (17,24) (20,28) (21,29) (24,29) (27,30) (30,31)\nQ: Is there a path between node 2 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1531"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,2) (1,5) (1,2) (2,5) (2,10) (3,10) (3,4) (3,8) (4,5) (5,10) (5,8) (7,11) (8,10) (9,11)\nQ: Is there a path between node 9 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1532"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,4) (1,5)\nQ: Is there a path between node 3 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1533"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,11) (0,5) (0,9) (0,6) (1,2) (1,7) (1,3) (1,10) (1,8) (2,7) (2,3) (2,10) (2,8) (3,7) (3,10) (3,8) (4,11) (4,5) (4,9) (4,6) (5,11) (5,9) (5,6) (6,11) (6,9) (7,10) (7,8) (8,10) (9,11)\nQ: Is there a path between node 5 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1534"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,12) (1,25) (1,2) (1,10) (1,12) (1,3) (2,8) (2,22) (2,25) (2,26) (2,19) (2,11) (2,12) (2,7) (2,21) (3,25) (3,26) (3,10) (3,27) (3,21) (5,24) (5,6) (6,23) (6,9) (7,22) (7,25) (7,11) (8,20) (8,22) (8,25) (8,26) (8,27) (9,24) (10,14) (10,25) (10,13) (10,27) (10,21) (11,22) (11,12) (11,17) (11,21) (12,19) (12,18) (12,17) (12,27) (12,21) (13,17) (13,21) (14,17) (14,21) (15,23) (15,24) (16,22) (17,22) (17,25) (17,19) (18,20) (18,26) (18,21) (19,22) (19,26) (19,27) (20,27) (22,25) (25,26)\nQ: Is there a path between node 0 and node 18?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1535"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,21) (0,8) (0,11) (0,16) (0,13) (0,10) (0,20) (0,6) (0,4) (1,14) (1,17) (1,18) (1,5) (1,19) (1,2) (2,22) (2,14) (2,5) (3,8) (3,11) (3,10) (3,12) (3,6) (4,11) (4,13) (4,20) (4,12) (5,22) (5,14) (5,17) (5,18) (5,9) (5,19) (6,8) (6,11) (6,16) (6,13) (6,10) (6,20) (6,12) (7,15) (8,11) (8,13) (8,10) (8,20) (8,12) (9,22) (9,14) (9,17) (9,18) (9,19) (10,21) (10,13) (11,16) (11,13) (11,20) (11,12) (12,21) (12,16) (12,13) (12,20) (13,21) (13,16) (13,20) (14,22) (14,18) (16,21) (16,20) (17,22) (17,18) (17,19) (18,19) (20,21)\nQ: Is there a path between node 12 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1536"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,26) (2,26) (2,30) (2,6) (3,19) (4,29) (4,8) (4,11) (4,9) (5,25) (6,30) (6,19) (6,13) (6,25) (7,23) (7,29) (7,10) (7,28) (7,14) (8,23) (8,15) (8,27) (8,18) (8,11) (8,28) (8,9) (9,23) (9,29) (9,15) (9,18) (9,12) (10,15) (11,29) (11,27) (11,28) (11,14) (12,27) (13,16) (13,26) (14,17) (15,29) (15,21) (15,28) (16,25) (17,23) (17,29) (17,18) (19,20) (19,22) (20,22) (21,27) (21,28) (22,26) (23,29) (23,28) (24,26) (24,30) (25,26) (25,30) (27,28)\nQ: Is there a path between node 5 and node 14?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1537"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (1,3) (1,2) (1,6) (2,5) (2,6) (3,5) (5,6)\nQ: Is there a path between node 5 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1538"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,30) (0,27) (0,33) (0,11) (0,5) (0,12) (0,20) (0,7) (0,28) (0,17) (0,6) (0,4) (0,32) (0,13) (0,3) (0,22) (0,31) (1,25) (1,29) (1,30) (1,27) (1,33) (1,2) (1,5) (1,12) (1,20) (1,28) (1,18) (1,16) (1,24) (1,6) (1,13) (1,3) (1,22) (1,31) (2,25) (2,23) (2,29) (2,30) (2,27) (2,33) (2,11) (2,5) (2,12) (2,7) (2,18) (2,16) (2,17) (2,24) (2,13) (2,22) (2,15) (3,25) (3,23) (3,29) (3,30) (3,12) (3,7) (3,18) (3,16) (3,24) (3,4) (3,13) (3,22) (3,31) (4,23) (4,29) (4,27) (4,33) (4,11) (4,5) (4,7) (4,18) (4,24) (4,32) (4,15) (4,31) (5,25) (5,23) (5,30) (5,27) (5,33) (5,11) (5,12) (5,20) (5,7) (5,28) (5,24) (5,6) (5,32) (5,13) (5,22) (5,15) (5,31) (6,25) (6,23) (6,30) (6,27) (6,33) (6,12) (6,20) (6,7) (6,18) (6,24) (6,32) (6,13) (7,25) (7,30) (7,27) (7,33) (7,20) (7,28) (7,18) (7,24) (7,32) (7,13) (7,22) (7,15) (7,31) (8,14) (8,26) (8,19) (9,14) (9,26) (9,19) (9,21) (9,10) (10,14) (10,26) (10,19) (11,23) (11,29) (11,30) (11,27) (11,33) (11,20) (11,18) (11,16) (11,17) (11,32) (11,13) (11,22) (11,15) (11,31) (12,25) (12,23) (12,29) (12,27) (12,33) (12,28) (12,16) (12,24) (12,13) (12,22) (12,15) (12,31) (13,25) (13,23) (13,29) (13,27) (13,33) (13,20) (13,28) (13,18) (13,16) (13,17) (13,24) (13,32) (13,15) (13,31) (14,26) (15,25) (15,23) (15,29) (15,30) (15,33) (15,16) (15,17) (15,24) (15,22) (15,31) (16,25) (16,23) (16,29) (16,30) (16,27) (16,28) (16,17) (16,24) (16,32) (16,22) (17,25) (17,23) (17,29) (17,33) (17,20) (17,18) (17,24) (17,31) (18,25) (18,29) (18,30) (18,33) (18,28) (18,24) (18,31) (20,25) (20,23) (20,30) (20,24) (20,32) (20,22) (20,31) (21,26) (22,25) (22,29) (22,30) (22,28) (22,24) (23,25) (23,29) (23,27) (23,28) (23,24) (23,32) (24,25) (24,29) (24,27) (24,33) (24,28) (24,31) (25,29) (25,30) (25,27) (25,28) (25,32) (25,31) (27,29) (27,30) (27,33) (27,28) (28,29) (28,30) (28,33) (28,32) (28,31) (29,30) (29,33) (29,32) (29,31) (30,33) (30,32) (30,31) (31,33) (31,32) (32,33)\nQ: Is there a path between node 9 and node 18?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1539"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,6) (2,7) (2,6) (2,4) (5,7) (6,8)\nQ: Is there a path between node 7 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1540"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,9) (0,13) (0,3) (0,1) (0,2) (0,7) (0,8) (0,11) (1,14) (1,13) (1,8) (1,10) (1,11) (1,5) (2,9) (2,13) (2,3) (2,7) (2,8) (2,10) (3,14) (3,9) (3,13) (3,8) (3,11) (3,5) (4,6) (4,12) (5,14) (5,9) (5,7) (5,8) (5,10) (5,11) (6,12) (7,14) (7,13) (7,8) (7,10) (8,14) (8,9) (8,10) (9,14) (9,13) (10,14) (10,13) (11,14) (13,14)\nQ: Is there a path between node 11 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1541"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,26) (2,26) (2,30) (2,6) (3,19) (4,29) (4,8) (4,11) (4,9) (5,25) (6,30) (6,19) (6,13) (6,25) (7,23) (7,29) (7,10) (7,28) (7,14) (8,23) (8,15) (8,27) (8,18) (8,11) (8,28) (8,9) (9,23) (9,29) (9,15) (9,18) (9,12) (10,15) (11,29) (11,27) (11,28) (11,14) (12,27) (13,16) (13,26) (14,17) (15,29) (15,21) (15,28) (16,25) (17,23) (17,29) (17,18) (19,20) (19,22) (20,22) (21,27) (21,28) (22,26) (23,29) (23,28) (24,26) (24,30) (25,26) (25,30) (27,28)\nQ: Is there a path between node 7 and node 30?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1542"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,8) (1,5) (2,3) (3,5) (3,11) (4,8) (5,9) (5,7) (5,10) (6,11)\nQ: Is there a path between node 3 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1543"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,4) (0,9) (0,12) (0,11) (0,5) (1,6) (1,17) (1,8) (1,15) (1,3) (1,2) (1,18) (1,19) (1,13) (1,14) (1,10) (2,6) (2,17) (2,8) (2,15) (2,3) (2,18) (2,19) (2,13) (2,14) (2,10) (3,6) (3,17) (3,8) (3,15) (3,18) (3,19) (3,13) (3,14) (3,10) (4,7) (4,9) (4,12) (4,11) (4,5) (5,7) (5,9) (5,12) (5,11) (6,17) (6,8) (6,15) (6,18) (6,19) (6,13) (6,14) (6,10) (7,9) (7,12) (7,11) (8,17) (8,15) (8,18) (8,19) (8,13) (8,14) (8,10) (9,12) (9,11) (10,17) (10,15) (10,18) (10,19) (10,13) (10,14) (11,12) (13,17) (13,15) (13,18) (13,19) (13,14) (14,17) (14,15) (14,18) (14,19) (15,17) (15,18) (15,19) (17,18) (17,19) (18,19)\nQ: Is there a path between node 10 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1544"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,19) (0,17) (0,3) (0,10) (0,14) (1,7) (1,8) (1,15) (1,13) (2,9) (2,12) (2,18) (2,4) (3,6) (3,19) (3,17) (3,16) (3,10) (3,14) (4,12) (4,18) (5,9) (5,18) (6,19) (6,17) (6,16) (6,14) (6,20) (7,8) (7,15) (7,13) (9,12) (9,18) (10,16) (10,14) (10,20) (11,15) (12,18) (13,15) (14,19) (14,17) (14,20) (16,19) (16,17) (17,20) (19,20)\nQ: Is there a path between node 5 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1545"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,9) (1,8) (1,4) (2,8) (2,4) (2,3) (3,7) (3,6) (3,10) (3,12) (3,11) (4,10) (4,12) (6,14) (6,8) (6,10) (7,14) (7,11) (8,14) (8,12) (10,14) (11,14) (12,14)\nQ: Is there a path between node 5 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1546"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (1,18) (1,8) (1,4) (2,15) (2,18) (2,11) (2,23) (2,4) (3,12) (3,5) (4,23) (4,25) (5,12) (5,17) (6,22) (6,13) (7,18) (7,23) (7,8) (9,17) (10,19) (10,17) (11,15) (12,24) (14,20) (14,22) (15,18) (16,20) (16,22) (20,22) (21,22) (23,25)\nQ: Is there a path between node 21 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1547"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (1,20) (2,11) (2,23) (2,14) (2,8) (3,17) (3,14) (3,16) (4,7) (4,16) (4,8) (4,24) (5,6) (5,10) (5,20) (6,20) (7,12) (7,16) (7,8) (7,24) (8,12) (8,23) (8,21) (9,18) (10,18) (10,20) (11,17) (11,19) (11,24) (12,22) (12,17) (12,14) (13,24) (14,23) (14,24) (15,17) (15,19) (15,24) (16,22) (16,19) (17,19) (17,24) (19,24) (23,24)\nQ: Is there a path between node 10 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1548"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,5) (0,1) (0,9) (0,3) (0,4) (1,6) (1,5) (1,9) (1,3) (1,4) (2,7) (2,8) (2,10) (3,6) (3,5) (3,9) (3,4) (4,6) (4,5) (4,9) (5,6) (5,9) (6,9) (7,8) (7,10) (8,10)\nQ: Is there a path between node 0 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1549"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (0,3) (0,4) (0,1) (1,2) (1,5) (1,6) (1,3) (1,4) (2,5) (2,6) (2,3) (2,4) (3,5) (3,6) (3,4) (4,5) (4,6) (5,6)\nQ: Is there a path between node 2 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1550"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,1) (0,3) (1,5) (1,3) (2,4) (3,5)\nQ: Is there a path between node 5 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1551"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,30) (0,6) (0,12) (1,15) (2,17) (2,4) (3,25) (3,30) (3,12) (4,18) (4,16) (4,20) (4,22) (4,28) (4,8) (4,17) (5,12) (5,11) (6,19) (7,9) (7,10) (8,22) (8,28) (8,21) (9,23) (10,12) (10,11) (11,30) (11,19) (11,12) (12,25) (12,19) (13,27) (13,26) (15,26) (16,18) (16,29) (16,20) (16,24) (16,22) (16,28) (16,17) (17,22) (17,28) (17,21) (18,29) (18,20) (18,24) (18,22) (19,30) (20,22) (20,28) (21,24) (24,28) (25,30)\nQ: Is there a path between node 15 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1552"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (1,24) (1,13) (1,7) (2,24) (2,15) (2,18) (2,8) (2,13) (2,7) (3,23) (3,6) (5,20) (5,14) (6,11) (6,23) (7,12) (7,10) (7,21) (7,8) (7,13) (8,10) (8,15) (8,18) (8,22) (8,13) (9,21) (9,13) (10,12) (10,15) (10,13) (12,24) (13,24) (13,22) (14,20) (15,24) (17,24) (19,20) (21,24)\nQ: Is there a path between node 17 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1553"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,4) (0,9) (0,1) (0,11) (0,2) (1,10) (1,6) (1,9) (1,15) (1,13) (2,12) (2,9) (2,17) (2,15) (3,4) (3,6) (3,11) (4,12) (4,9) (4,11) (6,10) (6,12) (6,9) (6,15) (6,13) (8,12) (8,9) (8,15) (8,13) (9,10) (9,11) (10,13) (10,11) (11,13) (12,13) (14,16)\nQ: Is there a path between node 2 and node 13?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1554"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (0,3) (0,4) (0,1) (1,2) (1,5) (1,6) (1,3) (1,4) (2,5) (2,6) (2,3) (2,4) (3,5) (3,6) (3,4) (4,5) (4,6) (5,6)\nQ: Is there a path between node 7 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1555"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,4) (0,1) (0,5) (0,24) (0,3) (0,21) (0,19) (0,9) (0,15) (0,20) (0,27) (0,13) (1,24) (1,21) (1,31) (1,10) (1,7) (1,20) (1,27) (1,13) (2,6) (2,5) (2,24) (2,3) (2,21) (2,19) (2,9) (2,31) (2,15) (2,7) (2,27) (2,13) (3,6) (3,4) (3,5) (3,22) (3,24) (3,21) (3,19) (3,9) (3,31) (3,18) (3,7) (3,20) (4,5) (4,21) (4,19) (4,9) (4,31) (4,7) (4,20) (4,27) (4,13) (5,6) (5,22) (5,24) (5,21) (5,9) (5,31) (5,10) (5,15) (5,18) (5,20) (5,27) (5,13) (6,22) (6,21) (6,19) (6,9) (6,31) (6,10) (6,15) (6,18) (6,7) (6,27) (6,13) (7,22) (7,9) (7,10) (7,15) (7,18) (7,20) (7,27) (7,13) (8,16) (8,11) (8,28) (8,12) (8,25) (8,30) (8,14) (8,32) (8,29) (9,22) (9,24) (9,21) (9,19) (9,31) (9,10) (9,15) (9,18) (9,20) (10,22) (10,19) (10,31) (10,15) (10,20) (10,27) (10,13) (11,16) (11,28) (11,26) (11,23) (11,30) (11,14) (11,32) (11,17) (12,16) (12,28) (12,23) (12,30) (12,14) (12,33) (12,32) (12,17) (12,29) (13,22) (13,24) (13,21) (13,19) (13,15) (13,18) (13,20) (14,28) (14,26) (14,23) (14,25) (14,33) (14,32) (14,29) (15,22) (15,24) (15,21) (15,19) (15,20) (15,27) (16,26) (16,25) (16,30) (16,33) (16,32) (16,17) (16,29) (17,28) (17,26) (17,25) (17,30) (17,33) (17,32) (17,29) (18,24) (18,19) (18,31) (19,22) (19,24) (19,31) (19,20) (19,27) (20,21) (20,31) (20,27) (21,31) (23,28) (23,26) (23,25) (23,30) (24,31) (24,27) (25,26) (25,30) (25,33) (25,32) (25,29) (26,28) (26,33) (26,32) (28,30) (28,29) (29,30) (29,33) (29,32) (30,32)\nQ: Is there a path between node 8 and node 21?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1556"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,6) (0,4) (1,3) (1,7) (1,2) (2,3) (3,9) (4,6) (5,9) (6,8) (7,9)\nQ: Is there a path between node 9 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1557"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (0,11) (0,8) (0,17) (0,13) (0,6) (0,3) (0,15) (0,7) (1,14) (1,19) (1,9) (1,21) (1,12) (1,22) (1,4) (1,18) (1,5) (1,10) (1,20) (2,16) (3,23) (3,11) (3,8) (3,17) (3,13) (3,6) (3,15) (3,7) (4,14) (4,19) (4,9) (4,21) (4,12) (4,22) (4,18) (4,5) (4,10) (4,20) (5,14) (5,19) (5,9) (5,21) (5,12) (5,22) (5,18) (5,10) (5,20) (6,23) (6,11) (6,8) (6,17) (6,13) (6,15) (6,7) (7,23) (7,11) (7,8) (7,17) (7,13) (7,15) (8,23) (8,11) (8,17) (8,13) (8,15) (9,14) (9,19) (9,21) (9,12) (9,22) (9,18) (9,10) (9,20) (10,14) (10,19) (10,21) (10,12) (10,22) (10,18) (10,20) (11,23) (11,17) (11,13) (11,15) (12,14) (12,19) (12,21) (12,22) (12,18) (12,20) (13,23) (13,17) (13,15) (14,19) (14,21) (14,22) (14,18) (14,20) (15,23) (15,17) (17,23) (18,19) (18,21) (18,22) (18,20) (19,21) (19,22) (19,20) (20,21) (20,22) (21,22)\nQ: Is there a path between node 7 and node 22?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1558"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (0,11) (0,8) (0,17) (0,13) (0,6) (0,3) (0,15) (0,7) (1,14) (1,19) (1,9) (1,21) (1,12) (1,22) (1,4) (1,18) (1,5) (1,10) (1,20) (2,16) (3,23) (3,11) (3,8) (3,17) (3,13) (3,6) (3,15) (3,7) (4,14) (4,19) (4,9) (4,21) (4,12) (4,22) (4,18) (4,5) (4,10) (4,20) (5,14) (5,19) (5,9) (5,21) (5,12) (5,22) (5,18) (5,10) (5,20) (6,23) (6,11) (6,8) (6,17) (6,13) (6,15) (6,7) (7,23) (7,11) (7,8) (7,17) (7,13) (7,15) (8,23) (8,11) (8,17) (8,13) (8,15) (9,14) (9,19) (9,21) (9,12) (9,22) (9,18) (9,10) (9,20) (10,14) (10,19) (10,21) (10,12) (10,22) (10,18) (10,20) (11,23) (11,17) (11,13) (11,15) (12,14) (12,19) (12,21) (12,22) (12,18) (12,20) (13,23) (13,17) (13,15) (14,19) (14,21) (14,22) (14,18) (14,20) (15,23) (15,17) (17,23) (18,19) (18,21) (18,22) (18,20) (19,21) (19,22) (19,20) (20,21) (20,22) (21,22)\nQ: Is there a path between node 0 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1559"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,10) (0,17) (0,4) (0,21) (0,1) (0,2) (0,18) (0,7) (0,19) (0,11) (0,3) (0,5) (0,14) (1,6) (1,10) (1,17) (1,21) (1,16) (1,18) (1,7) (1,8) (1,11) (2,6) (2,10) (2,17) (2,4) (2,21) (2,16) (2,13) (2,18) (2,7) (2,8) (2,19) (2,3) (2,5) (3,6) (3,10) (3,17) (3,4) (3,21) (3,16) (3,13) (3,18) (3,7) (3,19) (4,10) (4,16) (4,18) (4,7) (4,8) (4,19) (4,5) (5,6) (5,16) (5,13) (5,18) (5,7) (5,8) (5,19) (5,14) (6,10) (6,17) (6,21) (6,16) (6,13) (6,18) (6,7) (6,19) (6,11) (6,14) (7,10) (7,17) (7,21) (7,16) (7,13) (7,18) (7,8) (7,19) (7,11) (7,14) (8,10) (8,17) (8,21) (8,16) (8,13) (8,18) (8,19) (8,11) (9,20) (10,17) (10,21) (10,13) (10,18) (10,19) (10,11) (10,14) (11,17) (11,16) (11,13) (11,18) (11,19) (12,15) (13,21) (13,16) (13,18) (13,19) (13,14) (14,17) (14,21) (14,16) (14,18) (14,19) (16,17) (16,21) (16,18) (17,18) (18,21) (18,19) (19,21)\nQ: Is there a path between node 14 and node 15?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1560"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,10) (0,18) (0,21) (0,30) (0,28) (0,15) (1,27) (1,24) (1,22) (1,32) (1,14) (1,5) (2,29) (2,10) (2,18) (2,21) (2,19) (2,30) (2,16) (2,28) (2,15) (3,24) (3,13) (3,22) (3,20) (3,5) (4,17) (4,11) (4,6) (4,26) (4,23) (4,31) (4,25) (5,27) (5,13) (5,22) (5,20) (5,32) (5,14) (6,17) (6,9) (6,23) (6,31) (6,25) (7,29) (7,10) (7,18) (7,19) (7,30) (7,16) (7,15) (8,17) (8,11) (8,26) (8,23) (8,31) (9,17) (9,26) (9,23) (9,31) (9,25) (10,29) (10,18) (10,21) (10,30) (10,28) (10,15) (11,17) (11,26) (11,23) (12,27) (12,24) (12,13) (12,22) (12,32) (13,27) (13,24) (13,22) (13,20) (13,32) (13,14) (14,27) (14,22) (14,32) (15,29) (15,18) (15,21) (15,19) (15,28) (16,29) (16,21) (16,19) (16,28) (17,23) (18,29) (18,21) (18,30) (18,28) (19,29) (19,21) (19,30) (19,28) (20,24) (20,22) (20,32) (21,29) (21,30) (21,28) (22,27) (22,24) (22,32) (23,31) (24,27) (25,26) (26,31) (28,30)\nQ: Is there a path between node 30 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1561"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,18) (0,15) (0,12) (0,5) (1,24) (2,21) (2,23) (2,9) (2,15) (2,19) (3,23) (3,15) (3,8) (3,16) (5,21) (5,22) (5,6) (5,19) (5,8) (5,10) (5,16) (6,14) (6,22) (6,9) (6,12) (6,17) (9,23) (9,22) (9,20) (9,10) (10,22) (10,18) (10,19) (11,24) (12,14) (13,14) (13,21) (13,23) (13,18) (13,15) (14,21) (14,18) (14,15) (14,16) (15,20) (15,17) (17,23) (17,22) (17,18) (17,20) (17,19) (18,19) (19,20) (21,23)\nQ: Is there a path between node 12 and node 16?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1562"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,13) (0,8) (0,18) (0,25) (0,14) (0,17) (0,21) (1,13) (1,26) (1,14) (1,20) (1,17) (1,24) (1,6) (2,8) (2,18) (2,9) (2,26) (2,14) (2,10) (2,15) (3,16) (3,12) (4,13) (4,8) (4,18) (4,25) (4,6) (5,19) (5,13) (5,10) (5,20) (5,22) (5,17) (5,6) (6,8) (6,18) (6,9) (6,26) (6,14) (6,17) (6,21) (6,15) (6,23) (7,25) (7,14) (7,22) (7,24) (7,15) (7,23) (8,13) (8,25) (8,24) (8,23) (9,25) (9,27) (9,26) (9,14) (9,17) (9,24) (9,23) (10,19) (10,13) (10,25) (10,22) (11,12) (12,16) (13,19) (13,18) (13,21) (14,19) (14,18) (14,22) (15,19) (15,25) (15,23) (17,25) (17,22) (17,21) (17,24) (18,21) (18,24) (19,26) (19,22) (19,24) (19,23) (20,25) (20,26) (20,24) (20,23) (21,27) (21,23) (22,25) (22,26) (22,23) (25,27) (25,26)\nQ: Is there a path between node 22 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1563"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,3) (0,14) (1,8) (1,6) (1,14) (2,6) (2,12) (2,18) (3,8) (3,6) (3,12) (3,18) (4,12) (4,9) (4,14) (5,15) (5,16) (5,7) (6,8) (6,12) (6,14) (7,10) (9,11) (9,18) (15,17) (15,16)\nQ: Is there a path between node 2 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1564"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,21) (0,14) (0,1) (0,22) (0,16) (0,19) (0,5) (0,10) (0,20) (0,11) (0,24) (0,13) (1,21) (1,9) (1,3) (1,14) (1,22) (1,10) (1,20) (1,12) (1,11) (1,24) (1,13) (1,23) (2,8) (2,4) (2,18) (2,15) (3,9) (3,14) (3,16) (3,19) (3,7) (3,6) (3,5) (3,10) (3,11) (4,8) (4,17) (4,18) (4,15) (5,9) (5,14) (5,22) (5,7) (5,6) (5,10) (5,20) (5,12) (5,11) (5,13) (5,23) (6,21) (6,9) (6,22) (6,19) (6,7) (6,20) (6,12) (6,11) (6,13) (6,23) (7,21) (7,9) (7,14) (7,16) (7,19) (7,10) (7,20) (7,12) (7,11) (7,24) (7,13) (7,23) (8,17) (8,18) (8,15) (9,21) (9,16) (9,10) (9,20) (9,12) (9,11) (9,24) (9,13) (9,23) (10,22) (10,19) (10,12) (10,11) (10,13) (10,23) (11,21) (11,22) (11,19) (11,20) (11,12) (11,24) (11,13) (11,23) (12,21) (12,14) (12,22) (12,20) (12,24) (12,13) (12,23) (13,21) (13,14) (13,22) (13,16) (13,20) (13,23) (14,21) (14,16) (14,20) (14,24) (14,23) (15,18) (16,21) (16,22) (16,19) (16,20) (16,24) (16,23) (17,18) (19,21) (19,20) (19,24) (19,23) (20,21) (20,24) (20,23) (21,24) (21,23) (22,23) (23,24)\nQ: Is there a path between node 19 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1565"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,13) (0,6) (0,5) (0,15) (0,14) (0,1) (0,10) (0,8) (0,7) (0,2) (0,11) (0,3) (1,12) (1,13) (1,6) (1,5) (1,15) (1,14) (1,10) (1,8) (1,7) (1,2) (1,11) (1,3) (2,12) (2,13) (2,6) (2,5) (2,15) (2,14) (2,10) (2,8) (2,7) (2,11) (2,3) (3,12) (3,13) (3,6) (3,5) (3,15) (3,14) (3,10) (3,8) (3,7) (3,11) (4,9) (5,12) (5,13) (5,6) (5,15) (5,14) (5,10) (5,8) (5,7) (5,11) (6,12) (6,13) (6,15) (6,14) (6,10) (6,8) (6,7) (6,11) (7,12) (7,13) (7,15) (7,14) (7,10) (7,8) (7,11) (8,12) (8,13) (8,15) (8,14) (8,10) (8,11) (10,12) (10,13) (10,15) (10,14) (10,11) (11,12) (11,13) (11,15) (11,14) (12,13) (12,15) (12,14) (13,15) (13,14) (14,15)\nQ: Is there a path between node 3 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1566"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,10) (0,17) (0,15) (0,4) (0,12) (0,24) (0,9) (0,3) (0,13) (0,23) (0,7) (0,19) (0,16) (0,6) (0,25) (0,8) (1,10) (1,17) (1,4) (1,12) (1,24) (1,3) (1,13) (1,23) (1,26) (1,22) (1,19) (1,6) (1,14) (1,25) (1,8) (1,20) (2,10) (2,17) (2,11) (2,4) (2,24) (2,9) (2,3) (2,13) (2,23) (2,26) (2,7) (2,22) (2,19) (2,6) (2,14) (2,25) (2,8) (3,10) (3,17) (3,11) (3,15) (3,4) (3,12) (3,24) (3,9) (3,13) (3,26) (3,7) (3,19) (3,16) (3,14) (3,25) (3,8) (3,20) (4,10) (4,17) (4,11) (4,15) (4,12) (4,24) (4,9) (4,7) (4,19) (4,16) (4,6) (4,25) (4,20) (5,18) (6,10) (6,17) (6,15) (6,12) (6,24) (6,9) (6,23) (6,7) (6,16) (6,25) (6,8) (7,10) (7,11) (7,15) (7,12) (7,13) (7,22) (7,19) (7,16) (7,25) (7,8) (7,20) (8,10) (8,17) (8,11) (8,15) (8,12) (8,24) (8,9) (8,23) (8,22) (8,19) (8,16) (8,14) (8,25) (8,20) (9,10) (9,17) (9,11) (9,12) (9,24) (9,13) (9,23) (9,26) (9,22) (9,19) (9,16) (9,20) (10,17) (10,11) (10,15) (10,12) (10,24) (10,13) (10,23) (10,26) (10,19) (10,14) (10,20) (11,15) (11,12) (11,24) (11,13) (11,23) (11,26) (11,19) (11,16) (11,14) (11,20) (12,15) (12,24) (12,23) (12,22) (12,19) (12,16) (12,14) (12,25) (12,20) (13,15) (13,24) (13,23) (13,19) (13,16) (13,14) (13,25) (13,20) (14,17) (14,15) (14,24) (14,23) (14,26) (14,22) (14,19) (14,16) (14,25) (14,20) (15,17) (15,24) (15,23) (15,26) (15,16) (15,20) (16,24) (16,23) (16,26) (16,19) (16,25) (16,20) (17,23) (17,20) (18,21) (19,23) (19,22) (19,25) (19,20) (20,24) (20,23) (20,22) (20,25) (22,26) (22,25) (23,24) (23,26) (23,25) (24,26) (24,25) (25,26)\nQ: Is there a path between node 10 and node 16?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1567"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,8) (0,4) (0,5) (0,13) (0,2) (0,17) (1,15) (1,8) (1,3) (1,4) (1,5) (1,13) (1,17) (2,15) (2,8) (2,3) (2,4) (2,5) (2,13) (3,8) (3,5) (3,17) (4,15) (4,13) (4,17) (5,15) (5,8) (5,17) (6,14) (6,7) (6,10) (6,16) (6,9) (6,12) (7,14) (7,16) (7,9) (8,13) (9,14) (9,10) (9,11) (9,16) (9,12) (10,14) (10,12) (11,14) (11,12) (12,14) (12,16) (13,17) (15,17)\nQ: Is there a path between node 17 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1568"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,2) (0,1) (0,4) (1,3) (1,2) (1,4) (1,6) (2,3) (2,4) (2,5) (3,4) (3,6) (4,6) (5,6)\nQ: Is there a path between node 2 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1569"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,13) (2,25) (2,28) (2,21) (2,5) (2,23) (3,22) (3,8) (3,6) (3,19) (3,21) (3,31) (3,15) (5,20) (5,16) (5,21) (5,23) (6,18) (6,17) (6,23) (7,10) (8,21) (9,24) (12,22) (12,18) (13,30) (13,27) (14,26) (15,16) (15,19) (15,31) (16,22) (16,20) (16,19) (17,20) (17,21) (17,31) (18,22) (18,25) (18,20) (18,21) (18,23) (19,25) (19,28) (20,28) (20,21) (21,25) (22,25) (22,28) (23,28) (27,29) (29,30) (30,32)\nQ: Is there a path between node 14 and node 24?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1570"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,1) (3,4)\nQ: Is there a path between node 0 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1571"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,6) (0,2) (0,5) (1,7) (1,16) (1,14) (1,17) (1,3) (1,9) (1,13) (1,10) (2,11) (2,6) (2,5) (3,7) (3,16) (3,14) (3,17) (3,9) (3,13) (3,10) (4,8) (4,15) (4,12) (5,11) (5,6) (6,11) (7,16) (7,14) (7,17) (7,9) (7,13) (7,10) (8,15) (8,12) (9,16) (9,14) (9,17) (9,13) (9,10) (10,16) (10,14) (10,17) (10,13) (12,15) (13,16) (13,14) (13,17) (14,16) (14,17) (16,17)\nQ: Is there a path between node 1 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1572"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (0,1) (0,19) (0,15) (0,20) (0,9) (0,21) (0,3) (0,22) (0,32) (0,24) (0,14) (0,11) (0,17) (0,5) (0,34) (0,4) (0,26) (0,10) (0,8) (1,27) (1,23) (1,30) (1,6) (1,19) (1,20) (1,2) (1,9) (1,21) (1,3) (1,22) (1,24) (1,14) (1,11) (1,17) (1,5) (1,4) (1,26) (1,8) (2,27) (2,30) (2,6) (2,19) (2,20) (2,9) (2,21) (2,3) (2,22) (2,32) (2,7) (2,11) (2,17) (2,5) (2,34) (2,4) (2,26) (2,12) (2,10) (3,27) (3,23) (3,30) (3,6) (3,19) (3,15) (3,20) (3,9) (3,22) (3,24) (3,14) (3,34) (3,4) (3,12) (3,10) (3,8) (3,28) (4,27) (4,23) (4,30) (4,19) (4,15) (4,20) (4,9) (4,21) (4,32) (4,24) (4,14) (4,7) (4,11) (4,17) (4,5) (4,26) (4,12) (4,8) (4,28) (5,30) (5,19) (5,9) (5,21) (5,24) (5,7) (5,11) (5,17) (5,34) (5,12) (6,27) (6,23) (6,30) (6,19) (6,20) (6,9) (6,21) (6,22) (6,32) (6,24) (6,14) (6,7) (6,11) (6,17) (6,34) (6,26) (6,8) (6,28) (7,23) (7,30) (7,19) (7,15) (7,20) (7,21) (7,32) (7,24) (7,11) (7,17) (7,34) (7,12) (7,10) (7,8) (7,28) (8,23) (8,15) (8,20) (8,24) (8,14) (8,11) (8,17) (8,34) (8,26) (8,12) (8,10) (8,28) (9,30) (9,19) (9,15) (9,20) (9,22) (9,32) (9,24) (9,11) (9,34) (9,12) (9,10) (9,28) (10,27) (10,23) (10,30) (10,19) (10,21) (10,32) (10,24) (10,26) (10,12) (11,27) (11,30) (11,19) (11,20) (11,21) (11,22) (11,32) (11,24) (11,14) (11,17) (11,34) (11,12) (12,27) (12,30) (12,19) (12,20) (12,22) (12,32) (12,24) (12,14) (12,17) (12,34) (12,28) (14,27) (14,23) (14,30) (14,19) (14,15) (14,21) (14,22) (14,32) (14,17) (14,34) (14,28) (15,19) (15,20) (15,21) (15,22) (15,32) (15,24) (15,34) (15,26) (15,28) (16,33) (16,29) (16,18) (16,31) (17,27) (17,23) (17,30) (17,19) (17,20) (17,21) (17,22) (17,32) (17,24) (17,34) (17,28) (18,33) (18,31) (18,25) (19,27) (19,23) (19,30) (19,20) (19,22) (19,32) (19,34) (19,26) (19,28) (20,23) (20,30) (20,21) (20,22) (20,32) (20,24) (20,34) (20,26) (21,27) (21,23) (21,30) (21,22) (21,32) (21,24) (21,34) (21,26) (21,28) (22,27) (22,23) (22,24) (22,34) (22,26) (22,28) (23,32) (23,26) (23,28) (24,27) (24,32) (24,34) (24,26) (25,33) (26,30) (26,32) (26,34) (27,30) (27,32) (27,28) (28,30) (28,32) (28,34) (29,33) (29,31) (31,33) (32,34)\nQ: Is there a path between node 2 and node 22?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1573"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,1) (1,12) (1,15) (2,9) (2,6) (3,10) (3,17) (3,15) (5,7) (6,10) (6,9) (6,11) (7,13) (8,17) (8,16) (10,15) (11,12) (15,17)\nQ: Is there a path between node 9 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1574"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,27) (0,23) (0,4) (0,20) (0,17) (0,6) (1,5) (1,22) (1,11) (1,19) (1,24) (1,2) (1,15) (1,8) (1,30) (1,9) (1,28) (1,18) (2,5) (2,22) (2,24) (2,15) (2,8) (2,30) (2,9) (2,28) (2,18) (3,26) (3,13) (4,21) (4,29) (4,23) (4,20) (4,17) (4,6) (5,22) (5,19) (5,24) (5,14) (5,30) (5,28) (5,18) (6,21) (6,29) (6,27) (6,23) (6,20) (6,17) (7,26) (7,10) (7,13) (7,16) (7,12) (8,11) (8,24) (8,14) (8,30) (8,9) (8,28) (8,18) (9,22) (9,11) (9,19) (9,15) (9,28) (10,16) (10,12) (11,15) (11,30) (11,28) (11,18) (12,13) (12,16) (13,26) (13,16) (13,25) (14,22) (14,19) (14,15) (14,30) (15,19) (15,30) (15,28) (15,18) (16,26) (16,25) (17,29) (17,23) (18,19) (18,24) (18,28) (19,30) (19,28) (20,21) (20,27) (21,29) (21,27) (21,23) (22,24) (22,28) (23,27) (24,30) (24,28) (25,26) (28,30)\nQ: Is there a path between node 0 and node 26?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1575"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,2) (0,8) (0,4) (0,7) (0,3) (0,1) (1,5) (1,2) (1,8) (1,4) (1,7) (1,3) (2,5) (2,8) (2,4) (2,7) (2,3) (3,5) (3,8) (3,4) (3,7) (4,5) (4,8) (4,7) (5,8) (5,7) (6,9) (7,8)\nQ: Is there a path between node 1 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1576"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,13) (0,12) (0,14) (0,8) (0,3) (0,6) (0,2) (0,9) (0,5) (1,10) (1,7) (1,11) (2,4) (2,13) (2,12) (2,14) (2,8) (2,3) (2,6) (2,9) (2,5) (3,4) (3,13) (3,12) (3,14) (3,8) (3,6) (3,9) (3,5) (4,13) (4,12) (4,14) (4,8) (4,6) (4,9) (4,5) (5,13) (5,12) (5,14) (5,8) (5,6) (5,9) (6,13) (6,12) (6,14) (6,8) (6,9) (7,10) (7,11) (8,13) (8,12) (8,14) (8,9) (9,13) (9,12) (9,14) (10,11) (12,13) (12,14) (13,14)\nQ: Is there a path between node 7 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1577"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,28) (0,26) (0,7) (0,22) (0,6) (0,1) (0,30) (0,3) (1,16) (1,28) (1,26) (1,22) (1,10) (1,30) (2,4) (2,29) (2,24) (2,14) (2,21) (2,25) (2,13) (2,12) (2,31) (2,19) (2,33) (2,27) (2,23) (2,8) (2,18) (3,16) (3,28) (3,26) (3,9) (3,7) (3,10) (4,29) (4,32) (4,24) (4,21) (4,25) (4,15) (4,12) (4,31) (4,19) (4,33) (4,27) (4,17) (4,23) (4,18) (5,32) (5,14) (5,21) (5,15) (5,12) (5,19) (5,33) (5,27) (5,23) (5,8) (6,28) (6,26) (6,7) (6,22) (6,10) (7,16) (7,9) (7,22) (7,10) (8,29) (8,32) (8,24) (8,21) (8,15) (8,13) (8,33) (8,27) (8,23) (8,18) (9,16) (9,28) (9,26) (9,22) (9,10) (10,28) (10,22) (10,30) (12,29) (12,14) (12,21) (12,25) (12,15) (12,13) (12,31) (12,19) (12,33) (12,17) (12,23) (12,18) (13,20) (13,29) (13,24) (13,21) (13,25) (13,15) (13,31) (13,19) (13,33) (13,27) (13,17) (13,23) (13,18) (14,20) (14,29) (14,32) (14,24) (14,21) (14,15) (14,31) (14,19) (14,33) (14,17) (14,18) (15,20) (15,29) (15,32) (15,24) (15,21) (15,25) (15,31) (15,19) (15,33) (15,27) (15,17) (15,23) (15,18) (16,28) (16,26) (16,22) (16,30) (17,20) (17,29) (17,32) (17,24) (17,21) (17,25) (17,31) (17,19) (17,18) (18,20) (18,29) (18,32) (18,24) (18,21) (18,25) (18,31) (18,19) (18,27) (18,23) (19,32) (19,24) (19,33) (19,27) (19,23) (20,29) (20,32) (20,24) (20,21) (20,25) (20,31) (20,33) (20,27) (20,23) (21,32) (21,24) (21,25) (21,31) (21,33) (21,27) (21,23) (22,26) (22,30) (23,29) (23,32) (23,24) (23,25) (23,31) (23,33) (23,27) (24,32) (24,25) (24,31) (24,27) (25,29) (25,33) (25,27) (26,28) (26,30) (27,29) (27,31) (27,33) (28,30) (29,32) (29,31) (29,33) (31,32) (31,33) (32,33)\nQ: Is there a path between node 22 and node 21?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1578"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,31) (1,4) (1,27) (1,25) (2,31) (2,24) (2,13) (2,10) (3,30) (3,32) (3,27) (3,15) (4,30) (4,6) (4,28) (4,8) (5,22) (6,27) (7,20) (7,11) (7,12) (8,15) (9,14) (10,17) (10,23) (10,13) (11,14) (12,18) (13,23) (14,22) (15,30) (15,27) (15,25) (15,16) (15,28) (17,23) (17,21) (18,22) (18,33) (20,22) (21,31) (23,24) (25,30) (25,27) (25,28) (26,31) (27,30) (27,32) (28,32)\nQ: Is there a path between node 27 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1579"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,2) (0,1) (0,4) (1,3) (1,2) (1,4) (1,6) (2,3) (2,4) (2,5) (3,4) (3,6) (4,6) (5,6)\nQ: Is there a path between node 1 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1580"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,7) (0,6) (0,8) (0,4) (0,1) (1,2) (1,7) (1,6) (1,8) (1,4) (2,7) (2,6) (2,8) (2,4) (3,5) (4,7) (4,6) (4,8) (6,7) (6,8) (7,8)\nQ: Is there a path between node 0 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1581"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (1,3) (1,2) (1,6) (2,5) (2,6) (3,5) (5,6)\nQ: Is there a path between node 6 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1582"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (1,4) (2,4)\nQ: Is there a path between node 1 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1583"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,27) (0,13) (0,10) (0,15) (0,2) (0,17) (1,5) (1,22) (1,8) (1,19) (1,26) (1,24) (1,18) (1,16) (1,14) (1,12) (1,4) (1,9) (2,7) (2,27) (2,13) (2,3) (2,6) (2,10) (2,11) (2,17) (3,7) (3,27) (3,20) (3,6) (3,10) (3,15) (3,21) (3,17) (4,5) (4,8) (4,19) (4,26) (4,25) (4,18) (4,14) (4,12) (5,8) (5,26) (5,18) (5,16) (5,14) (5,12) (6,7) (6,13) (6,10) (6,21) (7,20) (7,13) (7,10) (7,15) (7,11) (8,19) (8,26) (8,18) (8,16) (8,14) (8,9) (9,22) (9,19) (9,26) (9,25) (9,16) (9,14) (9,12) (10,13) (10,21) (10,17) (11,27) (11,13) (11,15) (11,21) (11,17) (12,22) (12,19) (12,26) (12,24) (12,25) (12,16) (12,14) (13,27) (13,15) (14,22) (14,19) (14,26) (15,27) (15,20) (15,21) (15,17) (16,22) (16,19) (16,24) (16,25) (16,18) (17,27) (17,20) (17,21) (18,22) (18,19) (18,26) (18,24) (19,26) (19,25) (20,27) (20,21) (21,27) (22,26) (22,24) (24,26)\nQ: Is there a path between node 14 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1584"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,5) (0,2) (0,3) (0,10) (0,6) (0,1) (0,4) (0,9) (0,7) (0,12) (1,8) (1,5) (1,2) (1,3) (1,10) (1,6) (1,4) (1,9) (1,7) (1,12) (2,8) (2,5) (2,3) (2,10) (2,6) (2,4) (2,9) (2,7) (2,12) (3,8) (3,5) (3,10) (3,6) (3,4) (3,9) (3,7) (3,12) (4,8) (4,5) (4,10) (4,6) (4,9) (4,7) (4,12) (5,8) (5,10) (5,6) (5,9) (5,7) (5,12) (6,8) (6,10) (6,9) (6,7) (6,12) (7,8) (7,10) (7,9) (7,12) (8,10) (8,9) (8,12) (9,10) (9,12) (10,12) (11,13)\nQ: Is there a path between node 0 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1585"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,14) (0,20) (0,13) (1,2) (1,8) (1,9) (2,9) (4,10) (4,20) (5,21) (5,17) (5,9) (6,10) (6,14) (6,13) (7,21) (7,22) (8,9) (10,19) (10,18) (10,12) (10,13) (11,16) (11,18) (12,16) (12,19) (12,18) (13,19) (14,19) (16,18) (17,22) (18,19)\nQ: Is there a path between node 2 and node 18?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1586"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,22) (0,15) (0,8) (0,12) (0,14) (0,2) (0,9) (0,1) (1,15) (1,20) (1,12) (2,20) (2,12) (2,7) (2,16) (3,15) (3,7) (3,16) (3,13) (3,14) (3,17) (3,21) (4,22) (4,8) (4,12) (4,17) (4,11) (6,23) (7,15) (7,17) (7,11) (7,21) (7,18) (8,22) (8,15) (8,20) (8,16) (8,9) (9,22) (9,13) (9,11) (9,21) (9,18) (10,22) (10,13) (10,21) (11,22) (11,15) (11,20) (11,12) (11,21) (11,18) (12,15) (12,13) (13,20) (13,18) (14,20) (17,22) (17,18) (18,20) (19,23) (20,22) (21,22)\nQ: Is there a path between node 8 and node 19?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1587"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,3) (0,11) (0,18) (0,7) (0,8) (0,9) (0,1) (0,10) (0,15) (0,17) (0,13) (0,16) (0,19) (0,2) (0,6) (0,5) (0,14) (1,12) (1,3) (1,11) (1,18) (1,7) (1,8) (1,9) (1,10) (1,15) (1,17) (1,13) (1,16) (1,19) (1,2) (1,6) (1,5) (1,14) (2,12) (2,3) (2,11) (2,18) (2,7) (2,8) (2,9) (2,10) (2,15) (2,17) (2,13) (2,16) (2,19) (2,6) (2,5) (2,14) (3,12) (3,11) (3,18) (3,7) (3,8) (3,9) (3,10) (3,15) (3,17) (3,13) (3,16) (3,19) (3,6) (3,5) (3,14) (4,20) (4,21) (5,12) (5,11) (5,18) (5,7) (5,8) (5,9) (5,10) (5,15) (5,17) (5,13) (5,16) (5,19) (5,6) (5,14) (6,12) (6,11) (6,18) (6,7) (6,8) (6,9) (6,10) (6,15) (6,17) (6,13) (6,16) (6,19) (6,14) (7,12) (7,11) (7,18) (7,8) (7,9) (7,10) (7,15) (7,17) (7,13) (7,16) (7,19) (7,14) (8,12) (8,11) (8,18) (8,9) (8,10) (8,15) (8,17) (8,13) (8,16) (8,19) (8,14) (9,12) (9,11) (9,18) (9,10) (9,15) (9,17) (9,13) (9,16) (9,19) (9,14) (10,12) (10,11) (10,18) (10,15) (10,17) (10,13) (10,16) (10,19) (10,14) (11,12) (11,18) (11,15) (11,17) (11,13) (11,16) (11,19) (11,14) (12,18) (12,15) (12,17) (12,13) (12,16) (12,19) (12,14) (13,18) (13,15) (13,17) (13,16) (13,19) (13,14) (14,18) (14,15) (14,17) (14,16) (14,19) (15,18) (15,17) (15,16) (15,19) (16,18) (16,17) (16,19) (17,18) (17,19) (18,19) (20,21)\nQ: Is there a path between node 1 and node 20?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1588"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,5) (0,7) (0,2) (0,8) (0,4) (0,9) (0,1) (0,12) (0,3) (0,11) (0,13) (1,10) (1,5) (1,7) (1,2) (1,8) (1,4) (1,9) (1,12) (1,3) (1,11) (1,13) (2,10) (2,5) (2,7) (2,8) (2,4) (2,9) (2,12) (2,3) (2,11) (2,13) (3,10) (3,5) (3,7) (3,8) (3,4) (3,9) (3,12) (3,11) (3,13) (4,10) (4,5) (4,7) (4,8) (4,9) (4,12) (4,11) (4,13) (5,10) (5,7) (5,8) (5,9) (5,12) (5,11) (5,13) (7,10) (7,8) (7,9) (7,12) (7,11) (7,13) (8,10) (8,9) (8,12) (8,11) (8,13) (9,10) (9,12) (9,11) (9,13) (10,12) (10,11) (10,13) (11,12) (11,13) (12,13)\nQ: Is there a path between node 12 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1589"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,12) (0,5) (0,6) (0,4) (0,8) (0,2) (0,9) (0,1) (0,7) (1,12) (1,5) (1,6) (1,4) (1,8) (1,2) (1,9) (1,10) (1,7) (2,8) (2,10) (2,7) (4,11) (4,12) (4,5) (4,6) (4,8) (4,9) (4,7) (5,11) (5,6) (5,8) (5,10) (5,7) (6,11) (6,12) (6,8) (6,9) (7,11) (7,12) (7,9) (7,10) (8,12) (8,9) (8,10) (9,11) (9,12) (9,10) (10,11) (10,12) (11,12)\nQ: Is there a path between node 12 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1590"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,7) (0,2) (0,8) (1,6) (2,3) (3,6) (3,7) (4,6) (4,5) (5,8) (7,8)\nQ: Is there a path between node 0 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1591"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,8) (1,5) (2,3) (3,5) (3,11) (4,8) (5,9) (5,7) (5,10) (6,11)\nQ: Is there a path between node 5 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1592"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (1,15) (1,16) (2,18) (2,17) (2,7) (3,14) (3,7) (5,11) (6,13) (7,17) (8,15) (8,13) (9,17) (10,17) (13,15) (13,16) (16,19)\nQ: Is there a path between node 1 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1593"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,17) (0,10) (0,28) (0,30) (0,29) (0,3) (1,14) (1,2) (2,25) (2,20) (2,7) (2,32) (2,22) (3,24) (3,19) (3,23) (3,4) (3,12) (3,29) (4,26) (4,24) (4,23) (4,8) (4,13) (5,26) (5,19) (5,23) (5,8) (5,15) (5,21) (6,14) (7,32) (8,16) (8,12) (8,29) (9,26) (9,13) (9,18) (9,29) (9,31) (10,17) (10,11) (10,30) (10,23) (10,13) (11,16) (11,17) (11,19) (11,28) (11,23) (12,26) (12,24) (12,21) (13,26) (13,17) (13,19) (13,30) (13,31) (14,25) (14,22) (15,16) (15,17) (15,23) (15,18) (15,29) (16,26) (16,24) (16,18) (16,21) (17,24) (17,19) (17,28) (17,30) (17,23) (18,24) (18,21) (19,26) (19,24) (19,28) (19,23) (20,32) (22,32) (22,27) (24,26) (24,30) (26,29) (28,29)\nQ: Is there a path between node 18 and node 19?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1594"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,26) (2,26) (2,30) (2,6) (3,19) (4,29) (4,8) (4,11) (4,9) (5,25) (6,30) (6,19) (6,13) (6,25) (7,23) (7,29) (7,10) (7,28) (7,14) (8,23) (8,15) (8,27) (8,18) (8,11) (8,28) (8,9) (9,23) (9,29) (9,15) (9,18) (9,12) (10,15) (11,29) (11,27) (11,28) (11,14) (12,27) (13,16) (13,26) (14,17) (15,29) (15,21) (15,28) (16,25) (17,23) (17,29) (17,18) (19,20) (19,22) (20,22) (21,27) (21,28) (22,26) (23,29) (23,28) (24,26) (24,30) (25,26) (25,30) (27,28)\nQ: Is there a path between node 6 and node 27?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1595"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,8) (0,2) (0,20) (0,16) (0,14) (0,15) (0,7) (1,18) (1,24) (1,22) (1,5) (1,19) (1,11) (1,17) (2,6) (2,4) (2,23) (2,8) (2,20) (2,16) (2,21) (2,14) (2,15) (2,10) (3,6) (3,4) (3,23) (3,8) (3,16) (3,14) (3,25) (3,15) (3,7) (4,6) (4,23) (4,8) (4,20) (4,16) (4,21) (4,14) (4,15) (4,10) (4,7) (5,18) (5,24) (5,22) (5,13) (5,9) (5,11) (5,12) (6,23) (6,8) (6,20) (6,16) (6,14) (6,25) (6,15) (7,23) (7,20) (7,16) (7,21) (7,14) (7,25) (7,15) (7,10) (8,20) (8,16) (8,14) (8,25) (8,15) (9,18) (9,24) (9,22) (9,19) (9,11) (9,17) (9,12) (10,23) (10,20) (10,16) (10,21) (10,14) (10,25) (11,22) (11,19) (11,17) (11,12) (12,18) (12,13) (12,19) (13,18) (13,24) (13,22) (13,17) (14,23) (14,20) (14,16) (14,25) (15,20) (15,16) (15,21) (15,25) (16,23) (16,20) (16,25) (17,18) (17,22) (17,19) (18,24) (18,22) (18,19) (19,24) (19,22) (20,21) (20,25) (21,23) (21,25) (22,24) (23,25)\nQ: Is there a path between node 16 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1596"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (1,2) (1,5) (5,6)\nQ: Is there a path between node 6 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1597"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,13) (0,2) (0,15) (0,6) (0,17) (0,8) (0,16) (0,18) (0,9) (0,12) (0,11) (1,10) (1,14) (1,7) (1,5) (1,4) (2,3) (2,13) (2,15) (2,6) (2,17) (2,8) (2,16) (2,18) (2,9) (2,12) (2,11) (3,13) (3,15) (3,6) (3,17) (3,8) (3,16) (3,18) (3,9) (3,12) (3,11) (4,10) (4,14) (4,7) (4,5) (5,10) (5,14) (5,7) (6,13) (6,15) (6,17) (6,8) (6,16) (6,18) (6,9) (6,12) (6,11) (7,10) (7,14) (8,13) (8,15) (8,17) (8,16) (8,18) (8,9) (8,12) (8,11) (9,13) (9,15) (9,17) (9,16) (9,18) (9,12) (9,11) (10,14) (11,13) (11,15) (11,17) (11,16) (11,18) (11,12) (12,13) (12,15) (12,17) (12,16) (12,18) (13,15) (13,17) (13,16) (13,18) (15,17) (15,16) (15,18) (16,17) (16,18) (17,18)\nQ: Is there a path between node 18 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1598"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,10) (0,2) (2,15) (2,20) (2,23) (2,14) (2,17) (2,24) (2,18) (3,21) (4,27) (5,9) (5,22) (6,29) (6,8) (7,29) (7,25) (7,20) (7,17) (7,18) (7,8) (8,23) (8,24) (10,23) (10,18) (11,27) (12,13) (13,21) (14,25) (14,23) (14,17) (14,24) (15,29) (15,25) (15,23) (15,16) (16,29) (16,17) (17,25) (17,23) (17,24) (17,18) (18,29) (20,25) (22,26) (23,25) (24,29) (26,27)\nQ: Is there a path between node 15 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1599"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (1,17) (2,9) (3,16) (5,18) (5,11) (5,21) (6,21) (6,15) (7,19) (7,21) (8,10) (8,12) (8,16) (10,16) (14,23) (15,21) (16,19) (17,20) (18,19) (20,23)\nQ: Is there a path between node 17 and node 20?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1600"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,3) (1,20) (1,21) (1,8) (1,5) (1,16) (1,17) (1,19) (1,6) (1,12) (1,14) (1,9) (1,13) (1,18) (1,7) (1,11) (1,15) (1,2) (1,10) (2,20) (2,21) (2,8) (2,5) (2,16) (2,17) (2,19) (2,6) (2,12) (2,14) (2,9) (2,13) (2,18) (2,7) (2,11) (2,15) (2,10) (3,4) (5,20) (5,21) (5,8) (5,16) (5,17) (5,19) (5,6) (5,12) (5,14) (5,9) (5,13) (5,18) (5,7) (5,11) (5,15) (5,10) (6,20) (6,21) (6,8) (6,16) (6,17) (6,19) (6,12) (6,14) (6,9) (6,13) (6,18) (6,7) (6,11) (6,15) (6,10) (7,20) (7,21) (7,8) (7,16) (7,17) (7,19) (7,12) (7,14) (7,9) (7,13) (7,18) (7,11) (7,15) (7,10) (8,20) (8,21) (8,16) (8,17) (8,19) (8,12) (8,14) (8,9) (8,13) (8,18) (8,11) (8,15) (8,10) (9,20) (9,21) (9,16) (9,17) (9,19) (9,12) (9,14) (9,13) (9,18) (9,11) (9,15) (9,10) (10,20) (10,21) (10,16) (10,17) (10,19) (10,12) (10,14) (10,13) (10,18) (10,11) (10,15) (11,20) (11,21) (11,16) (11,17) (11,19) (11,12) (11,14) (11,13) (11,18) (11,15) (12,20) (12,21) (12,16) (12,17) (12,19) (12,14) (12,13) (12,18) (12,15) (13,20) (13,21) (13,16) (13,17) (13,19) (13,14) (13,18) (13,15) (14,20) (14,21) (14,16) (14,17) (14,19) (14,18) (14,15) (15,20) (15,21) (15,16) (15,17) (15,19) (15,18) (16,20) (16,21) (16,17) (16,19) (16,18) (17,20) (17,21) (17,19) (17,18) (18,20) (18,21) (18,19) (19,20) (19,21) (20,21)\nQ: Is there a path between node 3 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1601"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,15) (1,3) (1,20) (2,11) (3,12) (3,6) (3,16) (3,20) (5,14) (5,7) (6,20) (6,21) (7,13) (7,18) (8,14) (8,13) (9,12) (9,16) (9,21) (10,21) (11,17) (12,16) (14,18) (15,16) (15,21) (16,20) (20,21)\nQ: Is there a path between node 10 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1602"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,14) (0,10) (0,24) (0,2) (0,12) (0,19) (0,3) (0,17) (0,25) (0,23) (0,15) (1,18) (1,11) (1,8) (2,14) (2,10) (2,24) (2,7) (2,3) (2,21) (2,25) (2,23) (2,6) (3,14) (3,24) (3,12) (3,19) (3,17) (3,25) (3,23) (3,6) (3,15) (4,18) (4,8) (5,18) (5,11) (5,8) (6,16) (6,14) (6,10) (6,12) (6,7) (6,19) (6,21) (6,25) (6,23) (6,9) (6,15) (7,16) (7,10) (7,24) (7,12) (7,19) (7,17) (7,25) (7,9) (7,15) (8,18) (8,11) (9,16) (9,14) (9,10) (9,24) (9,12) (9,19) (9,17) (9,21) (9,23) (9,15) (10,16) (10,14) (10,19) (10,21) (10,25) (10,23) (10,15) (11,18) (12,16) (12,14) (12,24) (12,19) (12,17) (12,21) (12,25) (12,23) (12,15) (13,20) (14,16) (14,24) (14,17) (14,21) (14,25) (14,23) (14,15) (15,16) (15,24) (15,23) (16,21) (16,25) (16,23) (17,21) (17,23) (19,21) (19,25) (21,24) (21,25) (21,23) (23,25) (24,25)\nQ: Is there a path between node 14 and node 16?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1603"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,6) (0,1) (0,5) (1,7) (1,6) (1,8) (1,5) (2,7) (2,8) (2,5) (3,4) (5,7) (5,6) (5,8)\nQ: Is there a path between node 8 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1604"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,10) (0,26) (0,13) (0,23) (0,14) (0,27) (0,30) (0,31) (0,28) (0,2) (0,8) (0,12) (0,9) (0,24) (0,5) (1,19) (1,15) (1,6) (1,11) (1,29) (1,17) (1,21) (1,4) (1,25) (1,7) (2,3) (2,14) (2,31) (2,28) (2,18) (2,8) (2,12) (2,9) (2,24) (2,5) (3,10) (3,13) (3,23) (3,27) (3,30) (3,31) (3,28) (3,18) (3,8) (3,12) (3,9) (3,24) (3,5) (4,20) (4,19) (4,15) (4,11) (4,29) (4,16) (4,22) (4,7) (5,10) (5,13) (5,23) (5,14) (5,27) (5,31) (5,18) (5,8) (5,12) (5,9) (6,20) (6,15) (6,11) (6,29) (6,17) (6,21) (6,16) (6,25) (6,7) (7,20) (7,15) (7,11) (7,29) (7,17) (7,21) (7,25) (8,10) (8,26) (8,13) (8,23) (8,14) (8,27) (8,30) (8,12) (8,24) (9,10) (9,26) (9,13) (9,14) (9,27) (9,30) (9,31) (9,18) (9,24) (10,26) (10,13) (10,23) (10,14) (10,27) (10,30) (10,31) (10,18) (11,20) (11,19) (11,15) (11,29) (11,17) (11,21) (11,16) (11,25) (11,22) (12,13) (12,23) (12,14) (12,27) (12,28) (13,26) (13,23) (13,14) (13,27) (13,31) (13,28) (14,23) (14,30) (14,28) (14,18) (14,24) (15,19) (15,29) (15,21) (15,16) (15,22) (16,20) (16,19) (16,29) (16,17) (16,21) (16,25) (17,20) (17,19) (17,29) (17,21) (17,25) (17,22) (18,26) (18,27) (18,30) (18,31) (18,28) (19,29) (19,21) (19,25) (19,22) (20,29) (20,22) (21,29) (21,25) (21,22) (22,25) (23,26) (23,27) (23,30) (23,31) (23,24) (24,27) (24,30) (24,31) (25,29) (26,27) (26,30) (26,28) (27,30) (27,31) (28,30) (28,31) (30,31)\nQ: Is there a path between node 19 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1605"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,30) (0,6) (0,12) (1,15) (2,17) (2,4) (3,25) (3,30) (3,12) (4,18) (4,16) (4,20) (4,22) (4,28) (4,8) (4,17) (5,12) (5,11) (6,19) (7,9) (7,10) (8,22) (8,28) (8,21) (9,23) (10,12) (10,11) (11,30) (11,19) (11,12) (12,25) (12,19) (13,27) (13,26) (15,26) (16,18) (16,29) (16,20) (16,24) (16,22) (16,28) (16,17) (17,22) (17,28) (17,21) (18,29) (18,20) (18,24) (18,22) (19,30) (20,22) (20,28) (21,24) (24,28) (25,30)\nQ: Is there a path between node 3 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1606"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,11) (0,17) (0,3) (0,19) (0,9) (0,16) (0,15) (0,7) (0,12) (0,2) (1,11) (1,10) (1,3) (1,4) (1,8) (1,19) (1,13) (1,9) (1,16) (1,15) (1,7) (1,12) (1,2) (2,17) (2,5) (2,16) (2,15) (3,17) (3,10) (3,5) (3,6) (3,8) (3,13) (3,9) (3,16) (3,15) (3,7) (3,12) (4,11) (4,5) (4,8) (4,19) (4,13) (4,9) (4,7) (4,12) (5,11) (5,10) (5,6) (5,8) (5,19) (5,13) (5,7) (6,11) (6,17) (6,10) (6,8) (6,19) (6,13) (6,16) (6,15) (6,7) (6,12) (7,11) (7,17) (7,10) (7,19) (7,9) (7,16) (7,15) (8,11) (8,17) (8,10) (8,19) (8,13) (8,15) (8,12) (9,11) (9,17) (9,10) (9,13) (9,16) (9,15) (10,11) (10,17) (10,19) (10,13) (10,15) (10,12) (11,19) (11,15) (11,12) (12,17) (12,19) (12,13) (13,19) (13,16) (13,15) (14,18) (15,19) (15,16) (16,17) (17,19)\nQ: Is there a path between node 10 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1607"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,9) (1,10) (1,3) (2,6) (2,4) (2,7) (3,6) (3,10) (3,9) (3,12) (4,8) (5,9) (5,12) (6,9) (6,12) (6,7) (7,10) (7,9) (7,14) (8,10) (8,9) (8,14) (12,14)\nQ: Is there a path between node 2 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1608"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,3) (0,5) (1,2) (1,10) (1,3) (1,5) (2,6) (2,10) (3,17) (3,14) (3,6) (3,9) (4,14) (4,7) (4,9) (5,17) (5,14) (5,6) (5,10) (5,7) (6,14) (6,16) (6,7) (9,17) (9,16) (9,10) (10,14) (11,15) (12,13) (14,17) (14,16) (14,15) (15,17)\nQ: Is there a path between node 7 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1609"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,8) (1,5) (2,3) (3,5) (3,11) (4,8) (5,9) (5,7) (5,10) (6,11)\nQ: Is there a path between node 6 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1610"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,25) (0,13) (0,3) (0,1) (1,11) (1,25) (1,13) (1,2) (1,3) (1,8) (2,21) (2,22) (2,25) (2,13) (2,3) (3,18) (3,22) (3,11) (3,13) (4,23) (4,14) (4,6) (4,12) (4,27) (4,15) (4,5) (4,16) (4,26) (4,20) (4,7) (4,19) (5,14) (5,6) (5,12) (5,27) (5,15) (5,16) (5,9) (5,20) (5,7) (6,23) (6,14) (6,12) (6,24) (6,15) (6,16) (6,9) (6,17) (6,26) (6,20) (6,7) (6,19) (7,23) (7,14) (7,12) (7,24) (7,10) (7,16) (7,9) (7,17) (7,26) (7,20) (7,19) (8,21) (8,18) (8,22) (8,11) (8,25) (8,13) (9,23) (9,12) (9,10) (9,16) (9,17) (9,26) (9,20) (10,23) (10,14) (10,12) (10,24) (10,27) (10,16) (10,17) (10,26) (10,19) (11,21) (11,22) (11,25) (11,13) (12,23) (12,14) (12,24) (12,27) (12,16) (12,26) (12,20) (12,19) (13,22) (13,25) (14,23) (14,24) (14,16) (14,26) (14,19) (15,24) (15,27) (15,16) (15,26) (16,23) (16,27) (16,17) (16,26) (16,20) (17,27) (17,26) (17,20) (17,19) (18,22) (19,23) (19,24) (19,27) (19,26) (19,20) (20,23) (20,26) (21,22) (21,25) (22,25) (23,24) (23,27) (24,27) (24,26) (26,27)\nQ: Is there a path between node 15 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1611"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,10) (0,17) (0,4) (0,21) (0,1) (0,2) (0,18) (0,7) (0,19) (0,11) (0,3) (0,5) (0,14) (1,6) (1,10) (1,17) (1,21) (1,16) (1,18) (1,7) (1,8) (1,11) (2,6) (2,10) (2,17) (2,4) (2,21) (2,16) (2,13) (2,18) (2,7) (2,8) (2,19) (2,3) (2,5) (3,6) (3,10) (3,17) (3,4) (3,21) (3,16) (3,13) (3,18) (3,7) (3,19) (4,10) (4,16) (4,18) (4,7) (4,8) (4,19) (4,5) (5,6) (5,16) (5,13) (5,18) (5,7) (5,8) (5,19) (5,14) (6,10) (6,17) (6,21) (6,16) (6,13) (6,18) (6,7) (6,19) (6,11) (6,14) (7,10) (7,17) (7,21) (7,16) (7,13) (7,18) (7,8) (7,19) (7,11) (7,14) (8,10) (8,17) (8,21) (8,16) (8,13) (8,18) (8,19) (8,11) (9,20) (10,17) (10,21) (10,13) (10,18) (10,19) (10,11) (10,14) (11,17) (11,16) (11,13) (11,18) (11,19) (12,15) (13,21) (13,16) (13,18) (13,19) (13,14) (14,17) (14,21) (14,16) (14,18) (14,19) (16,17) (16,21) (16,18) (17,18) (18,21) (18,19) (19,21)\nQ: Is there a path between node 4 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1612"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,18) (0,19) (0,20) (0,23) (0,9) (0,10) (0,22) (0,13) (0,1) (0,12) (0,5) (0,7) (0,15) (0,4) (1,11) (1,18) (1,19) (1,20) (1,23) (1,9) (1,10) (1,22) (1,13) (1,12) (1,5) (1,7) (1,15) (1,4) (2,8) (2,6) (2,3) (2,24) (2,16) (2,21) (2,17) (2,14) (3,8) (3,6) (3,24) (3,16) (3,21) (3,17) (3,14) (4,11) (4,18) (4,19) (4,20) (4,23) (4,9) (4,10) (4,22) (4,13) (4,12) (4,5) (4,7) (4,15) (5,11) (5,18) (5,19) (5,20) (5,23) (5,9) (5,10) (5,22) (5,13) (5,12) (5,7) (5,15) (6,8) (6,24) (6,16) (6,21) (6,17) (6,14) (7,11) (7,18) (7,19) (7,20) (7,23) (7,9) (7,10) (7,22) (7,13) (7,12) (7,15) (8,24) (8,16) (8,21) (8,17) (8,14) (9,11) (9,18) (9,19) (9,20) (9,23) (9,10) (9,22) (9,13) (9,12) (9,15) (10,11) (10,18) (10,19) (10,20) (10,23) (10,22) (10,13) (10,12) (10,15) (11,18) (11,19) (11,20) (11,23) (11,22) (11,13) (11,12) (11,15) (12,18) (12,19) (12,20) (12,23) (12,22) (12,13) (12,15) (13,18) (13,19) (13,20) (13,23) (13,22) (13,15) (14,24) (14,16) (14,21) (14,17) (15,18) (15,19) (15,20) (15,23) (15,22) (16,24) (16,21) (16,17) (17,24) (17,21) (18,19) (18,20) (18,23) (18,22) (19,20) (19,23) (19,22) (20,23) (20,22) (21,24) (22,23)\nQ: Is there a path between node 16 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1613"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,1) (0,14) (0,18) (1,17) (1,14) (1,18) (2,19) (2,7) (2,10) (2,3) (2,12) (2,16) (2,11) (2,5) (2,9) (2,15) (2,6) (2,20) (2,8) (2,4) (2,13) (3,19) (3,7) (3,10) (3,12) (3,16) (3,11) (3,5) (3,9) (3,15) (3,6) (3,20) (3,8) (3,4) (3,13) (4,19) (4,7) (4,10) (4,12) (4,16) (4,11) (4,5) (4,9) (4,15) (4,6) (4,20) (4,8) (4,13) (5,19) (5,7) (5,10) (5,12) (5,16) (5,11) (5,9) (5,15) (5,6) (5,20) (5,8) (5,13) (6,19) (6,7) (6,10) (6,12) (6,16) (6,11) (6,9) (6,15) (6,20) (6,8) (6,13) (7,19) (7,10) (7,12) (7,16) (7,11) (7,9) (7,15) (7,20) (7,8) (7,13) (8,19) (8,10) (8,12) (8,16) (8,11) (8,9) (8,15) (8,20) (8,13) (9,19) (9,10) (9,12) (9,16) (9,11) (9,15) (9,20) (9,13) (10,19) (10,12) (10,16) (10,11) (10,15) (10,20) (10,13) (11,19) (11,12) (11,16) (11,15) (11,20) (11,13) (12,19) (12,16) (12,15) (12,20) (12,13) (13,19) (13,16) (13,15) (13,20) (14,17) (14,18) (15,19) (15,16) (15,20) (16,19) (16,20) (17,18) (19,20)\nQ: Is there a path between node 19 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1614"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (0,13) (0,22) (1,12) (1,6) (2,20) (2,14) (2,11) (3,5) (3,23) (3,6) (5,17) (6,19) (7,23) (8,13) (8,15) (9,21) (9,18) (12,24) (12,17) (12,19) (13,21) (13,18) (13,25) (13,15) (13,16) (15,16) (16,21) (16,25) (17,23) (17,19) (19,26) (21,22) (22,25)\nQ: Is there a path between node 13 and node 18?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1615"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,10) (0,19) (0,16) (0,7) (0,8) (0,4) (0,3) (0,11) (0,1) (0,18) (0,9) (0,5) (0,2) (0,13) (1,17) (1,10) (1,19) (1,16) (1,7) (1,8) (1,4) (1,3) (1,11) (1,18) (1,9) (1,5) (1,2) (1,13) (2,17) (2,10) (2,19) (2,16) (2,7) (2,8) (2,4) (2,3) (2,11) (2,18) (2,9) (2,5) (2,13) (3,17) (3,10) (3,19) (3,16) (3,7) (3,8) (3,4) (3,11) (3,18) (3,9) (3,5) (3,13) (4,17) (4,10) (4,19) (4,16) (4,7) (4,8) (4,11) (4,18) (4,9) (4,5) (4,13) (5,17) (5,10) (5,19) (5,16) (5,7) (5,8) (5,11) (5,18) (5,9) (5,13) (6,15) (7,17) (7,10) (7,19) (7,16) (7,8) (7,11) (7,18) (7,9) (7,13) (8,17) (8,10) (8,19) (8,16) (8,11) (8,18) (8,9) (8,13) (9,17) (9,10) (9,19) (9,16) (9,11) (9,18) (9,13) (10,17) (10,19) (10,16) (10,11) (10,18) (10,13) (11,17) (11,19) (11,16) (11,18) (11,13) (12,14) (13,17) (13,19) (13,16) (13,18) (16,17) (16,19) (16,18) (17,19) (17,18) (18,19)\nQ: Is there a path between node 11 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1616"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,6) (0,1) (0,7) (0,4) (1,5) (1,6) (1,7) (1,4) (2,3) (4,5) (4,6) (4,7) (5,6) (5,7) (6,7)\nQ: Is there a path between node 2 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1617"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,3) (0,5) (1,2) (1,10) (1,3) (1,5) (2,6) (2,10) (3,17) (3,14) (3,6) (3,9) (4,14) (4,7) (4,9) (5,17) (5,14) (5,6) (5,10) (5,7) (6,14) (6,16) (6,7) (9,17) (9,16) (9,10) (10,14) (11,15) (12,13) (14,17) (14,16) (14,15) (15,17)\nQ: Is there a path between node 2 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1618"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,17) (0,24) (1,11) (1,9) (1,3) (2,19) (2,29) (2,27) (3,7) (3,20) (4,23) (4,25) (5,17) (6,22) (7,29) (7,27) (7,9) (8,16) (8,30) (8,26) (8,18) (8,31) (9,11) (9,27) (10,13) (10,12) (11,19) (11,27) (12,26) (12,18) (14,28) (15,27) (16,30) (17,23) (18,26) (19,28) (20,29) (21,22) (23,24) (24,25) (27,28) (30,31)\nQ: Is there a path between node 9 and node 27?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1619"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,7) (0,12) (0,32) (0,22) (0,9) (0,20) (0,2) (0,5) (0,14) (0,4) (0,26) (0,21) (1,11) (1,8) (1,24) (1,3) (1,31) (1,28) (1,6) (2,16) (2,7) (2,32) (2,22) (2,9) (2,20) (2,14) (2,4) (2,21) (3,11) (3,8) (3,24) (3,31) (3,28) (4,16) (4,32) (4,22) (4,9) (4,20) (4,5) (4,14) (4,26) (5,16) (5,7) (5,12) (5,32) (5,22) (5,9) (5,20) (5,14) (5,26) (5,21) (6,8) (6,24) (6,31) (6,28) (7,12) (7,32) (7,22) (7,9) (7,14) (7,26) (7,21) (8,24) (8,31) (8,28) (9,16) (9,12) (9,32) (9,20) (9,26) (9,21) (10,23) (10,13) (10,29) (10,19) (10,25) (10,18) (12,32) (12,22) (12,20) (12,26) (12,21) (13,30) (13,27) (13,29) (13,19) (13,25) (13,18) (14,16) (14,32) (14,22) (14,20) (14,26) (15,30) (15,29) (15,25) (15,18) (16,32) (16,22) (16,20) (16,26) (16,21) (17,30) (17,27) (18,30) (18,29) (19,30) (19,23) (19,27) (19,25) (20,32) (20,22) (20,26) (21,32) (21,26) (22,32) (22,26) (23,30) (23,29) (23,25) (24,28) (26,32) (27,30) (27,29) (28,31) (29,30)\nQ: Is there a path between node 12 and node 29?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1620"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,11) (0,6) (1,5) (1,8) (1,10) (1,15) (1,17) (1,13) (1,16) (2,5) (2,4) (2,8) (2,10) (2,14) (2,17) (2,13) (2,16) (3,9) (3,6) (3,12) (4,8) (4,15) (4,14) (4,17) (4,13) (5,8) (5,15) (5,17) (6,7) (6,9) (7,11) (7,9) (8,15) (8,17) (8,13) (8,16) (9,11) (10,15) (10,14) (10,17) (11,12) (13,15) (13,14) (13,16) (14,15) (14,17) (14,16) (15,17) (15,16) (16,17)\nQ: Is there a path between node 16 and node 17?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1621"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,10) (0,2) (2,15) (2,20) (2,23) (2,14) (2,17) (2,24) (2,18) (3,21) (4,27) (5,9) (5,22) (6,29) (6,8) (7,29) (7,25) (7,20) (7,17) (7,18) (7,8) (8,23) (8,24) (10,23) (10,18) (11,27) (12,13) (13,21) (14,25) (14,23) (14,17) (14,24) (15,29) (15,25) (15,23) (15,16) (16,29) (16,17) (17,25) (17,23) (17,24) (17,18) (18,29) (20,25) (22,26) (23,25) (24,29) (26,27)\nQ: Is there a path between node 1 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1622"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,12) (0,11) (0,8) (0,1) (0,13) (0,10) (0,3) (1,2) (1,5) (1,12) (1,11) (1,8) (1,13) (1,10) (1,3) (2,5) (2,12) (2,11) (2,8) (2,13) (2,10) (2,3) (3,5) (3,12) (3,11) (3,8) (3,13) (3,10) (4,9) (4,6) (4,7) (4,14) (5,12) (5,11) (5,8) (5,13) (5,10) (6,9) (6,7) (6,14) (7,9) (7,14) (8,12) (8,11) (8,13) (8,10) (9,14) (10,12) (10,11) (10,13) (11,12) (11,13) (12,13)\nQ: Is there a path between node 4 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1623"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,29) (0,1) (0,9) (0,20) (0,34) (0,7) (0,19) (0,22) (0,31) (1,11) (1,30) (1,6) (1,21) (1,14) (1,28) (1,19) (1,31) (1,4) (2,3) (2,11) (2,18) (2,21) (2,20) (2,14) (2,7) (2,17) (3,11) (3,33) (3,15) (3,30) (3,18) (3,21) (3,14) (3,5) (4,10) (4,26) (4,27) (4,21) (4,34) (5,9) (5,27) (5,30) (5,6) (5,24) (5,14) (5,34) (5,28) (5,17) (6,11) (6,25) (6,10) (6,26) (6,29) (6,15) (6,16) (6,14) (6,7) (6,12) (6,22) (7,10) (7,26) (7,27) (7,18) (7,24) (7,8) (7,31) (8,11) (8,33) (8,9) (8,30) (8,24) (8,20) (8,16) (8,22) (8,17) (9,10) (9,20) (9,16) (9,14) (10,25) (10,33) (10,30) (10,18) (10,24) (10,20) (10,31) (11,15) (11,12) (11,19) (11,17) (12,25) (12,29) (12,27) (12,30) (12,34) (12,28) (12,17) (14,25) (14,33) (14,26) (14,29) (14,30) (14,21) (14,17) (15,20) (15,17) (16,21) (16,28) (16,19) (16,22) (17,27) (17,30) (17,24) (17,19) (18,26) (18,21) (18,28) (19,33) (19,27) (19,34) (19,22) (20,25) (20,26) (20,27) (20,21) (20,28) (20,31) (21,22) (22,24) (22,31) (24,34) (24,28) (25,26) (25,29) (25,27) (26,33) (26,27) (26,30) (27,30) (27,28) (28,31) (29,30) (29,34) (29,31) (30,33) (30,34) (31,33) (31,34)\nQ: Is there a path between node 8 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1624"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,5) (0,11) (0,8) (0,6) (0,1) (1,10) (1,3) (1,5) (1,9) (1,6) (1,2) (2,10) (2,3) (2,5) (2,9) (2,8) (2,7) (2,6) (2,13) (3,9) (3,11) (3,8) (3,7) (4,12) (5,10) (5,9) (5,8) (5,7) (5,6) (6,10) (6,9) (6,11) (6,8) (7,10) (7,11) (7,8) (7,13) (8,10) (8,11) (8,13) (9,10) (9,11) (9,13) (10,11) (10,13)\nQ: Is there a path between node 1 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1625"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,31) (1,4) (1,27) (1,25) (2,31) (2,24) (2,13) (2,10) (3,30) (3,32) (3,27) (3,15) (4,30) (4,6) (4,28) (4,8) (5,22) (6,27) (7,20) (7,11) (7,12) (8,15) (9,14) (10,17) (10,23) (10,13) (11,14) (12,18) (13,23) (14,22) (15,30) (15,27) (15,25) (15,16) (15,28) (17,23) (17,21) (18,22) (18,33) (20,22) (21,31) (23,24) (25,30) (25,27) (25,28) (26,31) (27,30) (27,32) (28,32)\nQ: Is there a path between node 11 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1626"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 4 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1627"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (2,3)\nQ: Is there a path between node 2 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1628"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,25) (0,3) (1,25) (1,29) (2,14) (2,13) (2,20) (2,18) (2,31) (2,9) (2,27) (2,21) (2,12) (2,7) (2,33) (2,11) (2,24) (2,26) (2,30) (3,25) (4,23) (4,22) (4,34) (4,5) (5,23) (5,22) (5,34) (6,14) (6,13) (6,20) (6,18) (6,27) (6,21) (6,12) (6,7) (6,28) (6,24) (6,26) (6,30) (7,14) (7,13) (7,20) (7,31) (7,17) (7,9) (7,27) (7,21) (7,12) (7,10) (7,33) (7,28) (7,30) (8,14) (8,13) (8,31) (8,17) (8,9) (8,27) (8,12) (8,33) (8,11) (8,28) (8,26) (8,30) (9,14) (9,13) (9,20) (9,18) (9,27) (9,21) (9,12) (9,10) (9,33) (9,24) (9,26) (9,19) (9,30) (10,13) (10,20) (10,18) (10,31) (10,17) (10,27) (10,12) (10,33) (10,11) (10,28) (10,24) (11,14) (11,13) (11,20) (11,18) (11,31) (11,12) (11,33) (11,28) (11,24) (11,26) (11,30) (12,14) (12,13) (12,20) (12,18) (12,17) (12,27) (12,21) (12,33) (12,19) (13,14) (13,20) (13,18) (13,31) (13,17) (13,21) (13,28) (13,24) (13,26) (14,18) (14,31) (14,17) (14,27) (14,21) (14,33) (14,26) (15,32) (17,18) (17,31) (17,27) (17,33) (17,28) (17,24) (17,26) (17,19) (17,30) (18,20) (18,31) (18,33) (18,24) (18,26) (18,19) (18,30) (19,31) (19,27) (19,21) (19,33) (19,28) (19,26) (20,31) (20,27) (20,21) (20,33) (20,24) (20,26) (20,30) (21,27) (21,33) (21,28) (21,24) (21,30) (22,23) (22,34) (23,34) (24,33) (24,26) (25,29) (26,31) (26,33) (26,30) (27,31) (27,33) (27,28) (27,30) (28,31) (28,33) (28,30) (30,31) (30,33) (31,33)\nQ: Is there a path between node 8 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1629"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,4) (0,3) (0,6) (0,2) (0,8) (0,5) (0,11) (1,4) (1,3) (1,6) (1,2) (1,8) (1,5) (1,11) (2,4) (2,3) (2,6) (2,8) (2,5) (2,11) (3,4) (3,6) (3,8) (3,5) (3,11) (4,6) (4,8) (4,5) (4,11) (5,6) (5,8) (5,11) (6,8) (6,11) (7,9) (7,10) (8,11) (9,10)\nQ: Is there a path between node 4 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1630"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,3) (0,13) (0,15) (0,7) (1,4) (1,6) (2,9) (2,18) (2,13) (3,12) (4,11) (6,8) (6,17) (7,16) (7,12) (7,13) (7,14) (8,11) (8,17) (8,20) (9,18) (9,21) (9,14) (9,15) (10,12) (12,16) (12,15) (13,18) (13,15) (14,16) (14,21) (15,16) (15,18) (16,18)\nQ: Is there a path between node 9 and node 13?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1631"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,4) (0,11) (0,13) (1,8) (1,21) (1,10) (1,7) (1,2) (2,24) (2,8) (2,9) (2,10) (2,22) (3,5) (3,11) (3,13) (4,15) (4,6) (4,16) (4,11) (5,12) (5,15) (5,19) (5,18) (5,27) (6,19) (6,11) (7,26) (7,23) (7,9) (8,23) (8,9) (8,10) (8,22) (9,25) (9,14) (10,25) (10,17) (10,23) (11,20) (11,27) (12,15) (12,16) (12,18) (14,22) (15,19) (15,27) (16,19) (17,26) (17,24) (17,28) (17,23) (17,22) (19,20) (19,27) (21,26) (21,25) (21,29) (21,22) (22,29) (23,24) (23,29) (26,28)\nQ: Is there a path between node 29 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1632"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,13) (0,19) (0,11) (0,16) (0,20) (0,8) (0,5) (0,3) (0,2) (0,7) (0,6) (0,17) (0,14) (0,12) (0,1) (0,18) (0,10) (0,23) (0,9) (1,4) (1,13) (1,19) (1,11) (1,16) (1,20) (1,8) (1,5) (1,3) (1,2) (1,7) (1,6) (1,17) (1,14) (1,12) (1,18) (1,10) (1,23) (1,9) (2,4) (2,13) (2,19) (2,11) (2,16) (2,20) (2,8) (2,5) (2,3) (2,7) (2,6) (2,17) (2,14) (2,12) (2,18) (2,10) (2,23) (2,9) (3,4) (3,13) (3,19) (3,11) (3,16) (3,20) (3,8) (3,5) (3,7) (3,6) (3,17) (3,14) (3,12) (3,18) (3,10) (3,23) (3,9) (4,13) (4,19) (4,11) (4,16) (4,20) (4,8) (4,5) (4,7) (4,6) (4,17) (4,14) (4,12) (4,18) (4,10) (4,23) (4,9) (5,13) (5,19) (5,11) (5,16) (5,20) (5,8) (5,7) (5,6) (5,17) (5,14) (5,12) (5,18) (5,10) (5,23) (5,9) (6,13) (6,19) (6,11) (6,16) (6,20) (6,8) (6,7) (6,17) (6,14) (6,12) (6,18) (6,10) (6,23) (6,9) (7,13) (7,19) (7,11) (7,16) (7,20) (7,8) (7,17) (7,14) (7,12) (7,18) (7,10) (7,23) (7,9) (8,13) (8,19) (8,11) (8,16) (8,20) (8,17) (8,14) (8,12) (8,18) (8,10) (8,23) (8,9) (9,13) (9,19) (9,11) (9,16) (9,20) (9,17) (9,14) (9,12) (9,18) (9,10) (9,23) (10,13) (10,19) (10,11) (10,16) (10,20) (10,17) (10,14) (10,12) (10,18) (10,23) (11,13) (11,19) (11,16) (11,20) (11,17) (11,14) (11,12) (11,18) (11,23) (12,13) (12,19) (12,16) (12,20) (12,17) (12,14) (12,18) (12,23) (13,19) (13,16) (13,20) (13,17) (13,14) (13,18) (13,23) (14,19) (14,16) (14,20) (14,17) (14,18) (14,23) (15,21) (15,22) (16,19) (16,20) (16,17) (16,18) (16,23) (17,19) (17,20) (17,18) (17,23) (18,19) (18,20) (18,23) (19,20) (19,23) (20,23) (21,22)\nQ: Is there a path between node 17 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1633"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,13) (0,6) (0,5) (0,15) (0,14) (0,1) (0,10) (0,8) (0,7) (0,2) (0,11) (0,3) (1,12) (1,13) (1,6) (1,5) (1,15) (1,14) (1,10) (1,8) (1,7) (1,2) (1,11) (1,3) (2,12) (2,13) (2,6) (2,5) (2,15) (2,14) (2,10) (2,8) (2,7) (2,11) (2,3) (3,12) (3,13) (3,6) (3,5) (3,15) (3,14) (3,10) (3,8) (3,7) (3,11) (4,9) (5,12) (5,13) (5,6) (5,15) (5,14) (5,10) (5,8) (5,7) (5,11) (6,12) (6,13) (6,15) (6,14) (6,10) (6,8) (6,7) (6,11) (7,12) (7,13) (7,15) (7,14) (7,10) (7,8) (7,11) (8,12) (8,13) (8,15) (8,14) (8,10) (8,11) (10,12) (10,13) (10,15) (10,14) (10,11) (11,12) (11,13) (11,15) (11,14) (12,13) (12,15) (12,14) (13,15) (13,14) (14,15)\nQ: Is there a path between node 2 and node 13?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1634"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,12) (0,11) (0,4) (2,10) (2,8) (2,4) (4,6) (4,11) (5,9) (6,7) (6,10) (6,11) (7,8) (8,10) (8,9) (9,12) (10,11)\nQ: Is there a path between node 0 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1635"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (0,11) (0,8) (0,17) (0,13) (0,6) (0,3) (0,15) (0,7) (1,14) (1,19) (1,9) (1,21) (1,12) (1,22) (1,4) (1,18) (1,5) (1,10) (1,20) (2,16) (3,23) (3,11) (3,8) (3,17) (3,13) (3,6) (3,15) (3,7) (4,14) (4,19) (4,9) (4,21) (4,12) (4,22) (4,18) (4,5) (4,10) (4,20) (5,14) (5,19) (5,9) (5,21) (5,12) (5,22) (5,18) (5,10) (5,20) (6,23) (6,11) (6,8) (6,17) (6,13) (6,15) (6,7) (7,23) (7,11) (7,8) (7,17) (7,13) (7,15) (8,23) (8,11) (8,17) (8,13) (8,15) (9,14) (9,19) (9,21) (9,12) (9,22) (9,18) (9,10) (9,20) (10,14) (10,19) (10,21) (10,12) (10,22) (10,18) (10,20) (11,23) (11,17) (11,13) (11,15) (12,14) (12,19) (12,21) (12,22) (12,18) (12,20) (13,23) (13,17) (13,15) (14,19) (14,21) (14,22) (14,18) (14,20) (15,23) (15,17) (17,23) (18,19) (18,21) (18,22) (18,20) (19,21) (19,22) (19,20) (20,21) (20,22) (21,22)\nQ: Is there a path between node 20 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1636"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,9) (1,10) (1,3) (2,6) (2,4) (2,7) (3,6) (3,10) (3,9) (3,12) (4,8) (5,9) (5,12) (6,9) (6,12) (6,7) (7,10) (7,9) (7,14) (8,10) (8,9) (8,14) (12,14)\nQ: Is there a path between node 4 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1637"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (1,2)\nQ: Is there a path between node 3 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1638"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,19) (0,25) (0,2) (0,13) (0,1) (1,17) (1,24) (1,25) (1,11) (2,17) (2,25) (2,16) (2,13) (3,17) (4,23) (4,7) (4,14) (4,8) (5,18) (5,16) (6,18) (6,16) (6,21) (7,14) (7,15) (7,10) (8,23) (8,10) (9,14) (9,10) (10,23) (10,20) (11,17) (11,18) (11,25) (11,16) (11,13) (12,16) (13,17) (13,24) (13,25) (13,21) (14,15) (16,21) (17,19) (17,18) (17,25) (19,25) (19,21) (21,25)\nQ: Is there a path between node 5 and node 22?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1639"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,12) (0,11) (0,8) (0,1) (0,13) (0,10) (0,3) (1,2) (1,5) (1,12) (1,11) (1,8) (1,13) (1,10) (1,3) (2,5) (2,12) (2,11) (2,8) (2,13) (2,10) (2,3) (3,5) (3,12) (3,11) (3,8) (3,13) (3,10) (4,9) (4,6) (4,7) (4,14) (5,12) (5,11) (5,8) (5,13) (5,10) (6,9) (6,7) (6,14) (7,9) (7,14) (8,12) (8,11) (8,13) (8,10) (9,14) (10,12) (10,11) (10,13) (11,12) (11,13) (12,13)\nQ: Is there a path between node 9 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1640"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,12) (0,1) (0,7) (0,16) (0,13) (0,9) (0,2) (0,10) (0,21) (0,19) (0,3) (0,20) (0,8) (0,23) (0,5) (0,4) (0,6) (0,22) (1,15) (1,12) (1,7) (1,16) (1,13) (1,9) (1,2) (1,10) (1,21) (1,19) (1,3) (1,20) (1,8) (1,23) (1,5) (1,4) (1,6) (1,22) (2,15) (2,12) (2,7) (2,16) (2,13) (2,9) (2,10) (2,21) (2,19) (2,3) (2,20) (2,8) (2,23) (2,5) (2,4) (2,6) (2,22) (3,15) (3,12) (3,7) (3,16) (3,13) (3,9) (3,10) (3,21) (3,19) (3,20) (3,8) (3,23) (3,5) (3,4) (3,6) (3,22) (4,15) (4,12) (4,7) (4,16) (4,13) (4,9) (4,10) (4,21) (4,19) (4,20) (4,8) (4,23) (4,5) (4,6) (4,22) (5,15) (5,12) (5,7) (5,16) (5,13) (5,9) (5,10) (5,21) (5,19) (5,20) (5,8) (5,23) (5,6) (5,22) (6,15) (6,12) (6,7) (6,16) (6,13) (6,9) (6,10) (6,21) (6,19) (6,20) (6,8) (6,23) (6,22) (7,15) (7,12) (7,16) (7,13) (7,9) (7,10) (7,21) (7,19) (7,20) (7,8) (7,23) (7,22) (8,15) (8,12) (8,16) (8,13) (8,9) (8,10) (8,21) (8,19) (8,20) (8,23) (8,22) (9,15) (9,12) (9,16) (9,13) (9,10) (9,21) (9,19) (9,20) (9,23) (9,22) (10,15) (10,12) (10,16) (10,13) (10,21) (10,19) (10,20) (10,23) (10,22) (11,17) (11,14) (11,18) (12,15) (12,16) (12,13) (12,21) (12,19) (12,20) (12,23) (12,22) (13,15) (13,16) (13,21) (13,19) (13,20) (13,23) (13,22) (14,17) (14,18) (15,16) (15,21) (15,19) (15,20) (15,23) (15,22) (16,21) (16,19) (16,20) (16,23) (16,22) (17,18) (19,21) (19,20) (19,23) (19,22) (20,21) (20,23) (20,22) (21,23) (21,22) (22,23)\nQ: Is there a path between node 4 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1641"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,24) (0,2) (0,7) (0,15) (0,14) (0,22) (0,10) (0,18) (0,5) (0,9) (0,4) (0,11) (0,8) (0,20) (0,13) (1,2) (1,7) (1,15) (1,14) (1,18) (1,5) (1,16) (1,9) (1,4) (1,11) (1,8) (1,13) (2,24) (2,7) (2,15) (2,14) (2,22) (2,18) (2,16) (2,9) (2,4) (2,11) (2,8) (2,20) (2,23) (3,21) (4,7) (4,14) (4,22) (4,18) (4,16) (4,13) (4,23) (5,24) (5,7) (5,15) (5,14) (5,22) (5,10) (5,18) (5,20) (5,23) (6,12) (7,24) (7,15) (7,14) (7,10) (7,18) (7,16) (7,9) (7,11) (7,8) (7,20) (7,13) (7,23) (8,24) (8,14) (8,10) (8,18) (8,9) (8,13) (8,23) (9,24) (9,15) (9,14) (9,22) (9,10) (9,16) (9,20) (9,23) (10,24) (10,15) (10,14) (10,22) (10,18) (10,16) (10,20) (11,15) (11,14) (11,18) (11,16) (11,20) (11,13) (11,23) (13,24) (13,15) (13,18) (13,16) (13,23) (14,24) (14,15) (14,22) (14,18) (14,16) (14,23) (15,24) (15,22) (15,18) (15,16) (15,20) (15,23) (16,24) (16,20) (16,23) (18,22) (18,20) (18,23) (19,21) (20,22) (22,24) (22,23) (23,24)\nQ: Is there a path between node 18 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1642"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,11) (0,22) (0,30) (0,25) (0,19) (0,12) (0,13) (0,10) (0,29) (1,17) (1,4) (1,18) (1,7) (1,27) (1,2) (1,3) (1,9) (1,23) (1,28) (2,4) (2,21) (2,26) (2,7) (2,27) (2,9) (2,23) (2,28) (3,17) (3,4) (3,21) (3,26) (3,18) (3,7) (3,27) (3,14) (3,9) (3,23) (3,28) (3,24) (4,17) (4,21) (4,26) (4,18) (4,14) (4,9) (4,28) (4,24) (5,11) (5,22) (5,20) (5,25) (5,29) (6,8) (7,21) (7,26) (7,18) (7,27) (7,23) (7,28) (7,24) (9,21) (9,26) (9,18) (9,27) (9,14) (9,23) (9,28) (9,24) (10,11) (10,22) (10,20) (10,30) (10,25) (10,16) (10,19) (10,15) (10,13) (10,29) (11,22) (11,20) (11,30) (11,25) (11,16) (11,19) (11,12) (11,15) (11,13) (11,29) (12,22) (12,20) (12,30) (12,16) (12,15) (12,13) (13,22) (13,20) (13,30) (13,25) (13,16) (13,19) (13,15) (13,29) (14,26) (14,18) (14,23) (14,28) (14,24) (15,22) (15,30) (15,16) (15,19) (15,29) (16,22) (16,30) (16,25) (16,19) (16,29) (17,26) (17,18) (17,27) (17,23) (17,28) (18,21) (18,26) (18,27) (18,24) (19,20) (19,30) (19,25) (19,29) (20,22) (20,25) (20,29) (21,26) (21,27) (21,28) (21,24) (22,30) (22,29) (23,26) (23,27) (23,28) (23,24) (24,27) (24,28) (25,29) (26,27) (27,28) (29,30)\nQ: Is there a path between node 6 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1643"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,3) (0,13) (0,15) (0,7) (1,4) (1,6) (2,9) (2,18) (2,13) (3,12) (4,11) (6,8) (6,17) (7,16) (7,12) (7,13) (7,14) (8,11) (8,17) (8,20) (9,18) (9,21) (9,14) (9,15) (10,12) (12,16) (12,15) (13,18) (13,15) (14,16) (14,21) (15,16) (15,18) (16,18)\nQ: Is there a path between node 4 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1644"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,3) (0,7) (0,10) (0,13) (0,12) (0,16) (1,14) (1,2) (1,5) (1,9) (1,8) (1,15) (1,4) (1,6) (2,14) (2,5) (2,9) (2,8) (2,15) (2,4) (2,6) (3,11) (3,7) (3,10) (3,13) (3,12) (3,16) (4,14) (4,5) (4,9) (4,8) (4,15) (4,6) (5,14) (5,9) (5,8) (5,15) (5,6) (6,14) (6,9) (6,8) (6,15) (7,11) (7,10) (7,13) (7,12) (7,16) (8,14) (8,9) (8,15) (9,14) (9,15) (10,11) (10,13) (10,12) (10,16) (11,13) (11,12) (11,16) (12,13) (12,16) (13,16) (14,15)\nQ: Is there a path between node 0 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1645"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,2) (0,1) (1,5) (1,6) (2,6) (3,7) (4,7) (5,6)\nQ: Is there a path between node 4 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1646"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,25) (0,13) (0,3) (0,1) (1,11) (1,25) (1,13) (1,2) (1,3) (1,8) (2,21) (2,22) (2,25) (2,13) (2,3) (3,18) (3,22) (3,11) (3,13) (4,23) (4,14) (4,6) (4,12) (4,27) (4,15) (4,5) (4,16) (4,26) (4,20) (4,7) (4,19) (5,14) (5,6) (5,12) (5,27) (5,15) (5,16) (5,9) (5,20) (5,7) (6,23) (6,14) (6,12) (6,24) (6,15) (6,16) (6,9) (6,17) (6,26) (6,20) (6,7) (6,19) (7,23) (7,14) (7,12) (7,24) (7,10) (7,16) (7,9) (7,17) (7,26) (7,20) (7,19) (8,21) (8,18) (8,22) (8,11) (8,25) (8,13) (9,23) (9,12) (9,10) (9,16) (9,17) (9,26) (9,20) (10,23) (10,14) (10,12) (10,24) (10,27) (10,16) (10,17) (10,26) (10,19) (11,21) (11,22) (11,25) (11,13) (12,23) (12,14) (12,24) (12,27) (12,16) (12,26) (12,20) (12,19) (13,22) (13,25) (14,23) (14,24) (14,16) (14,26) (14,19) (15,24) (15,27) (15,16) (15,26) (16,23) (16,27) (16,17) (16,26) (16,20) (17,27) (17,26) (17,20) (17,19) (18,22) (19,23) (19,24) (19,27) (19,26) (19,20) (20,23) (20,26) (21,22) (21,25) (22,25) (23,24) (23,27) (24,27) (24,26) (26,27)\nQ: Is there a path between node 12 and node 22?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1647"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 2 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1648"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (0,8) (0,10) (0,12) (0,13) (1,10) (2,5) (2,16) (3,13) (4,16) (5,7) (5,14) (6,7) (7,16) (7,14) (9,13) (10,15) (11,12) (12,15)\nQ: Is there a path between node 16 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1649"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,15) (0,25) (0,14) (0,7) (0,2) (0,9) (0,5) (1,26) (1,15) (1,25) (1,7) (1,6) (1,2) (1,20) (1,22) (2,25) (2,19) (2,14) (2,4) (3,12) (3,16) (4,15) (4,7) (4,6) (4,8) (5,26) (5,20) (5,8) (5,9) (5,22) (5,13) (6,19) (6,17) (6,7) (6,20) (6,22) (7,19) (7,17) (7,9) (8,19) (9,26) (9,14) (9,24) (11,12) (12,21) (12,18) (12,16) (13,17) (13,22) (14,26) (14,22) (15,19) (15,20) (16,21) (18,23) (19,20) (19,22) (25,26)\nQ: Is there a path between node 1 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1650"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,4) (1,23) (1,7) (1,18) (1,24) (1,32) (1,31) (1,21) (1,27) (1,11) (1,6) (1,29) (1,17) (1,20) (2,23) (2,7) (2,18) (2,33) (2,24) (2,31) (2,21) (2,8) (2,27) (2,11) (2,29) (2,17) (2,26) (3,9) (3,22) (3,13) (3,5) (3,30) (3,28) (3,16) (3,14) (3,15) (4,19) (4,10) (5,9) (5,22) (5,13) (5,28) (5,16) (5,14) (6,18) (6,32) (6,25) (6,21) (6,8) (6,11) (6,17) (6,20) (6,26) (7,18) (7,33) (7,24) (7,32) (7,25) (7,31) (7,21) (7,17) (7,20) (7,26) (8,18) (8,33) (8,32) (8,25) (8,31) (8,27) (8,11) (8,29) (8,20) (8,26) (9,22) (9,13) (9,30) (9,28) (9,14) (9,15) (10,19) (10,12) (11,18) (11,33) (11,24) (11,25) (11,31) (11,27) (11,29) (11,26) (12,19) (13,28) (13,15) (14,30) (14,28) (14,16) (14,15) (15,22) (15,30) (15,16) (16,22) (17,23) (17,18) (17,33) (17,25) (17,31) (17,21) (17,27) (17,29) (17,20) (17,26) (18,23) (18,32) (18,25) (18,21) (18,29) (18,20) (18,26) (20,23) (20,33) (20,32) (20,25) (20,31) (20,21) (20,27) (20,29) (20,26) (21,23) (21,33) (21,24) (21,25) (21,29) (23,33) (23,24) (23,25) (23,31) (23,27) (23,29) (23,26) (24,33) (24,32) (24,25) (24,27) (24,29) (24,26) (25,32) (25,31) (25,27) (25,29) (25,26) (26,33) (26,31) (26,27) (27,31) (27,29) (28,30) (31,32) (32,33)\nQ: Is there a path between node 18 and node 23?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1651"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,6) (0,1) (0,5) (1,7) (1,6) (1,8) (1,5) (2,7) (2,8) (2,5) (3,4) (5,7) (5,6) (5,8)\nQ: Is there a path between node 4 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1652"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,6) (0,1) (0,7) (0,4) (1,5) (1,6) (1,7) (1,4) (2,3) (4,5) (4,6) (4,7) (5,6) (5,7) (6,7)\nQ: Is there a path between node 7 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1653"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,22) (0,15) (0,8) (0,12) (0,14) (0,2) (0,9) (0,1) (1,15) (1,20) (1,12) (2,20) (2,12) (2,7) (2,16) (3,15) (3,7) (3,16) (3,13) (3,14) (3,17) (3,21) (4,22) (4,8) (4,12) (4,17) (4,11) (6,23) (7,15) (7,17) (7,11) (7,21) (7,18) (8,22) (8,15) (8,20) (8,16) (8,9) (9,22) (9,13) (9,11) (9,21) (9,18) (10,22) (10,13) (10,21) (11,22) (11,15) (11,20) (11,12) (11,21) (11,18) (12,15) (12,13) (13,20) (13,18) (14,20) (17,22) (17,18) (18,20) (19,23) (20,22) (21,22)\nQ: Is there a path between node 19 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1654"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,12) (1,25) (1,2) (1,10) (1,12) (1,3) (2,8) (2,22) (2,25) (2,26) (2,19) (2,11) (2,12) (2,7) (2,21) (3,25) (3,26) (3,10) (3,27) (3,21) (5,24) (5,6) (6,23) (6,9) (7,22) (7,25) (7,11) (8,20) (8,22) (8,25) (8,26) (8,27) (9,24) (10,14) (10,25) (10,13) (10,27) (10,21) (11,22) (11,12) (11,17) (11,21) (12,19) (12,18) (12,17) (12,27) (12,21) (13,17) (13,21) (14,17) (14,21) (15,23) (15,24) (16,22) (17,22) (17,25) (17,19) (18,20) (18,26) (18,21) (19,22) (19,26) (19,27) (20,27) (22,25) (25,26)\nQ: Is there a path between node 4 and node 19?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1655"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,3) (0,5) (1,2) (1,10) (1,3) (1,5) (2,6) (2,10) (3,17) (3,14) (3,6) (3,9) (4,14) (4,7) (4,9) (5,17) (5,14) (5,6) (5,10) (5,7) (6,14) (6,16) (6,7) (9,17) (9,16) (9,10) (10,14) (11,15) (12,13) (14,17) (14,16) (14,15) (15,17)\nQ: Is there a path between node 6 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1656"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,11) (0,2) (0,7) (0,8) (0,16) (0,15) (1,11) (1,2) (1,7) (1,8) (1,16) (1,15) (1,14) (2,4) (2,11) (2,5) (2,7) (2,12) (2,16) (2,15) (3,13) (3,10) (4,6) (4,5) (4,7) (4,8) (4,12) (4,16) (4,15) (4,14) (5,6) (5,7) (5,8) (5,12) (5,16) (5,14) (6,11) (6,7) (6,8) (6,12) (6,16) (6,15) (6,14) (7,11) (7,8) (7,16) (7,14) (8,11) (8,12) (8,16) (11,12) (11,16) (11,15) (11,14) (12,14) (14,16) (14,15)\nQ: Is there a path between node 16 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1657"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (1,5) (1,18) (1,7) (1,22) (1,11) (1,20) (1,4) (1,23) (2,14) (2,10) (2,21) (2,15) (2,16) (2,3) (3,14) (3,10) (3,15) (3,16) (3,6) (3,19) (4,18) (4,7) (4,22) (4,11) (4,20) (4,23) (5,13) (5,7) (5,22) (5,11) (5,20) (5,23) (6,10) (6,21) (6,15) (6,16) (6,9) (6,8) (6,19) (7,13) (7,22) (7,20) (7,23) (8,10) (8,9) (8,19) (9,21) (9,15) (9,19) (10,21) (10,16) (10,19) (11,18) (11,13) (11,22) (11,23) (12,17) (13,22) (13,20) (14,15) (14,16) (14,19) (15,16) (15,19) (16,21) (16,19) (18,20) (18,23) (19,21) (20,22) (20,23) (22,23)\nQ: Is there a path between node 15 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1658"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,13) (0,12) (0,14) (0,8) (0,3) (0,6) (0,2) (0,9) (0,5) (1,10) (1,7) (1,11) (2,4) (2,13) (2,12) (2,14) (2,8) (2,3) (2,6) (2,9) (2,5) (3,4) (3,13) (3,12) (3,14) (3,8) (3,6) (3,9) (3,5) (4,13) (4,12) (4,14) (4,8) (4,6) (4,9) (4,5) (5,13) (5,12) (5,14) (5,8) (5,6) (5,9) (6,13) (6,12) (6,14) (6,8) (6,9) (7,10) (7,11) (8,13) (8,12) (8,14) (8,9) (9,13) (9,12) (9,14) (10,11) (12,13) (12,14) (13,14)\nQ: Is there a path between node 10 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1659"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (1,5) (1,18) (1,7) (1,22) (1,11) (1,20) (1,4) (1,23) (2,14) (2,10) (2,21) (2,15) (2,16) (2,3) (3,14) (3,10) (3,15) (3,16) (3,6) (3,19) (4,18) (4,7) (4,22) (4,11) (4,20) (4,23) (5,13) (5,7) (5,22) (5,11) (5,20) (5,23) (6,10) (6,21) (6,15) (6,16) (6,9) (6,8) (6,19) (7,13) (7,22) (7,20) (7,23) (8,10) (8,9) (8,19) (9,21) (9,15) (9,19) (10,21) (10,16) (10,19) (11,18) (11,13) (11,22) (11,23) (12,17) (13,22) (13,20) (14,15) (14,16) (14,19) (15,16) (15,19) (16,21) (16,19) (18,20) (18,23) (19,21) (20,22) (20,23) (22,23)\nQ: Is there a path between node 13 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1660"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,3) (0,14) (1,8) (1,6) (1,14) (2,6) (2,12) (2,18) (3,8) (3,6) (3,12) (3,18) (4,12) (4,9) (4,14) (5,15) (5,16) (5,7) (6,8) (6,12) (6,14) (7,10) (9,11) (9,18) (15,17) (15,16)\nQ: Is there a path between node 13 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1661"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,30) (0,27) (0,33) (0,11) (0,5) (0,12) (0,20) (0,7) (0,28) (0,17) (0,6) (0,4) (0,32) (0,13) (0,3) (0,22) (0,31) (1,25) (1,29) (1,30) (1,27) (1,33) (1,2) (1,5) (1,12) (1,20) (1,28) (1,18) (1,16) (1,24) (1,6) (1,13) (1,3) (1,22) (1,31) (2,25) (2,23) (2,29) (2,30) (2,27) (2,33) (2,11) (2,5) (2,12) (2,7) (2,18) (2,16) (2,17) (2,24) (2,13) (2,22) (2,15) (3,25) (3,23) (3,29) (3,30) (3,12) (3,7) (3,18) (3,16) (3,24) (3,4) (3,13) (3,22) (3,31) (4,23) (4,29) (4,27) (4,33) (4,11) (4,5) (4,7) (4,18) (4,24) (4,32) (4,15) (4,31) (5,25) (5,23) (5,30) (5,27) (5,33) (5,11) (5,12) (5,20) (5,7) (5,28) (5,24) (5,6) (5,32) (5,13) (5,22) (5,15) (5,31) (6,25) (6,23) (6,30) (6,27) (6,33) (6,12) (6,20) (6,7) (6,18) (6,24) (6,32) (6,13) (7,25) (7,30) (7,27) (7,33) (7,20) (7,28) (7,18) (7,24) (7,32) (7,13) (7,22) (7,15) (7,31) (8,14) (8,26) (8,19) (9,14) (9,26) (9,19) (9,21) (9,10) (10,14) (10,26) (10,19) (11,23) (11,29) (11,30) (11,27) (11,33) (11,20) (11,18) (11,16) (11,17) (11,32) (11,13) (11,22) (11,15) (11,31) (12,25) (12,23) (12,29) (12,27) (12,33) (12,28) (12,16) (12,24) (12,13) (12,22) (12,15) (12,31) (13,25) (13,23) (13,29) (13,27) (13,33) (13,20) (13,28) (13,18) (13,16) (13,17) (13,24) (13,32) (13,15) (13,31) (14,26) (15,25) (15,23) (15,29) (15,30) (15,33) (15,16) (15,17) (15,24) (15,22) (15,31) (16,25) (16,23) (16,29) (16,30) (16,27) (16,28) (16,17) (16,24) (16,32) (16,22) (17,25) (17,23) (17,29) (17,33) (17,20) (17,18) (17,24) (17,31) (18,25) (18,29) (18,30) (18,33) (18,28) (18,24) (18,31) (20,25) (20,23) (20,30) (20,24) (20,32) (20,22) (20,31) (21,26) (22,25) (22,29) (22,30) (22,28) (22,24) (23,25) (23,29) (23,27) (23,28) (23,24) (23,32) (24,25) (24,29) (24,27) (24,33) (24,28) (24,31) (25,29) (25,30) (25,27) (25,28) (25,32) (25,31) (27,29) (27,30) (27,33) (27,28) (28,29) (28,30) (28,33) (28,32) (28,31) (29,30) (29,33) (29,32) (29,31) (30,33) (30,32) (30,31) (31,33) (31,32) (32,33)\nQ: Is there a path between node 13 and node 31?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1662"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (3,7) (4,6) (5,6)\nQ: Is there a path between node 4 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1663"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,13) (0,19) (0,11) (0,16) (0,20) (0,8) (0,5) (0,3) (0,2) (0,7) (0,6) (0,17) (0,14) (0,12) (0,1) (0,18) (0,10) (0,23) (0,9) (1,4) (1,13) (1,19) (1,11) (1,16) (1,20) (1,8) (1,5) (1,3) (1,2) (1,7) (1,6) (1,17) (1,14) (1,12) (1,18) (1,10) (1,23) (1,9) (2,4) (2,13) (2,19) (2,11) (2,16) (2,20) (2,8) (2,5) (2,3) (2,7) (2,6) (2,17) (2,14) (2,12) (2,18) (2,10) (2,23) (2,9) (3,4) (3,13) (3,19) (3,11) (3,16) (3,20) (3,8) (3,5) (3,7) (3,6) (3,17) (3,14) (3,12) (3,18) (3,10) (3,23) (3,9) (4,13) (4,19) (4,11) (4,16) (4,20) (4,8) (4,5) (4,7) (4,6) (4,17) (4,14) (4,12) (4,18) (4,10) (4,23) (4,9) (5,13) (5,19) (5,11) (5,16) (5,20) (5,8) (5,7) (5,6) (5,17) (5,14) (5,12) (5,18) (5,10) (5,23) (5,9) (6,13) (6,19) (6,11) (6,16) (6,20) (6,8) (6,7) (6,17) (6,14) (6,12) (6,18) (6,10) (6,23) (6,9) (7,13) (7,19) (7,11) (7,16) (7,20) (7,8) (7,17) (7,14) (7,12) (7,18) (7,10) (7,23) (7,9) (8,13) (8,19) (8,11) (8,16) (8,20) (8,17) (8,14) (8,12) (8,18) (8,10) (8,23) (8,9) (9,13) (9,19) (9,11) (9,16) (9,20) (9,17) (9,14) (9,12) (9,18) (9,10) (9,23) (10,13) (10,19) (10,11) (10,16) (10,20) (10,17) (10,14) (10,12) (10,18) (10,23) (11,13) (11,19) (11,16) (11,20) (11,17) (11,14) (11,12) (11,18) (11,23) (12,13) (12,19) (12,16) (12,20) (12,17) (12,14) (12,18) (12,23) (13,19) (13,16) (13,20) (13,17) (13,14) (13,18) (13,23) (14,19) (14,16) (14,20) (14,17) (14,18) (14,23) (15,21) (15,22) (16,19) (16,20) (16,17) (16,18) (16,23) (17,19) (17,20) (17,18) (17,23) (18,19) (18,20) (18,23) (19,20) (19,23) (20,23) (21,22)\nQ: Is there a path between node 21 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1664"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,24) (0,1) (0,6) (0,14) (1,10) (2,25) (2,5) (2,20) (2,18) (3,22) (3,6) (3,19) (3,23) (4,9) (4,18) (5,15) (5,25) (5,17) (5,20) (6,11) (6,24) (6,14) (6,7) (6,21) (7,24) (8,25) (8,17) (8,20) (8,18) (9,25) (10,24) (10,22) (10,21) (11,22) (11,19) (11,23) (12,15) (12,16) (12,17) (13,19) (13,14) (14,22) (14,19) (15,16) (15,18) (16,17) (17,20) (18,25) (19,24) (19,22) (20,25) (21,23) (22,24) (22,23)\nQ: Is there a path between node 21 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1665"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,31) (1,4) (1,27) (1,25) (2,31) (2,24) (2,13) (2,10) (3,30) (3,32) (3,27) (3,15) (4,30) (4,6) (4,28) (4,8) (5,22) (6,27) (7,20) (7,11) (7,12) (8,15) (9,14) (10,17) (10,23) (10,13) (11,14) (12,18) (13,23) (14,22) (15,30) (15,27) (15,25) (15,16) (15,28) (17,23) (17,21) (18,22) (18,33) (20,22) (21,31) (23,24) (25,30) (25,27) (25,28) (26,31) (27,30) (27,32) (28,32)\nQ: Is there a path between node 4 and node 20?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1666"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,6) (0,11) (0,19) (0,20) (0,1) (0,15) (0,12) (0,7) (0,22) (0,5) (0,21) (0,3) (0,4) (0,18) (0,17) (1,14) (1,6) (1,11) (1,19) (1,20) (1,15) (1,12) (1,7) (1,22) (1,5) (1,21) (1,3) (1,4) (1,18) (1,17) (2,13) (2,10) (2,8) (2,16) (2,9) (3,14) (3,6) (3,11) (3,19) (3,20) (3,15) (3,12) (3,7) (3,22) (3,5) (3,21) (3,4) (3,18) (3,17) (4,14) (4,6) (4,11) (4,19) (4,20) (4,15) (4,12) (4,7) (4,22) (4,5) (4,21) (4,18) (4,17) (5,14) (5,6) (5,11) (5,19) (5,20) (5,15) (5,12) (5,7) (5,22) (5,21) (5,18) (5,17) (6,14) (6,11) (6,19) (6,20) (6,15) (6,12) (6,7) (6,22) (6,21) (6,18) (6,17) (7,14) (7,11) (7,19) (7,20) (7,15) (7,12) (7,22) (7,21) (7,18) (7,17) (8,13) (8,10) (8,16) (8,9) (9,13) (9,10) (9,16) (10,13) (10,16) (11,14) (11,19) (11,20) (11,15) (11,12) (11,22) (11,21) (11,18) (11,17) (12,14) (12,19) (12,20) (12,15) (12,22) (12,21) (12,18) (12,17) (13,16) (14,19) (14,20) (14,15) (14,22) (14,21) (14,18) (14,17) (15,19) (15,20) (15,22) (15,21) (15,18) (15,17) (17,19) (17,20) (17,22) (17,21) (17,18) (18,19) (18,20) (18,22) (18,21) (19,20) (19,22) (19,21) (20,22) (20,21) (21,22)\nQ: Is there a path between node 12 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1667"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,6) (0,1) (0,5) (1,7) (1,6) (1,8) (1,5) (2,7) (2,8) (2,5) (3,4) (5,7) (5,6) (5,8)\nQ: Is there a path between node 5 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1668"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,9) (0,14) (0,18) (0,3) (0,1) (0,17) (0,4) (0,8) (0,7) (0,15) (0,11) (0,10) (0,13) (1,5) (1,9) (1,14) (1,18) (1,3) (1,17) (1,4) (1,8) (1,7) (1,15) (1,11) (1,10) (1,13) (3,5) (3,9) (3,14) (3,18) (3,17) (3,4) (3,8) (3,7) (3,15) (3,11) (3,10) (3,13) (4,5) (4,9) (4,14) (4,18) (4,17) (4,8) (4,7) (4,15) (4,11) (4,10) (4,13) (5,9) (5,14) (5,18) (5,17) (5,8) (5,7) (5,15) (5,11) (5,10) (5,13) (6,12) (6,16) (7,9) (7,14) (7,18) (7,17) (7,8) (7,15) (7,11) (7,10) (7,13) (8,9) (8,14) (8,18) (8,17) (8,15) (8,11) (8,10) (8,13) (9,14) (9,18) (9,17) (9,15) (9,11) (9,10) (9,13) (10,14) (10,18) (10,17) (10,15) (10,11) (10,13) (11,14) (11,18) (11,17) (11,15) (11,13) (12,16) (13,14) (13,18) (13,17) (13,15) (14,18) (14,17) (14,15) (15,18) (15,17) (17,18)\nQ: Is there a path between node 12 and node 15?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1669"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,34) (0,1) (0,10) (0,12) (1,12) (2,24) (3,31) (3,30) (3,25) (4,19) (4,6) (5,8) (7,26) (10,20) (10,28) (10,17) (10,18) (12,20) (12,32) (12,17) (13,14) (13,15) (13,21) (13,26) (13,23) (14,15) (14,21) (15,26) (15,23) (16,21) (16,30) (17,20) (17,27) (17,32) (18,27) (18,34) (19,33) (20,27) (21,31) (21,22) (22,26) (22,31) (23,31) (26,31) (28,34) (30,31)\nQ: Is there a path between node 5 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1670"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,20) (0,13) (0,24) (0,4) (1,21) (1,3) (1,11) (1,10) (1,23) (1,8) (1,2) (1,22) (1,19) (1,18) (2,21) (2,3) (2,11) (2,10) (2,23) (2,8) (2,22) (2,19) (2,18) (3,21) (3,11) (3,10) (3,23) (3,8) (3,22) (3,19) (3,18) (4,14) (4,20) (4,13) (4,24) (5,7) (5,9) (5,12) (5,16) (5,15) (5,17) (5,6) (6,7) (6,9) (6,12) (6,16) (6,15) (6,17) (7,9) (7,12) (7,16) (7,15) (7,17) (8,21) (8,11) (8,10) (8,23) (8,22) (8,19) (8,18) (9,12) (9,16) (9,15) (9,17) (10,21) (10,11) (10,23) (10,22) (10,19) (10,18) (11,21) (11,23) (11,22) (11,19) (11,18) (12,16) (12,15) (12,17) (13,14) (13,20) (13,24) (14,20) (14,24) (15,16) (15,17) (16,17) (18,21) (18,23) (18,22) (18,19) (19,21) (19,23) (19,22) (20,24) (21,23) (21,22) (22,23)\nQ: Is there a path between node 21 and node 18?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1671"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,7) (0,4) (0,10) (0,5) (0,13) (0,12) (0,1) (0,2) (0,3) (0,15) (0,6) (0,8) (0,14) (1,11) (1,7) (1,4) (1,10) (1,5) (1,13) (1,12) (1,2) (1,3) (1,15) (1,6) (1,8) (1,14) (2,11) (2,7) (2,4) (2,10) (2,5) (2,13) (2,12) (2,3) (2,15) (2,6) (2,8) (2,14) (3,11) (3,7) (3,4) (3,10) (3,5) (3,13) (3,12) (3,15) (3,6) (3,8) (3,14) (4,11) (4,7) (4,10) (4,5) (4,13) (4,12) (4,15) (4,6) (4,8) (4,14) (5,11) (5,7) (5,10) (5,13) (5,12) (5,15) (5,6) (5,8) (5,14) (6,11) (6,7) (6,10) (6,13) (6,12) (6,15) (6,8) (6,14) (7,11) (7,10) (7,13) (7,12) (7,15) (7,8) (7,14) (8,11) (8,10) (8,13) (8,12) (8,15) (8,14) (10,11) (10,13) (10,12) (10,15) (10,14) (11,13) (11,12) (11,15) (11,14) (12,13) (12,15) (12,14) (13,15) (13,14) (14,15)\nQ: Is there a path between node 5 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1672"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,3) (0,4) (1,3) (1,4) (3,4)\nQ: Is there a path between node 2 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1673"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,9) (0,8) (0,19) (0,13) (0,11) (1,15) (1,6) (1,3) (1,12) (1,4) (1,2) (1,23) (1,5) (1,16) (1,22) (1,17) (1,18) (1,21) (1,24) (1,25) (2,15) (2,3) (2,4) (2,20) (2,23) (2,22) (2,27) (2,18) (2,21) (2,24) (3,15) (3,4) (3,26) (3,20) (3,23) (3,5) (3,16) (3,14) (3,22) (3,27) (3,18) (3,21) (3,24) (3,25) (4,15) (4,6) (4,12) (4,26) (4,20) (4,5) (4,22) (4,27) (4,17) (4,21) (4,25) (5,15) (5,6) (5,12) (5,20) (5,16) (5,14) (5,22) (5,27) (5,18) (5,21) (5,25) (6,15) (6,12) (6,27) (6,17) (6,21) (6,24) (6,25) (7,19) (7,13) (8,9) (8,19) (8,13) (9,19) (9,10) (10,19) (10,13) (10,11) (11,13) (12,15) (12,26) (12,20) (12,14) (12,22) (12,21) (12,24) (13,19) (14,15) (14,26) (14,20) (14,16) (14,22) (14,17) (14,21) (14,24) (14,25) (15,26) (15,20) (15,23) (15,16) (15,22) (15,17) (15,18) (15,24) (16,26) (16,27) (16,18) (16,25) (17,26) (17,23) (17,18) (17,21) (17,24) (17,25) (18,26) (18,20) (18,22) (18,27) (18,24) (18,25) (20,26) (20,23) (20,22) (20,27) (20,24) (20,25) (21,22) (21,27) (21,24) (21,25) (22,23) (22,27) (22,24) (22,25) (23,27) (23,25) (24,26) (24,27) (25,26) (25,27) (26,27)\nQ: Is there a path between node 21 and node 25?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1674"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,21) (0,17) (0,7) (0,29) (1,20) (2,32) (2,6) (2,13) (3,22) (3,23) (3,8) (4,30) (4,31) (6,23) (6,16) (6,32) (7,19) (8,14) (8,23) (8,16) (8,32) (8,13) (9,24) (9,17) (9,29) (13,14) (13,32) (14,16) (14,32) (16,20) (16,28) (17,24) (20,28) (21,29) (24,29) (27,30) (30,31)\nQ: Is there a path between node 17 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1675"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,17) (0,1) (0,4) (0,15) (0,2) (0,13) (0,10) (0,6) (0,18) (0,11) (0,12) (0,5) (1,19) (1,17) (1,4) (1,15) (1,2) (1,13) (1,10) (1,6) (1,18) (1,11) (1,12) (1,5) (2,19) (2,17) (2,4) (2,15) (2,13) (2,10) (2,6) (2,18) (2,11) (2,12) (2,5) (3,20) (3,16) (3,14) (3,8) (4,19) (4,17) (4,15) (4,13) (4,10) (4,6) (4,18) (4,11) (4,12) (4,5) (5,19) (5,17) (5,15) (5,13) (5,10) (5,6) (5,18) (5,11) (5,12) (6,19) (6,17) (6,15) (6,13) (6,10) (6,18) (6,11) (6,12) (7,9) (8,20) (8,16) (8,14) (10,19) (10,17) (10,15) (10,13) (10,18) (10,11) (10,12) (11,19) (11,17) (11,15) (11,13) (11,18) (11,12) (12,19) (12,17) (12,15) (12,13) (12,18) (13,19) (13,17) (13,15) (13,18) (14,20) (14,16) (15,19) (15,17) (15,18) (16,20) (17,19) (17,18) (18,19)\nQ: Is there a path between node 16 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1676"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,3) (0,4) (1,3) (1,4) (3,4)\nQ: Is there a path between node 3 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1677"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,14) (0,12) (1,20) (1,12) (2,13) (2,18) (3,17) (4,20) (7,21) (8,18) (9,20) (9,15) (10,13) (10,19) (13,18) (14,16) (14,15) (15,20)\nQ: Is there a path between node 2 and node 18?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1678"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,7) (0,8) (0,9) (0,13) (0,14) (0,15) (0,5) (1,2) (1,12) (1,16) (1,11) (1,3) (1,6) (1,14) (1,4) (2,12) (2,7) (2,9) (2,13) (2,14) (3,16) (3,11) (3,7) (3,8) (3,14) (3,15) (3,5) (3,4) (4,12) (4,11) (4,8) (4,9) (4,13) (4,14) (4,5) (5,12) (5,16) (5,11) (5,7) (5,8) (5,13) (5,14) (5,15) (6,12) (6,16) (6,11) (6,7) (6,14) (6,15) (7,12) (7,16) (7,11) (7,8) (7,9) (7,13) (8,12) (8,16) (8,11) (8,9) (8,13) (8,14) (9,12) (9,16) (9,11) (9,14) (9,15) (11,12) (11,16) (11,14) (12,13) (12,15) (13,16) (13,15) (14,16)\nQ: Is there a path between node 10 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1679"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,2) (0,3) (1,5) (2,4) (2,3) (3,4)\nQ: Is there a path between node 0 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1680"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,21) (1,17) (1,15) (1,2) (1,4) (1,18) (2,8) (2,13) (2,17) (2,15) (2,23) (2,22) (2,4) (2,18) (2,12) (4,21) (4,8) (4,13) (4,15) (4,23) (4,22) (4,18) (4,12) (5,21) (5,8) (5,13) (5,17) (5,15) (5,22) (5,18) (7,14) (7,16) (7,10) (7,11) (7,19) (8,21) (8,17) (8,23) (8,18) (9,14) (9,24) (10,14) (10,24) (10,19) (11,14) (11,16) (11,24) (12,21) (12,13) (12,17) (12,15) (12,23) (12,22) (12,18) (13,21) (13,17) (13,15) (13,23) (13,22) (14,24) (15,21) (15,17) (15,23) (15,22) (15,18) (16,19) (17,21) (17,18) (18,21) (18,23) (21,22) (22,23)\nQ: Is there a path between node 3 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1681"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,6) (0,1) (0,7) (0,4) (1,5) (1,6) (1,7) (1,4) (2,3) (4,5) (4,6) (4,7) (5,6) (5,7) (6,7)\nQ: Is there a path between node 6 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1682"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,32) (0,29) (0,7) (0,15) (1,30) (1,10) (1,8) (2,27) (2,18) (2,20) (2,7) (2,26) (3,14) (3,9) (4,18) (4,11) (4,13) (4,15) (5,30) (5,21) (6,14) (6,21) (6,17) (7,18) (7,22) (7,31) (7,29) (7,26) (8,14) (8,10) (9,21) (10,12) (10,21) (10,17) (11,19) (11,22) (11,28) (11,32) (11,29) (11,15) (11,26) (12,30) (12,21) (13,27) (13,20) (13,28) (13,31) (14,17) (15,20) (15,31) (15,26) (16,27) (16,32) (17,30) (18,27) (18,28) (18,32) (18,26) (18,24) (18,23) (19,27) (19,20) (19,31) (19,29) (19,26) (19,24) (20,25) (20,28) (20,32) (20,26) (22,31) (22,23) (23,27) (23,28) (23,26) (25,26) (26,27) (26,28) (26,29) (28,32) (28,31) (29,31)\nQ: Is there a path between node 2 and node 23?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1683"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,3) (0,2) (1,5) (1,3) (2,5) (2,3) (3,5)\nQ: Is there a path between node 5 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1684"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,11) (0,22) (0,30) (0,25) (0,19) (0,12) (0,13) (0,10) (0,29) (1,17) (1,4) (1,18) (1,7) (1,27) (1,2) (1,3) (1,9) (1,23) (1,28) (2,4) (2,21) (2,26) (2,7) (2,27) (2,9) (2,23) (2,28) (3,17) (3,4) (3,21) (3,26) (3,18) (3,7) (3,27) (3,14) (3,9) (3,23) (3,28) (3,24) (4,17) (4,21) (4,26) (4,18) (4,14) (4,9) (4,28) (4,24) (5,11) (5,22) (5,20) (5,25) (5,29) (6,8) (7,21) (7,26) (7,18) (7,27) (7,23) (7,28) (7,24) (9,21) (9,26) (9,18) (9,27) (9,14) (9,23) (9,28) (9,24) (10,11) (10,22) (10,20) (10,30) (10,25) (10,16) (10,19) (10,15) (10,13) (10,29) (11,22) (11,20) (11,30) (11,25) (11,16) (11,19) (11,12) (11,15) (11,13) (11,29) (12,22) (12,20) (12,30) (12,16) (12,15) (12,13) (13,22) (13,20) (13,30) (13,25) (13,16) (13,19) (13,15) (13,29) (14,26) (14,18) (14,23) (14,28) (14,24) (15,22) (15,30) (15,16) (15,19) (15,29) (16,22) (16,30) (16,25) (16,19) (16,29) (17,26) (17,18) (17,27) (17,23) (17,28) (18,21) (18,26) (18,27) (18,24) (19,20) (19,30) (19,25) (19,29) (20,22) (20,25) (20,29) (21,26) (21,27) (21,28) (21,24) (22,30) (22,29) (23,26) (23,27) (23,28) (23,24) (24,27) (24,28) (25,29) (26,27) (27,28) (29,30)\nQ: Is there a path between node 23 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1685"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (2,8) (2,4) (2,3) (3,8) (5,7) (6,7)\nQ: Is there a path between node 8 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1686"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,10) (0,17) (0,5) (0,13) (0,15) (0,16) (0,3) (0,7) (0,11) (0,1) (0,4) (0,14) (1,12) (1,10) (1,17) (1,5) (1,13) (1,15) (1,16) (1,3) (1,7) (1,11) (1,4) (1,14) (2,8) (2,6) (3,12) (3,10) (3,17) (3,5) (3,13) (3,15) (3,16) (3,7) (3,11) (3,4) (3,14) (4,12) (4,10) (4,17) (4,5) (4,13) (4,15) (4,16) (4,7) (4,11) (4,14) (5,12) (5,10) (5,17) (5,13) (5,15) (5,16) (5,7) (5,11) (5,14) (6,8) (7,12) (7,10) (7,17) (7,13) (7,15) (7,16) (7,11) (7,14) (10,12) (10,17) (10,13) (10,15) (10,16) (10,11) (10,14) (11,12) (11,17) (11,13) (11,15) (11,16) (11,14) (12,17) (12,13) (12,15) (12,16) (12,14) (13,17) (13,15) (13,16) (13,14) (14,17) (14,15) (14,16) (15,17) (15,16) (16,17)\nQ: Is there a path between node 2 and node 15?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1687"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,8) (1,5) (1,10) (1,8) (2,6) (2,7) (3,9) (3,10) (4,11) (4,8) (6,7) (8,9) (8,10) (11,12)\nQ: Is there a path between node 9 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1688"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,1) (3,4)\nQ: Is there a path between node 3 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1689"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,22) (0,15) (0,8) (0,12) (0,14) (0,2) (0,9) (0,1) (1,15) (1,20) (1,12) (2,20) (2,12) (2,7) (2,16) (3,15) (3,7) (3,16) (3,13) (3,14) (3,17) (3,21) (4,22) (4,8) (4,12) (4,17) (4,11) (6,23) (7,15) (7,17) (7,11) (7,21) (7,18) (8,22) (8,15) (8,20) (8,16) (8,9) (9,22) (9,13) (9,11) (9,21) (9,18) (10,22) (10,13) (10,21) (11,22) (11,15) (11,20) (11,12) (11,21) (11,18) (12,15) (12,13) (13,20) (13,18) (14,20) (17,22) (17,18) (18,20) (19,23) (20,22) (21,22)\nQ: Is there a path between node 1 and node 19?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1690"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (0,13) (0,3) (0,14) (0,15) (0,19) (0,7) (0,9) (0,10) (1,5) (1,18) (1,12) (1,13) (1,14) (1,6) (1,17) (1,16) (1,9) (1,10) (1,11) (2,18) (2,12) (2,13) (2,6) (2,15) (2,19) (2,7) (2,17) (2,16) (2,9) (2,10) (2,11) (3,18) (3,12) (3,13) (3,14) (3,6) (3,19) (3,17) (3,9) (3,10) (3,11) (5,18) (5,12) (5,13) (5,14) (5,6) (5,15) (5,19) (5,7) (5,16) (5,11) (6,18) (6,12) (6,7) (6,17) (6,16) (6,9) (6,10) (7,18) (7,12) (7,13) (7,15) (7,19) (7,17) (7,16) (7,10) (7,11) (9,18) (9,13) (9,15) (9,19) (9,16) (9,10) (10,18) (10,13) (10,14) (10,19) (10,17) (10,11) (11,12) (11,13) (11,14) (11,15) (11,19) (11,17) (11,16) (12,14) (12,19) (12,17) (12,16) (13,18) (13,15) (13,19) (13,17) (14,18) (14,15) (14,19) (14,17) (14,16) (15,18) (15,19) (15,16) (16,18) (17,18) (17,19) (18,19)\nQ: Is there a path between node 11 and node 18?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1691"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,11) (0,22) (0,30) (0,25) (0,19) (0,12) (0,13) (0,10) (0,29) (1,17) (1,4) (1,18) (1,7) (1,27) (1,2) (1,3) (1,9) (1,23) (1,28) (2,4) (2,21) (2,26) (2,7) (2,27) (2,9) (2,23) (2,28) (3,17) (3,4) (3,21) (3,26) (3,18) (3,7) (3,27) (3,14) (3,9) (3,23) (3,28) (3,24) (4,17) (4,21) (4,26) (4,18) (4,14) (4,9) (4,28) (4,24) (5,11) (5,22) (5,20) (5,25) (5,29) (6,8) (7,21) (7,26) (7,18) (7,27) (7,23) (7,28) (7,24) (9,21) (9,26) (9,18) (9,27) (9,14) (9,23) (9,28) (9,24) (10,11) (10,22) (10,20) (10,30) (10,25) (10,16) (10,19) (10,15) (10,13) (10,29) (11,22) (11,20) (11,30) (11,25) (11,16) (11,19) (11,12) (11,15) (11,13) (11,29) (12,22) (12,20) (12,30) (12,16) (12,15) (12,13) (13,22) (13,20) (13,30) (13,25) (13,16) (13,19) (13,15) (13,29) (14,26) (14,18) (14,23) (14,28) (14,24) (15,22) (15,30) (15,16) (15,19) (15,29) (16,22) (16,30) (16,25) (16,19) (16,29) (17,26) (17,18) (17,27) (17,23) (17,28) (18,21) (18,26) (18,27) (18,24) (19,20) (19,30) (19,25) (19,29) (20,22) (20,25) (20,29) (21,26) (21,27) (21,28) (21,24) (22,30) (22,29) (23,26) (23,27) (23,28) (23,24) (24,27) (24,28) (25,29) (26,27) (27,28) (29,30)\nQ: Is there a path between node 30 and node 13?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1692"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,4) (0,1) (1,2) (1,5) (1,4) (2,5) (2,4) (4,5)\nQ: Is there a path between node 0 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1693"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,15) (0,18) (0,27) (0,9) (0,13) (0,25) (0,3) (1,8) (1,5) (1,26) (1,12) (1,2) (1,16) (1,14) (2,8) (2,26) (2,12) (2,16) (2,14) (3,7) (3,4) (3,15) (3,18) (3,27) (3,13) (4,7) (4,15) (4,18) (4,27) (4,13) (5,8) (5,12) (5,11) (5,16) (5,14) (5,20) (6,17) (6,21) (6,29) (6,28) (7,15) (7,18) (7,27) (7,9) (7,13) (8,26) (8,23) (8,16) (8,14) (9,15) (10,29) (10,24) (11,12) (11,16) (11,14) (11,20) (12,22) (12,23) (12,14) (12,20) (13,18) (13,27) (14,26) (14,22) (14,23) (14,20) (15,18) (15,27) (15,25) (16,26) (16,22) (16,23) (16,20) (17,21) (17,19) (17,24) (17,28) (19,21) (19,29) (19,24) (19,28) (20,26) (20,22) (20,23) (21,29) (21,24) (22,26) (22,23) (24,29) (24,28) (25,27)\nQ: Is there a path between node 17 and node 15?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1694"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,4) (1,13) (2,11) (3,4) (3,6) (3,19) (4,20) (4,12) (4,16) (5,14) (5,9) (6,18) (6,8) (7,13) (7,8) (7,19) (7,15) (8,18) (8,20) (8,15) (11,14) (12,20) (12,13) (12,19) (12,16) (13,18) (13,15) (15,18) (15,19) (18,20) (18,19)\nQ: Is there a path between node 2 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1695"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,12) (0,1) (0,13) (0,14) (0,11) (0,20) (0,7) (0,21) (1,4) (1,13) (1,14) (1,16) (1,7) (1,21) (2,5) (2,22) (2,8) (2,15) (2,25) (2,9) (2,17) (2,26) (3,11) (3,20) (3,7) (4,13) (4,14) (4,11) (4,20) (4,21) (5,22) (5,18) (5,15) (5,23) (5,25) (5,17) (5,26) (5,24) (6,19) (7,12) (7,13) (7,14) (7,11) (7,20) (7,21) (8,22) (8,15) (8,23) (8,9) (8,17) (8,24) (9,18) (9,15) (9,23) (9,25) (9,17) (11,13) (11,14) (11,16) (11,20) (12,13) (12,14) (12,16) (12,20) (12,21) (13,16) (13,20) (14,16) (14,20) (14,21) (15,22) (15,18) (15,23) (15,25) (15,26) (15,24) (16,21) (17,22) (17,18) (17,23) (17,25) (18,25) (18,24) (20,21) (22,23) (22,25) (22,26) (22,24) (23,26) (23,24) (24,25) (25,26)\nQ: Is there a path between node 6 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1696"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,13) (0,1) (0,9) (0,5) (0,7) (0,3) (0,10) (0,23) (0,26) (0,27) (0,8) (0,14) (0,22) (0,20) (0,15) (0,4) (0,2) (1,25) (1,11) (1,21) (1,13) (1,9) (1,3) (1,10) (1,23) (1,26) (1,27) (1,14) (1,20) (1,15) (1,2) (1,28) (2,25) (2,11) (2,16) (2,21) (2,6) (2,13) (2,9) (2,7) (2,23) (2,26) (2,8) (2,20) (2,15) (3,25) (3,6) (3,13) (3,9) (3,10) (3,27) (3,20) (3,15) (3,4) (3,28) (4,11) (4,16) (4,6) (4,13) (4,10) (4,23) (4,26) (4,27) (4,8) (4,14) (4,22) (4,15) (4,28) (5,25) (5,16) (5,21) (5,6) (5,13) (5,9) (5,7) (5,26) (5,8) (5,22) (5,15) (5,28) (6,11) (6,16) (6,21) (6,13) (6,9) (6,7) (6,10) (6,27) (6,22) (6,20) (6,15) (7,25) (7,16) (7,21) (7,9) (7,10) (7,27) (7,8) (7,14) (7,22) (7,20) (7,15) (7,28) (8,25) (8,13) (8,23) (8,26) (8,27) (8,14) (8,20) (8,28) (9,25) (9,11) (9,16) (9,21) (9,10) (9,23) (9,26) (9,27) (9,22) (9,20) (9,28) (10,11) (10,16) (10,21) (10,13) (10,23) (10,26) (10,27) (10,14) (10,22) (10,20) (10,15) (10,28) (11,25) (11,16) (11,21) (11,13) (11,23) (11,26) (11,27) (11,14) (11,22) (11,20) (12,24) (12,19) (13,25) (13,16) (13,14) (13,22) (13,15) (13,28) (14,25) (14,21) (14,23) (14,26) (14,20) (14,15) (15,16) (15,21) (15,26) (15,27) (15,22) (15,28) (16,21) (16,23) (16,26) (16,27) (16,28) (17,18) (20,25) (20,23) (20,26) (20,27) (20,22) (20,28) (21,25) (21,23) (21,26) (21,22) (22,25) (22,23) (22,27) (23,25) (23,26) (23,27) (23,28) (25,26) (25,27) (26,27) (27,28)\nQ: Is there a path between node 7 and node 22?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1697"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,10) (0,12) (0,20) (0,14) (0,8) (0,3) (0,6) (0,5) (0,15) (0,19) (0,7) (0,9) (0,22) (0,2) (0,21) (0,18) (1,4) (1,10) (1,12) (1,20) (1,8) (1,5) (1,15) (1,16) (1,19) (1,7) (1,9) (1,22) (1,2) (1,18) (2,4) (2,10) (2,12) (2,14) (2,3) (2,5) (2,15) (2,19) (2,7) (2,22) (2,21) (2,18) (3,4) (3,12) (3,20) (3,14) (3,6) (3,5) (3,15) (3,16) (3,19) (3,7) (3,9) (3,22) (3,21) (3,18) (4,10) (4,12) (4,8) (4,6) (4,5) (4,15) (4,16) (4,19) (4,7) (4,9) (4,21) (4,18) (5,12) (5,14) (5,8) (5,6) (5,15) (5,16) (5,19) (5,7) (5,9) (5,22) (5,18) (6,10) (6,12) (6,20) (6,14) (6,16) (6,19) (6,7) (6,9) (6,22) (6,21) (6,18) (7,10) (7,12) (7,14) (7,8) (7,16) (7,9) (7,22) (7,21) (7,18) (8,10) (8,12) (8,14) (8,15) (8,16) (8,19) (8,9) (8,21) (9,12) (9,20) (9,15) (9,16) (9,22) (9,21) (9,18) (10,12) (10,20) (10,14) (10,15) (10,16) (10,18) (12,16) (12,19) (13,17) (14,20) (14,16) (15,16) (15,22) (15,21) (16,20) (16,21) (16,18) (18,22) (18,21) (19,20) (19,22) (19,21) (21,22)\nQ: Is there a path between node 0 and node 13?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1698"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,21) (0,11) (0,15) (0,4) (0,22) (0,5) (0,3) (0,6) (0,20) (0,13) (0,18) (0,9) (0,1) (0,12) (0,24) (0,16) (0,8) (0,23) (0,2) (1,21) (1,11) (1,15) (1,4) (1,22) (1,5) (1,3) (1,6) (1,20) (1,13) (1,18) (1,9) (1,12) (1,24) (1,16) (1,8) (1,23) (1,2) (2,21) (2,11) (2,15) (2,4) (2,22) (2,5) (2,3) (2,6) (2,20) (2,13) (2,18) (2,9) (2,12) (2,24) (2,16) (2,8) (2,23) (3,21) (3,11) (3,15) (3,4) (3,22) (3,5) (3,6) (3,20) (3,13) (3,18) (3,9) (3,12) (3,24) (3,16) (3,8) (3,23) (4,21) (4,11) (4,15) (4,22) (4,5) (4,6) (4,20) (4,13) (4,18) (4,9) (4,12) (4,24) (4,16) (4,8) (4,23) (5,21) (5,11) (5,15) (5,22) (5,6) (5,20) (5,13) (5,18) (5,9) (5,12) (5,24) (5,16) (5,8) (5,23) (6,21) (6,11) (6,15) (6,22) (6,20) (6,13) (6,18) (6,9) (6,12) (6,24) (6,16) (6,8) (6,23) (7,10) (7,14) (7,17) (7,19) (8,21) (8,11) (8,15) (8,22) (8,20) (8,13) (8,18) (8,9) (8,12) (8,24) (8,16) (8,23) (9,21) (9,11) (9,15) (9,22) (9,20) (9,13) (9,18) (9,12) (9,24) (9,16) (9,23) (10,14) (10,17) (10,19) (11,21) (11,15) (11,22) (11,20) (11,13) (11,18) (11,12) (11,24) (11,16) (11,23) (12,21) (12,15) (12,22) (12,20) (12,13) (12,18) (12,24) (12,16) (12,23) (13,21) (13,15) (13,22) (13,20) (13,18) (13,24) (13,16) (13,23) (14,17) (14,19) (15,21) (15,22) (15,20) (15,18) (15,24) (15,16) (15,23) (16,21) (16,22) (16,20) (16,18) (16,24) (16,23) (17,19) (18,21) (18,22) (18,20) (18,24) (18,23) (20,21) (20,22) (20,24) (20,23) (21,22) (21,24) (21,23) (22,24) (22,23) (23,24)\nQ: Is there a path between node 9 and node 16?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1699"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,32) (0,29) (0,7) (0,15) (1,30) (1,10) (1,8) (2,27) (2,18) (2,20) (2,7) (2,26) (3,14) (3,9) (4,18) (4,11) (4,13) (4,15) (5,30) (5,21) (6,14) (6,21) (6,17) (7,18) (7,22) (7,31) (7,29) (7,26) (8,14) (8,10) (9,21) (10,12) (10,21) (10,17) (11,19) (11,22) (11,28) (11,32) (11,29) (11,15) (11,26) (12,30) (12,21) (13,27) (13,20) (13,28) (13,31) (14,17) (15,20) (15,31) (15,26) (16,27) (16,32) (17,30) (18,27) (18,28) (18,32) (18,26) (18,24) (18,23) (19,27) (19,20) (19,31) (19,29) (19,26) (19,24) (20,25) (20,28) (20,32) (20,26) (22,31) (22,23) (23,27) (23,28) (23,26) (25,26) (26,27) (26,28) (26,29) (28,32) (28,31) (29,31)\nQ: Is there a path between node 5 and node 12?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1700"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,6) (0,1) (0,5) (1,7) (1,6) (1,8) (1,5) (2,7) (2,8) (2,5) (3,4) (5,7) (5,6) (5,8)\nQ: Is there a path between node 1 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1701"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,7) (0,13) (0,24) (0,19) (0,5) (0,10) (0,4) (0,2) (0,21) (0,17) (0,23) (0,9) (0,20) (0,15) (0,22) (1,3) (1,18) (1,6) (1,14) (1,8) (1,11) (2,12) (2,7) (2,13) (2,24) (2,19) (2,5) (2,10) (2,4) (2,21) (2,17) (2,23) (2,9) (2,20) (2,15) (2,22) (3,18) (3,6) (3,14) (3,8) (3,11) (4,12) (4,7) (4,13) (4,24) (4,19) (4,5) (4,10) (4,21) (4,17) (4,23) (4,9) (4,20) (4,15) (4,22) (5,12) (5,7) (5,13) (5,24) (5,19) (5,10) (5,21) (5,17) (5,23) (5,9) (5,20) (5,15) (5,22) (6,18) (6,14) (6,8) (6,11) (7,12) (7,13) (7,24) (7,19) (7,10) (7,21) (7,17) (7,23) (7,9) (7,20) (7,15) (7,22) (8,18) (8,14) (8,11) (9,12) (9,13) (9,24) (9,19) (9,10) (9,21) (9,17) (9,23) (9,20) (9,15) (9,22) (10,12) (10,13) (10,24) (10,19) (10,21) (10,17) (10,23) (10,20) (10,15) (10,22) (11,18) (11,14) (12,13) (12,24) (12,19) (12,21) (12,17) (12,23) (12,20) (12,15) (12,22) (13,24) (13,19) (13,21) (13,17) (13,23) (13,20) (13,15) (13,22) (14,18) (15,24) (15,19) (15,21) (15,17) (15,23) (15,20) (15,22) (17,24) (17,19) (17,21) (17,23) (17,20) (17,22) (19,24) (19,21) (19,23) (19,20) (19,22) (20,24) (20,21) (20,23) (20,22) (21,24) (21,23) (21,22) (22,24) (22,23) (23,24)\nQ: Is there a path between node 2 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1702"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,19) (0,25) (0,2) (0,13) (0,1) (1,17) (1,24) (1,25) (1,11) (2,17) (2,25) (2,16) (2,13) (3,17) (4,23) (4,7) (4,14) (4,8) (5,18) (5,16) (6,18) (6,16) (6,21) (7,14) (7,15) (7,10) (8,23) (8,10) (9,14) (9,10) (10,23) (10,20) (11,17) (11,18) (11,25) (11,16) (11,13) (12,16) (13,17) (13,24) (13,25) (13,21) (14,15) (16,21) (17,19) (17,18) (17,25) (19,25) (19,21) (21,25)\nQ: Is there a path between node 21 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1703"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (1,11) (1,9) (1,14) (2,5) (2,6) (3,11) (3,13) (4,11) (4,13) (4,15) (5,7) (5,6) (7,10) (8,11) (8,9) (9,14) (9,12) (11,13) (13,14) (13,15)\nQ: Is there a path between node 7 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1704"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,7) (0,12) (0,32) (0,22) (0,9) (0,20) (0,2) (0,5) (0,14) (0,4) (0,26) (0,21) (1,11) (1,8) (1,24) (1,3) (1,31) (1,28) (1,6) (2,16) (2,7) (2,32) (2,22) (2,9) (2,20) (2,14) (2,4) (2,21) (3,11) (3,8) (3,24) (3,31) (3,28) (4,16) (4,32) (4,22) (4,9) (4,20) (4,5) (4,14) (4,26) (5,16) (5,7) (5,12) (5,32) (5,22) (5,9) (5,20) (5,14) (5,26) (5,21) (6,8) (6,24) (6,31) (6,28) (7,12) (7,32) (7,22) (7,9) (7,14) (7,26) (7,21) (8,24) (8,31) (8,28) (9,16) (9,12) (9,32) (9,20) (9,26) (9,21) (10,23) (10,13) (10,29) (10,19) (10,25) (10,18) (12,32) (12,22) (12,20) (12,26) (12,21) (13,30) (13,27) (13,29) (13,19) (13,25) (13,18) (14,16) (14,32) (14,22) (14,20) (14,26) (15,30) (15,29) (15,25) (15,18) (16,32) (16,22) (16,20) (16,26) (16,21) (17,30) (17,27) (18,30) (18,29) (19,30) (19,23) (19,27) (19,25) (20,32) (20,22) (20,26) (21,32) (21,26) (22,32) (22,26) (23,30) (23,29) (23,25) (24,28) (26,32) (27,30) (27,29) (28,31) (29,30)\nQ: Is there a path between node 13 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1705"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,7) (0,8) (0,10) (0,3) (1,4) (1,11) (1,9) (1,6) (1,12) (1,2) (2,4) (2,11) (2,9) (2,6) (2,12) (3,5) (3,7) (3,8) (3,10) (4,11) (4,9) (4,6) (4,12) (5,7) (5,8) (5,10) (6,11) (6,9) (6,12) (7,8) (7,10) (8,10) (9,11) (9,12) (11,12)\nQ: Is there a path between node 4 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1706"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,6) (0,4) (1,3) (1,7) (1,2) (2,3) (3,9) (4,6) (5,9) (6,8) (7,9)\nQ: Is there a path between node 7 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1707"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,24) (0,2) (0,7) (0,15) (0,14) (0,22) (0,10) (0,18) (0,5) (0,9) (0,4) (0,11) (0,8) (0,20) (0,13) (1,2) (1,7) (1,15) (1,14) (1,18) (1,5) (1,16) (1,9) (1,4) (1,11) (1,8) (1,13) (2,24) (2,7) (2,15) (2,14) (2,22) (2,18) (2,16) (2,9) (2,4) (2,11) (2,8) (2,20) (2,23) (3,21) (4,7) (4,14) (4,22) (4,18) (4,16) (4,13) (4,23) (5,24) (5,7) (5,15) (5,14) (5,22) (5,10) (5,18) (5,20) (5,23) (6,12) (7,24) (7,15) (7,14) (7,10) (7,18) (7,16) (7,9) (7,11) (7,8) (7,20) (7,13) (7,23) (8,24) (8,14) (8,10) (8,18) (8,9) (8,13) (8,23) (9,24) (9,15) (9,14) (9,22) (9,10) (9,16) (9,20) (9,23) (10,24) (10,15) (10,14) (10,22) (10,18) (10,16) (10,20) (11,15) (11,14) (11,18) (11,16) (11,20) (11,13) (11,23) (13,24) (13,15) (13,18) (13,16) (13,23) (14,24) (14,15) (14,22) (14,18) (14,16) (14,23) (15,24) (15,22) (15,18) (15,16) (15,20) (15,23) (16,24) (16,20) (16,23) (18,22) (18,20) (18,23) (19,21) (20,22) (22,24) (22,23) (23,24)\nQ: Is there a path between node 18 and node 21?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1708"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,17) (0,13) (0,12) (0,4) (0,1) (1,3) (1,17) (1,16) (1,14) (1,4) (2,5) (2,7) (2,9) (2,11) (2,8) (3,15) (3,13) (3,16) (3,12) (3,14) (3,6) (4,15) (4,13) (4,16) (4,12) (4,6) (5,9) (5,11) (5,10) (6,17) (6,13) (6,12) (7,11) (7,10) (7,8) (8,9) (8,11) (9,10) (10,11) (12,15) (12,17) (12,16) (12,14) (13,17) (13,16) (14,15) (14,17) (15,17) (15,16) (16,17)\nQ: Is there a path between node 5 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1709"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,10) (2,9) (2,5) (3,12) (3,14) (3,4) (3,8) (3,18) (4,19) (4,16) (4,11) (5,20) (5,12) (5,14) (5,11) (6,18) (6,16) (7,15) (8,20) (8,12) (8,18) (8,16) (9,20) (9,14) (9,19) (9,11) (11,13) (11,12) (11,18) (11,16) (12,18) (13,19) (13,18) (14,19) (16,20) (18,19)\nQ: Is there a path between node 1 and node 15?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1710"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,11) (0,13) (0,3) (0,15) (0,4) (0,2) (1,7) (1,8) (2,14) (2,23) (2,21) (2,6) (2,10) (3,9) (3,17) (3,13) (3,5) (3,19) (3,4) (3,16) (3,10) (4,9) (4,22) (4,6) (5,11) (5,18) (5,23) (6,9) (6,14) (6,17) (6,20) (6,15) (6,21) (7,8) (9,17) (9,15) (9,21) (10,18) (10,12) (10,16) (11,17) (11,15) (11,22) (11,16) (12,15) (12,22) (13,23) (13,16) (14,17) (14,18) (14,20) (14,21) (14,22) (14,16) (15,20) (17,20) (17,19) (17,23) (18,19) (18,23) (19,20) (19,23) (21,23) (21,22)\nQ: Is there a path between node 11 and node 16?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1711"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,34) (0,1) (0,10) (0,12) (1,12) (2,24) (3,31) (3,30) (3,25) (4,19) (4,6) (5,8) (7,26) (10,20) (10,28) (10,17) (10,18) (12,20) (12,32) (12,17) (13,14) (13,15) (13,21) (13,26) (13,23) (14,15) (14,21) (15,26) (15,23) (16,21) (16,30) (17,20) (17,27) (17,32) (18,27) (18,34) (19,33) (20,27) (21,31) (21,22) (22,26) (22,31) (23,31) (26,31) (28,34) (30,31)\nQ: Is there a path between node 1 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1712"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,15) (0,25) (0,14) (0,7) (0,2) (0,9) (0,5) (1,26) (1,15) (1,25) (1,7) (1,6) (1,2) (1,20) (1,22) (2,25) (2,19) (2,14) (2,4) (3,12) (3,16) (4,15) (4,7) (4,6) (4,8) (5,26) (5,20) (5,8) (5,9) (5,22) (5,13) (6,19) (6,17) (6,7) (6,20) (6,22) (7,19) (7,17) (7,9) (8,19) (9,26) (9,14) (9,24) (11,12) (12,21) (12,18) (12,16) (13,17) (13,22) (14,26) (14,22) (15,19) (15,20) (16,21) (18,23) (19,20) (19,22) (25,26)\nQ: Is there a path between node 7 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1713"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,7) (0,2) (0,8) (1,6) (2,3) (3,6) (3,7) (4,6) (4,5) (5,8) (7,8)\nQ: Is there a path between node 8 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1714"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,8) (0,10) (0,4) (0,16) (0,5) (0,2) (0,7) (0,9) (0,15) (0,13) (0,1) (0,12) (0,14) (0,3) (1,11) (1,8) (1,10) (1,4) (1,16) (1,5) (1,2) (1,7) (1,9) (1,15) (1,13) (1,12) (1,14) (1,3) (2,11) (2,8) (2,10) (2,4) (2,16) (2,5) (2,7) (2,9) (2,15) (2,13) (2,12) (2,14) (2,3) (3,11) (3,8) (3,10) (3,4) (3,16) (3,5) (3,7) (3,9) (3,15) (3,13) (3,12) (3,14) (4,11) (4,8) (4,10) (4,16) (4,5) (4,7) (4,9) (4,15) (4,13) (4,12) (4,14) (5,11) (5,8) (5,10) (5,16) (5,7) (5,9) (5,15) (5,13) (5,12) (5,14) (7,11) (7,8) (7,10) (7,16) (7,9) (7,15) (7,13) (7,12) (7,14) (8,11) (8,10) (8,16) (8,9) (8,15) (8,13) (8,12) (8,14) (9,11) (9,10) (9,16) (9,15) (9,13) (9,12) (9,14) (10,11) (10,16) (10,15) (10,13) (10,12) (10,14) (11,16) (11,15) (11,13) (11,12) (11,14) (12,16) (12,15) (12,13) (12,14) (13,16) (13,15) (13,14) (14,16) (14,15) (15,16)\nQ: Is there a path between node 6 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1715"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,25) (0,3) (1,25) (1,29) (2,14) (2,13) (2,20) (2,18) (2,31) (2,9) (2,27) (2,21) (2,12) (2,7) (2,33) (2,11) (2,24) (2,26) (2,30) (3,25) (4,23) (4,22) (4,34) (4,5) (5,23) (5,22) (5,34) (6,14) (6,13) (6,20) (6,18) (6,27) (6,21) (6,12) (6,7) (6,28) (6,24) (6,26) (6,30) (7,14) (7,13) (7,20) (7,31) (7,17) (7,9) (7,27) (7,21) (7,12) (7,10) (7,33) (7,28) (7,30) (8,14) (8,13) (8,31) (8,17) (8,9) (8,27) (8,12) (8,33) (8,11) (8,28) (8,26) (8,30) (9,14) (9,13) (9,20) (9,18) (9,27) (9,21) (9,12) (9,10) (9,33) (9,24) (9,26) (9,19) (9,30) (10,13) (10,20) (10,18) (10,31) (10,17) (10,27) (10,12) (10,33) (10,11) (10,28) (10,24) (11,14) (11,13) (11,20) (11,18) (11,31) (11,12) (11,33) (11,28) (11,24) (11,26) (11,30) (12,14) (12,13) (12,20) (12,18) (12,17) (12,27) (12,21) (12,33) (12,19) (13,14) (13,20) (13,18) (13,31) (13,17) (13,21) (13,28) (13,24) (13,26) (14,18) (14,31) (14,17) (14,27) (14,21) (14,33) (14,26) (15,32) (17,18) (17,31) (17,27) (17,33) (17,28) (17,24) (17,26) (17,19) (17,30) (18,20) (18,31) (18,33) (18,24) (18,26) (18,19) (18,30) (19,31) (19,27) (19,21) (19,33) (19,28) (19,26) (20,31) (20,27) (20,21) (20,33) (20,24) (20,26) (20,30) (21,27) (21,33) (21,28) (21,24) (21,30) (22,23) (22,34) (23,34) (24,33) (24,26) (25,29) (26,31) (26,33) (26,30) (27,31) (27,33) (27,28) (27,30) (28,31) (28,33) (28,30) (30,31) (30,33) (31,33)\nQ: Is there a path between node 34 and node 24?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1716"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,6) (0,21) (0,18) (1,24) (1,3) (3,24) (3,14) (4,6) (4,5) (4,23) (6,14) (6,21) (6,23) (7,11) (8,19) (8,13) (9,15) (9,19) (10,11) (10,12) (10,16) (10,17) (11,12) (11,16) (12,17) (13,15) (13,22) (14,23) (15,22) (16,17) (18,24) (18,21)\nQ: Is there a path between node 21 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1717"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,6) (2,7) (2,6) (2,4) (5,7) (6,8)\nQ: Is there a path between node 3 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1718"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (1,5) (1,18) (1,7) (1,22) (1,11) (1,20) (1,4) (1,23) (2,14) (2,10) (2,21) (2,15) (2,16) (2,3) (3,14) (3,10) (3,15) (3,16) (3,6) (3,19) (4,18) (4,7) (4,22) (4,11) (4,20) (4,23) (5,13) (5,7) (5,22) (5,11) (5,20) (5,23) (6,10) (6,21) (6,15) (6,16) (6,9) (6,8) (6,19) (7,13) (7,22) (7,20) (7,23) (8,10) (8,9) (8,19) (9,21) (9,15) (9,19) (10,21) (10,16) (10,19) (11,18) (11,13) (11,22) (11,23) (12,17) (13,22) (13,20) (14,15) (14,16) (14,19) (15,16) (15,19) (16,21) (16,19) (18,20) (18,23) (19,21) (20,22) (20,23) (22,23)\nQ: Is there a path between node 23 and node 18?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1719"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,19) (0,17) (0,7) (0,16) (0,21) (1,22) (1,19) (1,20) (1,21) (2,23) (2,6) (3,13) (3,18) (3,4) (3,10) (3,21) (4,19) (4,10) (4,16) (5,14) (5,12) (5,9) (5,11) (6,14) (6,23) (7,15) (7,22) (7,18) (7,8) (7,17) (7,20) (8,13) (8,21) (9,12) (9,11) (10,17) (13,19) (13,17) (13,21) (15,20) (16,18) (16,20) (19,20) (19,21)\nQ: Is there a path between node 4 and node 17?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1720"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,18) (0,12) (0,2) (0,11) (0,8) (0,13) (1,4) (1,10) (1,17) (1,5) (1,14) (1,7) (1,6) (1,15) (2,3) (2,18) (2,12) (2,11) (2,8) (2,13) (3,18) (3,12) (3,11) (3,8) (3,13) (4,10) (4,17) (4,5) (4,14) (4,7) (4,6) (4,15) (5,10) (5,17) (5,14) (5,7) (5,6) (5,15) (6,10) (6,17) (6,14) (6,7) (6,15) (7,10) (7,17) (7,14) (7,15) (8,18) (8,12) (8,11) (8,13) (9,16) (10,17) (10,14) (10,15) (11,18) (11,12) (11,13) (12,18) (12,13) (13,18) (14,17) (14,15) (15,17)\nQ: Is there a path between node 16 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1721"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,2) (1,5) (1,2) (2,5) (2,10) (3,10) (3,4) (3,8) (4,5) (5,10) (5,8) (7,11) (8,10) (9,11)\nQ: Is there a path between node 8 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1722"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,3) (0,7) (0,10) (0,13) (0,12) (0,16) (1,14) (1,2) (1,5) (1,9) (1,8) (1,15) (1,4) (1,6) (2,14) (2,5) (2,9) (2,8) (2,15) (2,4) (2,6) (3,11) (3,7) (3,10) (3,13) (3,12) (3,16) (4,14) (4,5) (4,9) (4,8) (4,15) (4,6) (5,14) (5,9) (5,8) (5,15) (5,6) (6,14) (6,9) (6,8) (6,15) (7,11) (7,10) (7,13) (7,12) (7,16) (8,14) (8,9) (8,15) (9,14) (9,15) (10,11) (10,13) (10,12) (10,16) (11,13) (11,12) (11,16) (12,13) (12,16) (13,16) (14,15)\nQ: Is there a path between node 16 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1723"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,14) (0,10) (0,24) (0,2) (0,12) (0,19) (0,3) (0,17) (0,25) (0,23) (0,15) (1,18) (1,11) (1,8) (2,14) (2,10) (2,24) (2,7) (2,3) (2,21) (2,25) (2,23) (2,6) (3,14) (3,24) (3,12) (3,19) (3,17) (3,25) (3,23) (3,6) (3,15) (4,18) (4,8) (5,18) (5,11) (5,8) (6,16) (6,14) (6,10) (6,12) (6,7) (6,19) (6,21) (6,25) (6,23) (6,9) (6,15) (7,16) (7,10) (7,24) (7,12) (7,19) (7,17) (7,25) (7,9) (7,15) (8,18) (8,11) (9,16) (9,14) (9,10) (9,24) (9,12) (9,19) (9,17) (9,21) (9,23) (9,15) (10,16) (10,14) (10,19) (10,21) (10,25) (10,23) (10,15) (11,18) (12,16) (12,14) (12,24) (12,19) (12,17) (12,21) (12,25) (12,23) (12,15) (13,20) (14,16) (14,24) (14,17) (14,21) (14,25) (14,23) (14,15) (15,16) (15,24) (15,23) (16,21) (16,25) (16,23) (17,21) (17,23) (19,21) (19,25) (21,24) (21,25) (21,23) (23,25) (24,25)\nQ: Is there a path between node 19 and node 25?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1724"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,1) (3,4)\nQ: Is there a path between node 0 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1725"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,4) (0,15) (0,19) (0,8) (0,17) (0,13) (0,3) (0,14) (0,5) (0,2) (0,16) (0,1) (0,10) (1,20) (1,4) (1,15) (1,19) (1,8) (1,17) (1,13) (1,3) (1,14) (1,5) (1,2) (1,16) (1,10) (2,20) (2,4) (2,15) (2,19) (2,8) (2,17) (2,13) (2,3) (2,14) (2,5) (2,16) (2,10) (3,20) (3,4) (3,15) (3,19) (3,8) (3,17) (3,13) (3,14) (3,5) (3,16) (3,10) (4,20) (4,15) (4,19) (4,8) (4,17) (4,13) (4,14) (4,5) (4,16) (4,10) (5,20) (5,15) (5,19) (5,8) (5,17) (5,13) (5,14) (5,16) (5,10) (6,12) (6,22) (6,9) (6,18) (6,21) (6,7) (6,11) (7,12) (7,22) (7,9) (7,18) (7,21) (7,11) (8,20) (8,15) (8,19) (8,17) (8,13) (8,14) (8,16) (8,10) (9,12) (9,22) (9,18) (9,21) (9,11) (10,20) (10,15) (10,19) (10,17) (10,13) (10,14) (10,16) (11,12) (11,22) (11,18) (11,21) (12,22) (12,18) (12,21) (13,20) (13,15) (13,19) (13,17) (13,14) (13,16) (14,20) (14,15) (14,19) (14,17) (14,16) (15,20) (15,19) (15,17) (15,16) (16,20) (16,19) (16,17) (17,20) (17,19) (18,22) (18,21) (19,20) (21,22)\nQ: Is there a path between node 2 and node 20?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1726"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,11) (0,1) (0,3) (0,10) (0,4) (1,11) (1,3) (1,10) (1,4) (2,7) (3,11) (3,4) (4,5) (4,11) (5,11) (6,9) (6,8) (7,9) (7,8) (8,9) (10,11)\nQ: Is there a path between node 2 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1727"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,15) (0,18) (0,27) (0,9) (0,13) (0,25) (0,3) (1,8) (1,5) (1,26) (1,12) (1,2) (1,16) (1,14) (2,8) (2,26) (2,12) (2,16) (2,14) (3,7) (3,4) (3,15) (3,18) (3,27) (3,13) (4,7) (4,15) (4,18) (4,27) (4,13) (5,8) (5,12) (5,11) (5,16) (5,14) (5,20) (6,17) (6,21) (6,29) (6,28) (7,15) (7,18) (7,27) (7,9) (7,13) (8,26) (8,23) (8,16) (8,14) (9,15) (10,29) (10,24) (11,12) (11,16) (11,14) (11,20) (12,22) (12,23) (12,14) (12,20) (13,18) (13,27) (14,26) (14,22) (14,23) (14,20) (15,18) (15,27) (15,25) (16,26) (16,22) (16,23) (16,20) (17,21) (17,19) (17,24) (17,28) (19,21) (19,29) (19,24) (19,28) (20,26) (20,22) (20,23) (21,29) (21,24) (22,26) (22,23) (24,29) (24,28) (25,27)\nQ: Is there a path between node 1 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1728"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,3) (0,13) (0,15) (0,7) (1,4) (1,6) (2,9) (2,18) (2,13) (3,12) (4,11) (6,8) (6,17) (7,16) (7,12) (7,13) (7,14) (8,11) (8,17) (8,20) (9,18) (9,21) (9,14) (9,15) (10,12) (12,16) (12,15) (13,18) (13,15) (14,16) (14,21) (15,16) (15,18) (16,18)\nQ: Is there a path between node 18 and node 21?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1729"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,12) (0,5) (0,6) (0,4) (0,8) (0,2) (0,9) (0,1) (0,7) (1,12) (1,5) (1,6) (1,4) (1,8) (1,2) (1,9) (1,10) (1,7) (2,8) (2,10) (2,7) (4,11) (4,12) (4,5) (4,6) (4,8) (4,9) (4,7) (5,11) (5,6) (5,8) (5,10) (5,7) (6,11) (6,12) (6,8) (6,9) (7,11) (7,12) (7,9) (7,10) (8,12) (8,9) (8,10) (9,11) (9,12) (9,10) (10,11) (10,12) (11,12)\nQ: Is there a path between node 6 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1730"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,16) (0,9) (0,3) (0,4) (0,8) (0,17) (1,6) (1,12) (1,13) (1,18) (1,2) (1,4) (1,8) (1,17) (2,6) (2,12) (2,15) (2,9) (2,13) (2,18) (2,4) (2,8) (2,17) (3,6) (3,16) (3,12) (3,9) (3,13) (3,18) (3,8) (3,17) (3,5) (4,6) (4,16) (4,12) (4,9) (4,18) (4,17) (4,5) (5,6) (5,12) (5,15) (5,9) (5,17) (6,12) (6,15) (6,9) (6,13) (6,18) (6,8) (7,10) (7,11) (7,19) (8,16) (8,15) (8,9) (8,18) (9,16) (9,12) (9,15) (9,13) (9,18) (9,17) (10,19) (11,14) (11,19) (12,16) (12,15) (12,13) (12,17) (13,18) (14,19) (15,17) (16,17) (17,18)\nQ: Is there a path between node 14 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1731"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,1) (0,6) (0,2) (0,3) (0,7) (0,5) (1,8) (1,6) (1,2) (1,3) (1,7) (1,5) (2,8) (2,6) (2,3) (2,7) (2,5) (3,8) (3,6) (3,7) (3,5) (5,8) (5,6) (5,7) (6,8) (6,7) (7,8)\nQ: Is there a path between node 8 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1732"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,1) (2,3) (4,6) (5,6) (5,7)\nQ: Is there a path between node 0 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1733"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (0,8) (0,18) (0,6) (0,1) (0,12) (0,3) (0,7) (0,14) (0,10) (0,19) (0,16) (0,13) (1,17) (1,8) (1,18) (1,2) (1,19) (2,8) (2,6) (2,20) (2,14) (3,17) (3,18) (3,6) (3,14) (3,10) (3,19) (4,17) (4,18) (4,6) (4,19) (4,13) (5,15) (6,17) (6,8) (6,18) (6,13) (7,17) (7,14) (7,10) (8,20) (9,15) (9,11) (10,17) (10,18) (11,15) (12,17) (12,18) (12,14) (12,19) (13,17) (13,18) (13,20) (14,17) (14,18) (14,20) (18,20) (19,20)\nQ: Is there a path between node 1 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1734"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,28) (0,26) (0,7) (0,22) (0,6) (0,1) (0,30) (0,3) (1,16) (1,28) (1,26) (1,22) (1,10) (1,30) (2,4) (2,29) (2,24) (2,14) (2,21) (2,25) (2,13) (2,12) (2,31) (2,19) (2,33) (2,27) (2,23) (2,8) (2,18) (3,16) (3,28) (3,26) (3,9) (3,7) (3,10) (4,29) (4,32) (4,24) (4,21) (4,25) (4,15) (4,12) (4,31) (4,19) (4,33) (4,27) (4,17) (4,23) (4,18) (5,32) (5,14) (5,21) (5,15) (5,12) (5,19) (5,33) (5,27) (5,23) (5,8) (6,28) (6,26) (6,7) (6,22) (6,10) (7,16) (7,9) (7,22) (7,10) (8,29) (8,32) (8,24) (8,21) (8,15) (8,13) (8,33) (8,27) (8,23) (8,18) (9,16) (9,28) (9,26) (9,22) (9,10) (10,28) (10,22) (10,30) (12,29) (12,14) (12,21) (12,25) (12,15) (12,13) (12,31) (12,19) (12,33) (12,17) (12,23) (12,18) (13,20) (13,29) (13,24) (13,21) (13,25) (13,15) (13,31) (13,19) (13,33) (13,27) (13,17) (13,23) (13,18) (14,20) (14,29) (14,32) (14,24) (14,21) (14,15) (14,31) (14,19) (14,33) (14,17) (14,18) (15,20) (15,29) (15,32) (15,24) (15,21) (15,25) (15,31) (15,19) (15,33) (15,27) (15,17) (15,23) (15,18) (16,28) (16,26) (16,22) (16,30) (17,20) (17,29) (17,32) (17,24) (17,21) (17,25) (17,31) (17,19) (17,18) (18,20) (18,29) (18,32) (18,24) (18,21) (18,25) (18,31) (18,19) (18,27) (18,23) (19,32) (19,24) (19,33) (19,27) (19,23) (20,29) (20,32) (20,24) (20,21) (20,25) (20,31) (20,33) (20,27) (20,23) (21,32) (21,24) (21,25) (21,31) (21,33) (21,27) (21,23) (22,26) (22,30) (23,29) (23,32) (23,24) (23,25) (23,31) (23,33) (23,27) (24,32) (24,25) (24,31) (24,27) (25,29) (25,33) (25,27) (26,28) (26,30) (27,29) (27,31) (27,33) (28,30) (29,32) (29,31) (29,33) (31,32) (31,33) (32,33)\nQ: Is there a path between node 3 and node 23?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1735"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,4) (0,16) (0,21) (0,1) (0,25) (0,14) (0,9) (0,5) (0,6) (0,12) (0,17) (0,24) (0,23) (1,29) (1,4) (1,27) (1,16) (1,21) (1,14) (1,9) (1,6) (1,24) (1,23) (2,26) (2,10) (2,22) (2,15) (2,28) (2,8) (2,30) (2,19) (3,26) (3,10) (3,11) (3,22) (3,15) (3,28) (3,8) (3,30) (3,19) (3,20) (4,29) (4,27) (4,16) (4,21) (4,14) (4,9) (4,5) (4,6) (4,12) (4,24) (5,29) (5,27) (5,21) (5,7) (5,14) (5,12) (5,17) (5,24) (5,23) (6,29) (6,27) (6,7) (6,25) (6,14) (6,9) (6,12) (6,24) (6,23) (7,25) (7,14) (7,9) (7,12) (7,17) (7,23) (8,26) (8,10) (8,11) (8,13) (8,30) (8,19) (9,29) (9,27) (9,16) (9,14) (9,12) (9,24) (9,23) (10,26) (10,13) (10,15) (10,28) (10,19) (10,20) (11,26) (11,13) (11,15) (11,28) (11,30) (11,19) (11,20) (12,29) (12,27) (12,16) (12,21) (12,25) (12,17) (12,24) (12,23) (13,26) (13,28) (13,30) (14,29) (14,16) (14,21) (14,25) (14,17) (14,24) (14,23) (15,26) (15,28) (15,30) (15,20) (16,27) (16,21) (16,17) (16,24) (16,23) (17,29) (17,27) (17,21) (17,25) (17,24) (19,26) (19,22) (19,30) (19,20) (20,26) (20,22) (20,28) (21,29) (21,27) (21,25) (21,24) (21,23) (22,26) (22,28) (22,30) (23,29) (23,27) (23,25) (24,29) (24,27) (24,25) (25,29) (26,28) (28,30)\nQ: Is there a path between node 3 and node 17?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1736"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,11) (0,17) (0,3) (0,19) (0,9) (0,16) (0,15) (0,7) (0,12) (0,2) (1,11) (1,10) (1,3) (1,4) (1,8) (1,19) (1,13) (1,9) (1,16) (1,15) (1,7) (1,12) (1,2) (2,17) (2,5) (2,16) (2,15) (3,17) (3,10) (3,5) (3,6) (3,8) (3,13) (3,9) (3,16) (3,15) (3,7) (3,12) (4,11) (4,5) (4,8) (4,19) (4,13) (4,9) (4,7) (4,12) (5,11) (5,10) (5,6) (5,8) (5,19) (5,13) (5,7) (6,11) (6,17) (6,10) (6,8) (6,19) (6,13) (6,16) (6,15) (6,7) (6,12) (7,11) (7,17) (7,10) (7,19) (7,9) (7,16) (7,15) (8,11) (8,17) (8,10) (8,19) (8,13) (8,15) (8,12) (9,11) (9,17) (9,10) (9,13) (9,16) (9,15) (10,11) (10,17) (10,19) (10,13) (10,15) (10,12) (11,19) (11,15) (11,12) (12,17) (12,19) (12,13) (13,19) (13,16) (13,15) (14,18) (15,19) (15,16) (16,17) (17,19)\nQ: Is there a path between node 14 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1737"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,11) (3,15) (3,8) (5,18) (5,7) (6,17) (6,7) (7,13) (7,8) (7,14) (8,18) (8,12) (9,11) (9,15) (9,13) (9,17) (10,18) (11,13) (11,17) (12,18) (12,17) (12,14) (13,17) (14,17) (17,18)\nQ: Is there a path between node 14 and node 17?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1738"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,4) (0,16) (0,21) (0,1) (0,25) (0,14) (0,9) (0,5) (0,6) (0,12) (0,17) (0,24) (0,23) (1,29) (1,4) (1,27) (1,16) (1,21) (1,14) (1,9) (1,6) (1,24) (1,23) (2,26) (2,10) (2,22) (2,15) (2,28) (2,8) (2,30) (2,19) (3,26) (3,10) (3,11) (3,22) (3,15) (3,28) (3,8) (3,30) (3,19) (3,20) (4,29) (4,27) (4,16) (4,21) (4,14) (4,9) (4,5) (4,6) (4,12) (4,24) (5,29) (5,27) (5,21) (5,7) (5,14) (5,12) (5,17) (5,24) (5,23) (6,29) (6,27) (6,7) (6,25) (6,14) (6,9) (6,12) (6,24) (6,23) (7,25) (7,14) (7,9) (7,12) (7,17) (7,23) (8,26) (8,10) (8,11) (8,13) (8,30) (8,19) (9,29) (9,27) (9,16) (9,14) (9,12) (9,24) (9,23) (10,26) (10,13) (10,15) (10,28) (10,19) (10,20) (11,26) (11,13) (11,15) (11,28) (11,30) (11,19) (11,20) (12,29) (12,27) (12,16) (12,21) (12,25) (12,17) (12,24) (12,23) (13,26) (13,28) (13,30) (14,29) (14,16) (14,21) (14,25) (14,17) (14,24) (14,23) (15,26) (15,28) (15,30) (15,20) (16,27) (16,21) (16,17) (16,24) (16,23) (17,29) (17,27) (17,21) (17,25) (17,24) (19,26) (19,22) (19,30) (19,20) (20,26) (20,22) (20,28) (21,29) (21,27) (21,25) (21,24) (21,23) (22,26) (22,28) (22,30) (23,29) (23,27) (23,25) (24,29) (24,27) (24,25) (25,29) (26,28) (28,30)\nQ: Is there a path between node 12 and node 17?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1739"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,8) (0,2) (0,20) (0,16) (0,14) (0,15) (0,7) (1,18) (1,24) (1,22) (1,5) (1,19) (1,11) (1,17) (2,6) (2,4) (2,23) (2,8) (2,20) (2,16) (2,21) (2,14) (2,15) (2,10) (3,6) (3,4) (3,23) (3,8) (3,16) (3,14) (3,25) (3,15) (3,7) (4,6) (4,23) (4,8) (4,20) (4,16) (4,21) (4,14) (4,15) (4,10) (4,7) (5,18) (5,24) (5,22) (5,13) (5,9) (5,11) (5,12) (6,23) (6,8) (6,20) (6,16) (6,14) (6,25) (6,15) (7,23) (7,20) (7,16) (7,21) (7,14) (7,25) (7,15) (7,10) (8,20) (8,16) (8,14) (8,25) (8,15) (9,18) (9,24) (9,22) (9,19) (9,11) (9,17) (9,12) (10,23) (10,20) (10,16) (10,21) (10,14) (10,25) (11,22) (11,19) (11,17) (11,12) (12,18) (12,13) (12,19) (13,18) (13,24) (13,22) (13,17) (14,23) (14,20) (14,16) (14,25) (15,20) (15,16) (15,21) (15,25) (16,23) (16,20) (16,25) (17,18) (17,22) (17,19) (18,24) (18,22) (18,19) (19,24) (19,22) (20,21) (20,25) (21,23) (21,25) (22,24) (23,25)\nQ: Is there a path between node 15 and node 24?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1740"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,21) (0,8) (0,11) (0,16) (0,13) (0,10) (0,20) (0,6) (0,4) (1,14) (1,17) (1,18) (1,5) (1,19) (1,2) (2,22) (2,14) (2,5) (3,8) (3,11) (3,10) (3,12) (3,6) (4,11) (4,13) (4,20) (4,12) (5,22) (5,14) (5,17) (5,18) (5,9) (5,19) (6,8) (6,11) (6,16) (6,13) (6,10) (6,20) (6,12) (7,15) (8,11) (8,13) (8,10) (8,20) (8,12) (9,22) (9,14) (9,17) (9,18) (9,19) (10,21) (10,13) (11,16) (11,13) (11,20) (11,12) (12,21) (12,16) (12,13) (12,20) (13,21) (13,16) (13,20) (14,22) (14,18) (16,21) (16,20) (17,22) (17,18) (17,19) (18,19) (20,21)\nQ: Is there a path between node 12 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1741"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 2 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1742"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,7) (0,13) (0,24) (0,19) (0,5) (0,10) (0,4) (0,2) (0,21) (0,17) (0,23) (0,9) (0,20) (0,15) (0,22) (1,3) (1,18) (1,6) (1,14) (1,8) (1,11) (2,12) (2,7) (2,13) (2,24) (2,19) (2,5) (2,10) (2,4) (2,21) (2,17) (2,23) (2,9) (2,20) (2,15) (2,22) (3,18) (3,6) (3,14) (3,8) (3,11) (4,12) (4,7) (4,13) (4,24) (4,19) (4,5) (4,10) (4,21) (4,17) (4,23) (4,9) (4,20) (4,15) (4,22) (5,12) (5,7) (5,13) (5,24) (5,19) (5,10) (5,21) (5,17) (5,23) (5,9) (5,20) (5,15) (5,22) (6,18) (6,14) (6,8) (6,11) (7,12) (7,13) (7,24) (7,19) (7,10) (7,21) (7,17) (7,23) (7,9) (7,20) (7,15) (7,22) (8,18) (8,14) (8,11) (9,12) (9,13) (9,24) (9,19) (9,10) (9,21) (9,17) (9,23) (9,20) (9,15) (9,22) (10,12) (10,13) (10,24) (10,19) (10,21) (10,17) (10,23) (10,20) (10,15) (10,22) (11,18) (11,14) (12,13) (12,24) (12,19) (12,21) (12,17) (12,23) (12,20) (12,15) (12,22) (13,24) (13,19) (13,21) (13,17) (13,23) (13,20) (13,15) (13,22) (14,18) (15,24) (15,19) (15,21) (15,17) (15,23) (15,20) (15,22) (17,24) (17,19) (17,21) (17,23) (17,20) (17,22) (19,24) (19,21) (19,23) (19,20) (19,22) (20,24) (20,21) (20,23) (20,22) (21,24) (21,23) (21,22) (22,24) (22,23) (23,24)\nQ: Is there a path between node 10 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1743"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,13) (2,25) (2,28) (2,21) (2,5) (2,23) (3,22) (3,8) (3,6) (3,19) (3,21) (3,31) (3,15) (5,20) (5,16) (5,21) (5,23) (6,18) (6,17) (6,23) (7,10) (8,21) (9,24) (12,22) (12,18) (13,30) (13,27) (14,26) (15,16) (15,19) (15,31) (16,22) (16,20) (16,19) (17,20) (17,21) (17,31) (18,22) (18,25) (18,20) (18,21) (18,23) (19,25) (19,28) (20,28) (20,21) (21,25) (22,25) (22,28) (23,28) (27,29) (29,30) (30,32)\nQ: Is there a path between node 32 and node 11?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1744"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,10) (0,25) (0,16) (0,24) (0,4) (0,8) (0,27) (0,19) (1,5) (1,28) (2,15) (3,12) (3,13) (3,21) (3,24) (3,4) (3,8) (4,26) (4,20) (4,21) (4,11) (4,9) (6,13) (6,14) (6,22) (6,21) (6,7) (6,23) (6,11) (7,12) (7,26) (7,20) (7,17) (7,14) (7,10) (7,25) (7,24) (7,8) (7,11) (7,19) (7,9) (8,25) (8,27) (8,11) (9,17) (9,14) (9,21) (9,23) (9,27) (9,11) (10,26) (10,20) (10,14) (10,25) (10,23) (10,24) (11,13) (11,17) (11,21) (11,25) (11,23) (11,19) (12,20) (12,17) (12,24) (13,26) (13,20) (13,17) (13,22) (13,25) (13,24) (13,19) (14,20) (14,16) (15,28) (15,18) (16,26) (16,21) (16,23) (17,26) (17,22) (17,23) (17,27) (18,28) (19,22) (20,23) (20,24) (20,27) (21,26) (21,27) (23,25) (24,25) (24,27) (25,27)\nQ: Is there a path between node 5 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1745"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,4) (0,9) (0,12) (0,11) (0,5) (1,6) (1,17) (1,8) (1,15) (1,3) (1,2) (1,18) (1,19) (1,13) (1,14) (1,10) (2,6) (2,17) (2,8) (2,15) (2,3) (2,18) (2,19) (2,13) (2,14) (2,10) (3,6) (3,17) (3,8) (3,15) (3,18) (3,19) (3,13) (3,14) (3,10) (4,7) (4,9) (4,12) (4,11) (4,5) (5,7) (5,9) (5,12) (5,11) (6,17) (6,8) (6,15) (6,18) (6,19) (6,13) (6,14) (6,10) (7,9) (7,12) (7,11) (8,17) (8,15) (8,18) (8,19) (8,13) (8,14) (8,10) (9,12) (9,11) (10,17) (10,15) (10,18) (10,19) (10,13) (10,14) (11,12) (13,17) (13,15) (13,18) (13,19) (13,14) (14,17) (14,15) (14,18) (14,19) (15,17) (15,18) (15,19) (17,18) (17,19) (18,19)\nQ: Is there a path between node 14 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1746"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,30) (0,27) (0,33) (0,11) (0,5) (0,12) (0,20) (0,7) (0,28) (0,17) (0,6) (0,4) (0,32) (0,13) (0,3) (0,22) (0,31) (1,25) (1,29) (1,30) (1,27) (1,33) (1,2) (1,5) (1,12) (1,20) (1,28) (1,18) (1,16) (1,24) (1,6) (1,13) (1,3) (1,22) (1,31) (2,25) (2,23) (2,29) (2,30) (2,27) (2,33) (2,11) (2,5) (2,12) (2,7) (2,18) (2,16) (2,17) (2,24) (2,13) (2,22) (2,15) (3,25) (3,23) (3,29) (3,30) (3,12) (3,7) (3,18) (3,16) (3,24) (3,4) (3,13) (3,22) (3,31) (4,23) (4,29) (4,27) (4,33) (4,11) (4,5) (4,7) (4,18) (4,24) (4,32) (4,15) (4,31) (5,25) (5,23) (5,30) (5,27) (5,33) (5,11) (5,12) (5,20) (5,7) (5,28) (5,24) (5,6) (5,32) (5,13) (5,22) (5,15) (5,31) (6,25) (6,23) (6,30) (6,27) (6,33) (6,12) (6,20) (6,7) (6,18) (6,24) (6,32) (6,13) (7,25) (7,30) (7,27) (7,33) (7,20) (7,28) (7,18) (7,24) (7,32) (7,13) (7,22) (7,15) (7,31) (8,14) (8,26) (8,19) (9,14) (9,26) (9,19) (9,21) (9,10) (10,14) (10,26) (10,19) (11,23) (11,29) (11,30) (11,27) (11,33) (11,20) (11,18) (11,16) (11,17) (11,32) (11,13) (11,22) (11,15) (11,31) (12,25) (12,23) (12,29) (12,27) (12,33) (12,28) (12,16) (12,24) (12,13) (12,22) (12,15) (12,31) (13,25) (13,23) (13,29) (13,27) (13,33) (13,20) (13,28) (13,18) (13,16) (13,17) (13,24) (13,32) (13,15) (13,31) (14,26) (15,25) (15,23) (15,29) (15,30) (15,33) (15,16) (15,17) (15,24) (15,22) (15,31) (16,25) (16,23) (16,29) (16,30) (16,27) (16,28) (16,17) (16,24) (16,32) (16,22) (17,25) (17,23) (17,29) (17,33) (17,20) (17,18) (17,24) (17,31) (18,25) (18,29) (18,30) (18,33) (18,28) (18,24) (18,31) (20,25) (20,23) (20,30) (20,24) (20,32) (20,22) (20,31) (21,26) (22,25) (22,29) (22,30) (22,28) (22,24) (23,25) (23,29) (23,27) (23,28) (23,24) (23,32) (24,25) (24,29) (24,27) (24,33) (24,28) (24,31) (25,29) (25,30) (25,27) (25,28) (25,32) (25,31) (27,29) (27,30) (27,33) (27,28) (28,29) (28,30) (28,33) (28,32) (28,31) (29,30) (29,33) (29,32) (29,31) (30,33) (30,32) (30,31) (31,33) (31,32) (32,33)\nQ: Is there a path between node 22 and node 21?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1747"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,9) (1,8) (1,4) (2,8) (2,4) (2,3) (3,7) (3,6) (3,10) (3,12) (3,11) (4,10) (4,12) (6,14) (6,8) (6,10) (7,14) (7,11) (8,14) (8,12) (10,14) (11,14) (12,14)\nQ: Is there a path between node 11 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1748"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,12) (1,25) (1,2) (1,10) (1,12) (1,3) (2,8) (2,22) (2,25) (2,26) (2,19) (2,11) (2,12) (2,7) (2,21) (3,25) (3,26) (3,10) (3,27) (3,21) (5,24) (5,6) (6,23) (6,9) (7,22) (7,25) (7,11) (8,20) (8,22) (8,25) (8,26) (8,27) (9,24) (10,14) (10,25) (10,13) (10,27) (10,21) (11,22) (11,12) (11,17) (11,21) (12,19) (12,18) (12,17) (12,27) (12,21) (13,17) (13,21) (14,17) (14,21) (15,23) (15,24) (16,22) (17,22) (17,25) (17,19) (18,20) (18,26) (18,21) (19,22) (19,26) (19,27) (20,27) (22,25) (25,26)\nQ: Is there a path between node 3 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1749"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,10) (0,18) (0,21) (0,30) (0,28) (0,15) (1,27) (1,24) (1,22) (1,32) (1,14) (1,5) (2,29) (2,10) (2,18) (2,21) (2,19) (2,30) (2,16) (2,28) (2,15) (3,24) (3,13) (3,22) (3,20) (3,5) (4,17) (4,11) (4,6) (4,26) (4,23) (4,31) (4,25) (5,27) (5,13) (5,22) (5,20) (5,32) (5,14) (6,17) (6,9) (6,23) (6,31) (6,25) (7,29) (7,10) (7,18) (7,19) (7,30) (7,16) (7,15) (8,17) (8,11) (8,26) (8,23) (8,31) (9,17) (9,26) (9,23) (9,31) (9,25) (10,29) (10,18) (10,21) (10,30) (10,28) (10,15) (11,17) (11,26) (11,23) (12,27) (12,24) (12,13) (12,22) (12,32) (13,27) (13,24) (13,22) (13,20) (13,32) (13,14) (14,27) (14,22) (14,32) (15,29) (15,18) (15,21) (15,19) (15,28) (16,29) (16,21) (16,19) (16,28) (17,23) (18,29) (18,21) (18,30) (18,28) (19,29) (19,21) (19,30) (19,28) (20,24) (20,22) (20,32) (21,29) (21,30) (21,28) (22,27) (22,24) (22,32) (23,31) (24,27) (25,26) (26,31) (28,30)\nQ: Is there a path between node 17 and node 20?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1750"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,12) (0,5) (0,6) (0,4) (0,8) (0,2) (0,9) (0,1) (0,7) (1,12) (1,5) (1,6) (1,4) (1,8) (1,2) (1,9) (1,10) (1,7) (2,8) (2,10) (2,7) (4,11) (4,12) (4,5) (4,6) (4,8) (4,9) (4,7) (5,11) (5,6) (5,8) (5,10) (5,7) (6,11) (6,12) (6,8) (6,9) (7,11) (7,12) (7,9) (7,10) (8,12) (8,9) (8,10) (9,11) (9,12) (9,10) (10,11) (10,12) (11,12)\nQ: Is there a path between node 12 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1751"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,21) (0,8) (0,11) (0,16) (0,13) (0,10) (0,20) (0,6) (0,4) (1,14) (1,17) (1,18) (1,5) (1,19) (1,2) (2,22) (2,14) (2,5) (3,8) (3,11) (3,10) (3,12) (3,6) (4,11) (4,13) (4,20) (4,12) (5,22) (5,14) (5,17) (5,18) (5,9) (5,19) (6,8) (6,11) (6,16) (6,13) (6,10) (6,20) (6,12) (7,15) (8,11) (8,13) (8,10) (8,20) (8,12) (9,22) (9,14) (9,17) (9,18) (9,19) (10,21) (10,13) (11,16) (11,13) (11,20) (11,12) (12,21) (12,16) (12,13) (12,20) (13,21) (13,16) (13,20) (14,22) (14,18) (16,21) (16,20) (17,22) (17,18) (17,19) (18,19) (20,21)\nQ: Is there a path between node 22 and node 15?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1752"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,2) (1,5) (1,2) (2,5) (2,10) (3,10) (3,4) (3,8) (4,5) (5,10) (5,8) (7,11) (8,10) (9,11)\nQ: Is there a path between node 3 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1753"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (2,3) (2,5) (3,5) (4,6)\nQ: Is there a path between node 3 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1754"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,31) (0,11) (0,27) (0,18) (1,4) (1,12) (1,31) (1,7) (1,25) (1,8) (1,18) (2,17) (2,14) (2,6) (2,10) (2,19) (3,17) (3,22) (3,9) (4,12) (4,30) (4,31) (4,13) (4,27) (4,18) (5,29) (5,16) (5,22) (5,21) (5,20) (5,28) (5,19) (6,29) (6,9) (6,10) (6,28) (7,11) (7,27) (7,15) (7,18) (8,30) (8,23) (8,11) (9,14) (9,21) (9,10) (11,23) (11,18) (12,30) (12,31) (12,27) (12,25) (12,15) (12,18) (13,23) (13,25) (13,15) (14,29) (14,17) (16,24) (16,17) (16,20) (17,29) (18,30) (18,26) (20,29) (21,24) (22,24) (23,27) (23,25) (25,26) (25,27) (26,31) (27,31) (28,29)\nQ: Is there a path between node 6 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1755"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,10) (0,18) (0,21) (0,30) (0,28) (0,15) (1,27) (1,24) (1,22) (1,32) (1,14) (1,5) (2,29) (2,10) (2,18) (2,21) (2,19) (2,30) (2,16) (2,28) (2,15) (3,24) (3,13) (3,22) (3,20) (3,5) (4,17) (4,11) (4,6) (4,26) (4,23) (4,31) (4,25) (5,27) (5,13) (5,22) (5,20) (5,32) (5,14) (6,17) (6,9) (6,23) (6,31) (6,25) (7,29) (7,10) (7,18) (7,19) (7,30) (7,16) (7,15) (8,17) (8,11) (8,26) (8,23) (8,31) (9,17) (9,26) (9,23) (9,31) (9,25) (10,29) (10,18) (10,21) (10,30) (10,28) (10,15) (11,17) (11,26) (11,23) (12,27) (12,24) (12,13) (12,22) (12,32) (13,27) (13,24) (13,22) (13,20) (13,32) (13,14) (14,27) (14,22) (14,32) (15,29) (15,18) (15,21) (15,19) (15,28) (16,29) (16,21) (16,19) (16,28) (17,23) (18,29) (18,21) (18,30) (18,28) (19,29) (19,21) (19,30) (19,28) (20,24) (20,22) (20,32) (21,29) (21,30) (21,28) (22,27) (22,24) (22,32) (23,31) (24,27) (25,26) (26,31) (28,30)\nQ: Is there a path between node 12 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1756"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,2) (2,3)\nQ: Is there a path between node 0 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1757"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,20) (0,27) (0,29) (0,26) (0,17) (0,3) (0,1) (0,16) (1,6) (1,7) (1,20) (1,19) (1,3) (1,33) (1,4) (2,27) (2,34) (2,26) (2,19) (2,17) (2,3) (2,21) (2,4) (3,6) (3,7) (3,11) (3,28) (3,29) (4,6) (4,28) (4,27) (4,29) (4,26) (4,19) (4,33) (4,23) (5,7) (5,11) (5,28) (5,19) (5,33) (5,16) (6,7) (6,28) (6,27) (6,26) (6,21) (7,34) (8,13) (8,12) (8,22) (8,15) (9,24) (9,12) (9,10) (10,25) (11,16) (11,23) (12,32) (12,18) (12,22) (12,15) (13,14) (14,18) (14,15) (15,30) (15,18) (16,27) (16,17) (16,23) (17,29) (17,19) (17,33) (17,23) (18,31) (18,24) (19,28) (19,27) (19,34) (19,29) (19,33) (19,21) (20,21) (21,26) (21,33) (22,30) (22,25) (25,30) (25,31) (26,28) (26,34) (26,29) (27,28) (30,32) (31,32)\nQ: Is there a path between node 26 and node 22?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1758"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,8) (0,10) (0,4) (0,16) (0,5) (0,2) (0,7) (0,9) (0,15) (0,13) (0,1) (0,12) (0,14) (0,3) (1,11) (1,8) (1,10) (1,4) (1,16) (1,5) (1,2) (1,7) (1,9) (1,15) (1,13) (1,12) (1,14) (1,3) (2,11) (2,8) (2,10) (2,4) (2,16) (2,5) (2,7) (2,9) (2,15) (2,13) (2,12) (2,14) (2,3) (3,11) (3,8) (3,10) (3,4) (3,16) (3,5) (3,7) (3,9) (3,15) (3,13) (3,12) (3,14) (4,11) (4,8) (4,10) (4,16) (4,5) (4,7) (4,9) (4,15) (4,13) (4,12) (4,14) (5,11) (5,8) (5,10) (5,16) (5,7) (5,9) (5,15) (5,13) (5,12) (5,14) (7,11) (7,8) (7,10) (7,16) (7,9) (7,15) (7,13) (7,12) (7,14) (8,11) (8,10) (8,16) (8,9) (8,15) (8,13) (8,12) (8,14) (9,11) (9,10) (9,16) (9,15) (9,13) (9,12) (9,14) (10,11) (10,16) (10,15) (10,13) (10,12) (10,14) (11,16) (11,15) (11,13) (11,12) (11,14) (12,16) (12,15) (12,13) (12,14) (13,16) (13,15) (13,14) (14,16) (14,15) (15,16)\nQ: Is there a path between node 10 and node 13?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1759"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,21) (0,7) (0,6) (0,3) (0,17) (0,20) (0,22) (0,16) (0,23) (0,25) (0,27) (1,5) (1,21) (1,4) (1,7) (1,15) (1,18) (1,2) (1,24) (1,20) (1,11) (1,16) (1,25) (1,27) (2,14) (2,5) (2,21) (2,4) (2,15) (2,24) (2,22) (2,11) (2,23) (2,25) (2,27) (3,14) (3,13) (3,21) (3,7) (3,15) (3,6) (3,17) (3,24) (3,22) (3,11) (3,16) (3,23) (4,14) (4,13) (4,5) (4,19) (4,7) (4,18) (4,17) (4,22) (4,11) (4,23) (4,25) (4,27) (5,13) (5,19) (5,15) (5,18) (5,24) (5,20) (5,22) (5,11) (5,23) (5,27) (6,14) (6,21) (6,19) (6,7) (6,15) (6,18) (6,17) (6,24) (6,20) (6,11) (6,16) (6,25) (6,27) (7,14) (7,13) (7,21) (7,19) (7,15) (7,18) (7,17) (7,20) (7,22) (7,11) (7,23) (7,27) (8,30) (8,28) (9,31) (9,10) (9,26) (9,29) (10,31) (10,26) (10,29) (11,13) (11,21) (11,19) (11,15) (11,24) (11,22) (11,25) (11,27) (12,28) (13,14) (13,21) (13,15) (13,18) (13,17) (13,24) (13,20) (13,16) (13,23) (13,25) (13,27) (14,21) (14,19) (14,24) (14,20) (14,22) (14,16) (14,23) (14,25) (15,21) (15,18) (15,17) (15,24) (15,20) (15,22) (15,16) (15,25) (15,27) (16,21) (16,18) (16,17) (16,24) (16,20) (16,22) (16,25) (17,21) (17,19) (17,18) (17,24) (17,20) (17,22) (17,23) (17,25) (17,27) (18,21) (18,24) (18,20) (18,25) (18,27) (19,21) (19,20) (19,22) (19,27) (20,21) (20,24) (20,22) (20,23) (20,27) (21,24) (21,22) (21,25) (21,27) (22,25) (23,25) (23,27) (25,27) (26,31) (26,29) (29,31)\nQ: Is there a path between node 4 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1760"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,13) (1,6) (1,8) (1,3) (1,4) (2,5) (2,9) (3,12) (3,9) (3,13) (4,6) (4,10) (5,6) (5,9) (6,12) (6,8) (8,9) (9,10) (12,13)\nQ: Is there a path between node 11 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1761"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,11) (0,1) (0,25) (0,28) (0,16) (0,31) (0,2) (0,23) (1,20) (1,26) (1,24) (1,10) (1,31) (1,21) (2,26) (2,19) (2,11) (2,5) (2,15) (2,32) (2,33) (2,8) (2,16) (2,31) (2,21) (2,30) (3,12) (3,4) (4,18) (5,11) (5,24) (6,14) (6,12) (6,9) (6,13) (7,26) (7,25) (7,33) (7,8) (7,21) (8,26) (8,19) (8,32) (8,31) (9,12) (10,19) (10,11) (10,25) (11,33) (11,24) (12,14) (14,18) (15,19) (15,17) (15,32) (15,25) (15,31) (15,21) (16,26) (16,32) (17,20) (17,19) (17,23) (19,24) (19,31) (19,21) (19,30) (21,32) (21,25) (21,24) (21,31) (23,31) (24,28) (25,32) (25,33) (25,28) (26,32) (26,33) (26,28) (26,31) (26,30) (28,33) (28,30) (31,32)\nQ: Is there a path between node 13 and node 25?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1762"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,8) (0,11) (0,17) (0,1) (0,2) (0,12) (0,6) (0,18) (0,7) (0,15) (1,19) (1,8) (1,9) (1,11) (1,2) (1,12) (1,6) (1,7) (1,15) (2,19) (2,4) (2,9) (2,11) (2,17) (2,12) (2,6) (2,18) (2,15) (3,5) (3,13) (3,10) (4,19) (4,8) (4,9) (4,11) (4,17) (4,12) (4,6) (4,7) (4,15) (5,13) (5,10) (6,9) (6,11) (6,12) (6,18) (7,19) (7,8) (7,9) (7,11) (7,17) (7,15) (8,19) (8,11) (8,17) (8,12) (9,17) (9,12) (9,18) (10,13) (11,17) (11,15) (12,19) (12,17) (12,18) (12,15) (14,20) (14,21) (15,17) (15,18) (17,19) (17,18) (18,19) (20,21)\nQ: Is there a path between node 14 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1763"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,24) (0,1) (0,6) (0,14) (1,10) (2,25) (2,5) (2,20) (2,18) (3,22) (3,6) (3,19) (3,23) (4,9) (4,18) (5,15) (5,25) (5,17) (5,20) (6,11) (6,24) (6,14) (6,7) (6,21) (7,24) (8,25) (8,17) (8,20) (8,18) (9,25) (10,24) (10,22) (10,21) (11,22) (11,19) (11,23) (12,15) (12,16) (12,17) (13,19) (13,14) (14,22) (14,19) (15,16) (15,18) (16,17) (17,20) (18,25) (19,24) (19,22) (20,25) (21,23) (22,24) (22,23)\nQ: Is there a path between node 21 and node 24?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1764"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,18) (1,4) (1,11) (2,21) (2,20) (2,24) (3,24) (4,13) (4,15) (4,8) (5,19) (5,24) (6,20) (6,24) (7,25) (7,21) (8,17) (8,15) (8,12) (9,13) (9,12) (10,16) (11,13) (11,18) (11,23) (11,14) (11,12) (13,17) (14,23) (15,18) (15,23) (18,23) (19,25) (19,24) (20,21) (21,25) (24,25)\nQ: Is there a path between node 23 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1765"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,18) (0,15) (0,12) (0,5) (1,24) (2,21) (2,23) (2,9) (2,15) (2,19) (3,23) (3,15) (3,8) (3,16) (5,21) (5,22) (5,6) (5,19) (5,8) (5,10) (5,16) (6,14) (6,22) (6,9) (6,12) (6,17) (9,23) (9,22) (9,20) (9,10) (10,22) (10,18) (10,19) (11,24) (12,14) (13,14) (13,21) (13,23) (13,18) (13,15) (14,21) (14,18) (14,15) (14,16) (15,20) (15,17) (17,23) (17,22) (17,18) (17,20) (17,19) (18,19) (19,20) (21,23)\nQ: Is there a path between node 4 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1766"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,6) (0,3) (0,18) (0,1) (0,15) (0,12) (0,14) (0,9) (0,16) (0,8) (0,2) (0,11) (0,19) (1,7) (1,6) (1,3) (1,18) (1,15) (1,9) (1,8) (1,2) (1,20) (2,7) (2,3) (2,18) (2,15) (2,12) (2,14) (2,9) (2,16) (2,8) (2,11) (2,19) (2,20) (3,18) (3,15) (3,12) (3,9) (3,16) (3,8) (3,19) (3,20) (4,13) (4,17) (5,17) (6,7) (6,18) (6,15) (6,14) (6,9) (6,16) (6,11) (6,19) (6,20) (7,15) (7,12) (7,14) (7,9) (7,16) (8,18) (8,12) (8,14) (8,9) (8,16) (8,11) (8,19) (8,20) (9,18) (9,15) (9,12) (9,11) (9,19) (9,20) (10,13) (11,18) (11,12) (11,14) (11,16) (11,19) (11,20) (12,18) (12,15) (12,14) (12,19) (12,20) (13,17) (14,19) (16,18) (16,19) (18,20)\nQ: Is there a path between node 20 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1767"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,14) (0,5) (0,9) (0,8) (0,6) (0,21) (1,4) (1,15) (1,18) (1,11) (1,10) (1,12) (2,20) (2,14) (2,5) (2,9) (2,22) (2,6) (2,16) (3,9) (3,23) (3,22) (3,6) (3,21) (4,15) (4,11) (4,19) (4,13) (5,20) (5,14) (5,9) (5,8) (5,6) (5,21) (6,20) (6,14) (6,9) (6,23) (6,8) (6,16) (7,18) (7,11) (7,10) (7,12) (7,19) (7,13) (8,20) (8,14) (8,23) (8,21) (9,20) (9,23) (9,22) (9,21) (10,15) (10,18) (10,11) (10,12) (10,19) (10,13) (11,15) (11,13) (12,18) (12,19) (13,18) (13,19) (14,23) (14,22) (14,21) (15,19) (16,23) (16,22) (20,21) (22,23)\nQ: Is there a path between node 3 and node 16?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1768"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,21) (1,17) (1,15) (1,2) (1,4) (1,18) (2,8) (2,13) (2,17) (2,15) (2,23) (2,22) (2,4) (2,18) (2,12) (4,21) (4,8) (4,13) (4,15) (4,23) (4,22) (4,18) (4,12) (5,21) (5,8) (5,13) (5,17) (5,15) (5,22) (5,18) (7,14) (7,16) (7,10) (7,11) (7,19) (8,21) (8,17) (8,23) (8,18) (9,14) (9,24) (10,14) (10,24) (10,19) (11,14) (11,16) (11,24) (12,21) (12,13) (12,17) (12,15) (12,23) (12,22) (12,18) (13,21) (13,17) (13,15) (13,23) (13,22) (14,24) (15,21) (15,17) (15,23) (15,22) (15,18) (16,19) (17,21) (17,18) (18,21) (18,23) (21,22) (22,23)\nQ: Is there a path between node 21 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1769"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,15) (1,14) (1,3) (1,9) (1,10) (1,4) (1,7) (1,6) (1,13) (1,12) (1,11) (2,15) (3,14) (3,8) (3,9) (3,10) (3,4) (3,12) (3,11) (4,8) (4,9) (4,10) (4,7) (4,5) (4,11) (5,9) (5,7) (5,13) (5,12) (5,11) (6,14) (6,8) (6,7) (6,13) (6,11) (7,8) (7,9) (7,10) (7,11) (8,14) (8,10) (8,12) (8,11) (9,14) (9,10) (9,13) (9,12) (10,14) (10,13) (10,12) (11,14) (11,13) (11,12) (12,14)\nQ: Is there a path between node 8 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1770"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,10) (0,17) (0,4) (0,21) (0,1) (0,2) (0,18) (0,7) (0,19) (0,11) (0,3) (0,5) (0,14) (1,6) (1,10) (1,17) (1,21) (1,16) (1,18) (1,7) (1,8) (1,11) (2,6) (2,10) (2,17) (2,4) (2,21) (2,16) (2,13) (2,18) (2,7) (2,8) (2,19) (2,3) (2,5) (3,6) (3,10) (3,17) (3,4) (3,21) (3,16) (3,13) (3,18) (3,7) (3,19) (4,10) (4,16) (4,18) (4,7) (4,8) (4,19) (4,5) (5,6) (5,16) (5,13) (5,18) (5,7) (5,8) (5,19) (5,14) (6,10) (6,17) (6,21) (6,16) (6,13) (6,18) (6,7) (6,19) (6,11) (6,14) (7,10) (7,17) (7,21) (7,16) (7,13) (7,18) (7,8) (7,19) (7,11) (7,14) (8,10) (8,17) (8,21) (8,16) (8,13) (8,18) (8,19) (8,11) (9,20) (10,17) (10,21) (10,13) (10,18) (10,19) (10,11) (10,14) (11,17) (11,16) (11,13) (11,18) (11,19) (12,15) (13,21) (13,16) (13,18) (13,19) (13,14) (14,17) (14,21) (14,16) (14,18) (14,19) (16,17) (16,21) (16,18) (17,18) (18,21) (18,19) (19,21)\nQ: Is there a path between node 9 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1771"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,13) (0,8) (0,18) (0,25) (0,14) (0,17) (0,21) (1,13) (1,26) (1,14) (1,20) (1,17) (1,24) (1,6) (2,8) (2,18) (2,9) (2,26) (2,14) (2,10) (2,15) (3,16) (3,12) (4,13) (4,8) (4,18) (4,25) (4,6) (5,19) (5,13) (5,10) (5,20) (5,22) (5,17) (5,6) (6,8) (6,18) (6,9) (6,26) (6,14) (6,17) (6,21) (6,15) (6,23) (7,25) (7,14) (7,22) (7,24) (7,15) (7,23) (8,13) (8,25) (8,24) (8,23) (9,25) (9,27) (9,26) (9,14) (9,17) (9,24) (9,23) (10,19) (10,13) (10,25) (10,22) (11,12) (12,16) (13,19) (13,18) (13,21) (14,19) (14,18) (14,22) (15,19) (15,25) (15,23) (17,25) (17,22) (17,21) (17,24) (18,21) (18,24) (19,26) (19,22) (19,24) (19,23) (20,25) (20,26) (20,24) (20,23) (21,27) (21,23) (22,25) (22,26) (22,23) (25,27) (25,26)\nQ: Is there a path between node 19 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1772"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,11) (0,1) (0,13) (0,15) (0,16) (0,9) (0,14) (0,3) (0,12) (0,17) (0,2) (0,18) (1,11) (1,13) (1,15) (1,16) (1,9) (1,8) (1,14) (1,3) (1,4) (1,17) (1,18) (2,11) (2,13) (2,15) (2,9) (2,8) (2,14) (2,3) (2,12) (2,17) (2,18) (3,11) (3,13) (3,15) (3,16) (3,9) (3,8) (3,14) (3,12) (3,17) (3,18) (4,13) (4,15) (4,16) (4,8) (4,14) (4,12) (4,18) (5,6) (5,7) (5,10) (6,7) (6,10) (7,10) (8,11) (8,15) (8,16) (8,18) (9,11) (9,13) (9,15) (9,16) (9,14) (9,12) (9,17) (9,18) (11,13) (11,16) (11,17) (11,18) (12,15) (12,16) (12,17) (12,18) (13,15) (13,18) (14,15) (14,17) (15,16) (16,17) (16,18) (17,18)\nQ: Is there a path between node 4 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1773"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (0,11) (0,8) (0,17) (0,13) (0,6) (0,3) (0,15) (0,7) (1,14) (1,19) (1,9) (1,21) (1,12) (1,22) (1,4) (1,18) (1,5) (1,10) (1,20) (2,16) (3,23) (3,11) (3,8) (3,17) (3,13) (3,6) (3,15) (3,7) (4,14) (4,19) (4,9) (4,21) (4,12) (4,22) (4,18) (4,5) (4,10) (4,20) (5,14) (5,19) (5,9) (5,21) (5,12) (5,22) (5,18) (5,10) (5,20) (6,23) (6,11) (6,8) (6,17) (6,13) (6,15) (6,7) (7,23) (7,11) (7,8) (7,17) (7,13) (7,15) (8,23) (8,11) (8,17) (8,13) (8,15) (9,14) (9,19) (9,21) (9,12) (9,22) (9,18) (9,10) (9,20) (10,14) (10,19) (10,21) (10,12) (10,22) (10,18) (10,20) (11,23) (11,17) (11,13) (11,15) (12,14) (12,19) (12,21) (12,22) (12,18) (12,20) (13,23) (13,17) (13,15) (14,19) (14,21) (14,22) (14,18) (14,20) (15,23) (15,17) (17,23) (18,19) (18,21) (18,22) (18,20) (19,21) (19,22) (19,20) (20,21) (20,22) (21,22)\nQ: Is there a path between node 13 and node 18?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1774"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,1) (0,15) (0,6) (0,9) (0,4) (0,16) (0,19) (1,20) (1,15) (1,6) (1,9) (1,4) (1,16) (1,19) (2,14) (2,10) (2,3) (2,11) (2,7) (2,18) (2,5) (2,12) (2,17) (2,8) (3,14) (3,10) (3,11) (3,7) (3,18) (3,5) (3,12) (3,17) (3,8) (4,20) (4,15) (4,6) (4,9) (4,16) (4,19) (5,14) (5,10) (5,11) (5,7) (5,18) (5,12) (5,17) (5,8) (6,20) (6,15) (6,9) (6,16) (6,19) (7,14) (7,10) (7,11) (7,18) (7,12) (7,17) (7,8) (8,14) (8,10) (8,11) (8,18) (8,12) (8,17) (9,20) (9,15) (9,16) (9,19) (10,14) (10,11) (10,18) (10,12) (10,17) (11,14) (11,18) (11,12) (11,17) (12,14) (12,18) (12,17) (14,18) (14,17) (15,20) (15,16) (15,19) (16,20) (16,19) (17,18) (19,20)\nQ: Is there a path between node 6 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1775"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,4) (0,1) (0,11) (0,9) (0,12) (1,2) (1,4) (1,11) (1,9) (1,13) (1,8) (1,12) (2,6) (2,3) (2,4) (2,11) (2,9) (2,13) (2,8) (3,6) (3,9) (3,13) (3,8) (3,12) (4,6) (4,11) (4,9) (4,13) (4,8) (4,12) (5,7) (5,10) (6,11) (6,9) (6,8) (6,12) (8,9) (8,12) (9,11) (9,12) (11,13) (12,13)\nQ: Is there a path between node 10 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1776"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,6) (2,7) (2,6) (2,4) (5,7) (6,8)\nQ: Is there a path between node 1 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1777"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,34) (0,4) (0,7) (0,28) (0,8) (0,15) (0,23) (0,13) (0,22) (0,32) (0,11) (0,18) (1,7) (1,2) (1,13) (1,27) (1,26) (1,9) (2,14) (2,31) (2,15) (2,23) (2,13) (2,9) (2,22) (2,17) (2,32) (2,18) (3,24) (4,7) (4,27) (4,17) (5,16) (5,12) (5,29) (5,20) (6,34) (6,7) (6,14) (6,31) (6,10) (6,23) (6,26) (6,21) (6,17) (6,18) (7,33) (7,14) (7,28) (7,15) (7,26) (7,19) (8,14) (8,28) (8,31) (8,10) (8,13) (8,25) (8,30) (8,18) (9,14) (9,21) (9,25) (9,22) (9,11) (10,31) (10,15) (10,27) (10,25) (10,17) (10,32) (11,28) (11,31) (11,15) (11,13) (11,27) (11,21) (11,25) (11,22) (12,16) (13,33) (13,14) (13,28) (13,26) (13,21) (13,17) (13,32) (13,18) (14,33) (14,31) (14,23) (14,27) (14,25) (15,34) (15,30) (15,17) (15,19) (16,24) (17,23) (17,26) (17,19) (18,34) (18,21) (18,30) (19,33) (19,21) (19,25) (19,30) (21,33) (21,28) (21,25) (21,30) (22,33) (22,23) (22,26) (22,25) (23,34) (23,25) (25,33) (25,32) (26,33) (26,28) (26,31) (26,32) (27,33) (27,32) (32,33)\nQ: Is there a path between node 30 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1778"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (3,7) (4,6) (5,6)\nQ: Is there a path between node 3 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1779"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,11) (0,22) (0,30) (0,25) (0,19) (0,12) (0,13) (0,10) (0,29) (1,17) (1,4) (1,18) (1,7) (1,27) (1,2) (1,3) (1,9) (1,23) (1,28) (2,4) (2,21) (2,26) (2,7) (2,27) (2,9) (2,23) (2,28) (3,17) (3,4) (3,21) (3,26) (3,18) (3,7) (3,27) (3,14) (3,9) (3,23) (3,28) (3,24) (4,17) (4,21) (4,26) (4,18) (4,14) (4,9) (4,28) (4,24) (5,11) (5,22) (5,20) (5,25) (5,29) (6,8) (7,21) (7,26) (7,18) (7,27) (7,23) (7,28) (7,24) (9,21) (9,26) (9,18) (9,27) (9,14) (9,23) (9,28) (9,24) (10,11) (10,22) (10,20) (10,30) (10,25) (10,16) (10,19) (10,15) (10,13) (10,29) (11,22) (11,20) (11,30) (11,25) (11,16) (11,19) (11,12) (11,15) (11,13) (11,29) (12,22) (12,20) (12,30) (12,16) (12,15) (12,13) (13,22) (13,20) (13,30) (13,25) (13,16) (13,19) (13,15) (13,29) (14,26) (14,18) (14,23) (14,28) (14,24) (15,22) (15,30) (15,16) (15,19) (15,29) (16,22) (16,30) (16,25) (16,19) (16,29) (17,26) (17,18) (17,27) (17,23) (17,28) (18,21) (18,26) (18,27) (18,24) (19,20) (19,30) (19,25) (19,29) (20,22) (20,25) (20,29) (21,26) (21,27) (21,28) (21,24) (22,30) (22,29) (23,26) (23,27) (23,28) (23,24) (24,27) (24,28) (25,29) (26,27) (27,28) (29,30)\nQ: Is there a path between node 1 and node 9?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1780"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (1,4) (2,4)\nQ: Is there a path between node 0 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1781"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,4) (0,1) (0,5) (0,24) (0,3) (0,21) (0,19) (0,9) (0,15) (0,20) (0,27) (0,13) (1,24) (1,21) (1,31) (1,10) (1,7) (1,20) (1,27) (1,13) (2,6) (2,5) (2,24) (2,3) (2,21) (2,19) (2,9) (2,31) (2,15) (2,7) (2,27) (2,13) (3,6) (3,4) (3,5) (3,22) (3,24) (3,21) (3,19) (3,9) (3,31) (3,18) (3,7) (3,20) (4,5) (4,21) (4,19) (4,9) (4,31) (4,7) (4,20) (4,27) (4,13) (5,6) (5,22) (5,24) (5,21) (5,9) (5,31) (5,10) (5,15) (5,18) (5,20) (5,27) (5,13) (6,22) (6,21) (6,19) (6,9) (6,31) (6,10) (6,15) (6,18) (6,7) (6,27) (6,13) (7,22) (7,9) (7,10) (7,15) (7,18) (7,20) (7,27) (7,13) (8,16) (8,11) (8,28) (8,12) (8,25) (8,30) (8,14) (8,32) (8,29) (9,22) (9,24) (9,21) (9,19) (9,31) (9,10) (9,15) (9,18) (9,20) (10,22) (10,19) (10,31) (10,15) (10,20) (10,27) (10,13) (11,16) (11,28) (11,26) (11,23) (11,30) (11,14) (11,32) (11,17) (12,16) (12,28) (12,23) (12,30) (12,14) (12,33) (12,32) (12,17) (12,29) (13,22) (13,24) (13,21) (13,19) (13,15) (13,18) (13,20) (14,28) (14,26) (14,23) (14,25) (14,33) (14,32) (14,29) (15,22) (15,24) (15,21) (15,19) (15,20) (15,27) (16,26) (16,25) (16,30) (16,33) (16,32) (16,17) (16,29) (17,28) (17,26) (17,25) (17,30) (17,33) (17,32) (17,29) (18,24) (18,19) (18,31) (19,22) (19,24) (19,31) (19,20) (19,27) (20,21) (20,31) (20,27) (21,31) (23,28) (23,26) (23,25) (23,30) (24,31) (24,27) (25,26) (25,30) (25,33) (25,32) (25,29) (26,28) (26,33) (26,32) (28,30) (28,29) (29,30) (29,33) (29,32) (30,32)\nQ: Is there a path between node 28 and node 17?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1782"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,4) (1,2) (3,4)\nQ: Is there a path between node 2 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1783"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,13) (0,5) (0,11) (0,15) (0,10) (0,16) (0,14) (0,8) (0,9) (1,18) (1,12) (1,7) (1,6) (2,13) (2,11) (2,15) (2,17) (2,16) (2,14) (2,3) (2,8) (2,9) (3,5) (3,11) (3,4) (3,15) (3,10) (3,14) (3,8) (3,9) (4,13) (4,5) (4,17) (4,16) (4,14) (4,8) (5,17) (5,16) (5,14) (6,12) (6,19) (6,20) (6,7) (7,18) (8,15) (8,17) (8,16) (8,14) (8,9) (9,13) (9,11) (9,17) (9,16) (9,14) (10,11) (10,15) (10,17) (10,16) (10,14) (11,13) (11,15) (11,16) (12,18) (12,19) (12,20) (13,17) (13,14) (14,15) (14,17) (14,16) (15,17) (16,17) (18,19) (18,20) (19,20)\nQ: Is there a path between node 17 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1784"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,4) (1,2) (3,4)\nQ: Is there a path between node 0 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1785"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,18) (0,15) (0,12) (0,5) (1,24) (2,21) (2,23) (2,9) (2,15) (2,19) (3,23) (3,15) (3,8) (3,16) (5,21) (5,22) (5,6) (5,19) (5,8) (5,10) (5,16) (6,14) (6,22) (6,9) (6,12) (6,17) (9,23) (9,22) (9,20) (9,10) (10,22) (10,18) (10,19) (11,24) (12,14) (13,14) (13,21) (13,23) (13,18) (13,15) (14,21) (14,18) (14,15) (14,16) (15,20) (15,17) (17,23) (17,22) (17,18) (17,20) (17,19) (18,19) (19,20) (21,23)\nQ: Is there a path between node 19 and node 18?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1786"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,7) (0,8) (0,10) (0,3) (1,4) (1,11) (1,9) (1,6) (1,12) (1,2) (2,4) (2,11) (2,9) (2,6) (2,12) (3,5) (3,7) (3,8) (3,10) (4,11) (4,9) (4,6) (4,12) (5,7) (5,8) (5,10) (6,11) (6,9) (6,12) (7,8) (7,10) (8,10) (9,11) (9,12) (11,12)\nQ: Is there a path between node 3 and node 12?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1787"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,3) (0,2) (0,1) (1,6) (1,3) (1,2) (2,6) (2,3) (3,6) (4,5)\nQ: Is there a path between node 5 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1788"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (1,8) (1,4) (1,5) (1,7) (1,2) (1,9) (1,6) (2,8) (2,4) (2,5) (2,7) (2,9) (2,6) (4,8) (4,5) (4,7) (4,9) (4,6) (5,8) (5,7) (5,9) (5,6) (6,8) (6,7) (6,9) (7,8) (7,9) (8,9)\nQ: Is there a path between node 0 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1789"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,9) (0,8) (0,19) (0,13) (0,11) (1,15) (1,6) (1,3) (1,12) (1,4) (1,2) (1,23) (1,5) (1,16) (1,22) (1,17) (1,18) (1,21) (1,24) (1,25) (2,15) (2,3) (2,4) (2,20) (2,23) (2,22) (2,27) (2,18) (2,21) (2,24) (3,15) (3,4) (3,26) (3,20) (3,23) (3,5) (3,16) (3,14) (3,22) (3,27) (3,18) (3,21) (3,24) (3,25) (4,15) (4,6) (4,12) (4,26) (4,20) (4,5) (4,22) (4,27) (4,17) (4,21) (4,25) (5,15) (5,6) (5,12) (5,20) (5,16) (5,14) (5,22) (5,27) (5,18) (5,21) (5,25) (6,15) (6,12) (6,27) (6,17) (6,21) (6,24) (6,25) (7,19) (7,13) (8,9) (8,19) (8,13) (9,19) (9,10) (10,19) (10,13) (10,11) (11,13) (12,15) (12,26) (12,20) (12,14) (12,22) (12,21) (12,24) (13,19) (14,15) (14,26) (14,20) (14,16) (14,22) (14,17) (14,21) (14,24) (14,25) (15,26) (15,20) (15,23) (15,16) (15,22) (15,17) (15,18) (15,24) (16,26) (16,27) (16,18) (16,25) (17,26) (17,23) (17,18) (17,21) (17,24) (17,25) (18,26) (18,20) (18,22) (18,27) (18,24) (18,25) (20,26) (20,23) (20,22) (20,27) (20,24) (20,25) (21,22) (21,27) (21,24) (21,25) (22,23) (22,27) (22,24) (22,25) (23,27) (23,25) (24,26) (24,27) (25,26) (25,27) (26,27)\nQ: Is there a path between node 27 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1790"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,4) (0,1) (0,5) (0,24) (0,3) (0,21) (0,19) (0,9) (0,15) (0,20) (0,27) (0,13) (1,24) (1,21) (1,31) (1,10) (1,7) (1,20) (1,27) (1,13) (2,6) (2,5) (2,24) (2,3) (2,21) (2,19) (2,9) (2,31) (2,15) (2,7) (2,27) (2,13) (3,6) (3,4) (3,5) (3,22) (3,24) (3,21) (3,19) (3,9) (3,31) (3,18) (3,7) (3,20) (4,5) (4,21) (4,19) (4,9) (4,31) (4,7) (4,20) (4,27) (4,13) (5,6) (5,22) (5,24) (5,21) (5,9) (5,31) (5,10) (5,15) (5,18) (5,20) (5,27) (5,13) (6,22) (6,21) (6,19) (6,9) (6,31) (6,10) (6,15) (6,18) (6,7) (6,27) (6,13) (7,22) (7,9) (7,10) (7,15) (7,18) (7,20) (7,27) (7,13) (8,16) (8,11) (8,28) (8,12) (8,25) (8,30) (8,14) (8,32) (8,29) (9,22) (9,24) (9,21) (9,19) (9,31) (9,10) (9,15) (9,18) (9,20) (10,22) (10,19) (10,31) (10,15) (10,20) (10,27) (10,13) (11,16) (11,28) (11,26) (11,23) (11,30) (11,14) (11,32) (11,17) (12,16) (12,28) (12,23) (12,30) (12,14) (12,33) (12,32) (12,17) (12,29) (13,22) (13,24) (13,21) (13,19) (13,15) (13,18) (13,20) (14,28) (14,26) (14,23) (14,25) (14,33) (14,32) (14,29) (15,22) (15,24) (15,21) (15,19) (15,20) (15,27) (16,26) (16,25) (16,30) (16,33) (16,32) (16,17) (16,29) (17,28) (17,26) (17,25) (17,30) (17,33) (17,32) (17,29) (18,24) (18,19) (18,31) (19,22) (19,24) (19,31) (19,20) (19,27) (20,21) (20,31) (20,27) (21,31) (23,28) (23,26) (23,25) (23,30) (24,31) (24,27) (25,26) (25,30) (25,33) (25,32) (25,29) (26,28) (26,33) (26,32) (28,30) (28,29) (29,30) (29,33) (29,32) (30,32)\nQ: Is there a path between node 12 and node 24?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1791"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,14) (0,5) (0,9) (0,8) (0,6) (0,21) (1,4) (1,15) (1,18) (1,11) (1,10) (1,12) (2,20) (2,14) (2,5) (2,9) (2,22) (2,6) (2,16) (3,9) (3,23) (3,22) (3,6) (3,21) (4,15) (4,11) (4,19) (4,13) (5,20) (5,14) (5,9) (5,8) (5,6) (5,21) (6,20) (6,14) (6,9) (6,23) (6,8) (6,16) (7,18) (7,11) (7,10) (7,12) (7,19) (7,13) (8,20) (8,14) (8,23) (8,21) (9,20) (9,23) (9,22) (9,21) (10,15) (10,18) (10,11) (10,12) (10,19) (10,13) (11,15) (11,13) (12,18) (12,19) (13,18) (13,19) (14,23) (14,22) (14,21) (15,19) (16,23) (16,22) (20,21) (22,23)\nQ: Is there a path between node 13 and node 11?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1792"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,21) (0,17) (0,7) (0,29) (1,20) (2,32) (2,6) (2,13) (3,22) (3,23) (3,8) (4,30) (4,31) (6,23) (6,16) (6,32) (7,19) (8,14) (8,23) (8,16) (8,32) (8,13) (9,24) (9,17) (9,29) (13,14) (13,32) (14,16) (14,32) (16,20) (16,28) (17,24) (20,28) (21,29) (24,29) (27,30) (30,31)\nQ: Is there a path between node 20 and node 2?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1793"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,5) (3,5)\nQ: Is there a path between node 0 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1794"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,1) (0,6) (0,2) (0,3) (0,7) (0,5) (1,8) (1,6) (1,2) (1,3) (1,7) (1,5) (2,8) (2,6) (2,3) (2,7) (2,5) (3,8) (3,6) (3,7) (3,5) (5,8) (5,6) (5,7) (6,8) (6,7) (7,8)\nQ: Is there a path between node 1 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1795"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,12) (0,2) (0,3) (1,13) (1,22) (1,7) (1,11) (1,19) (1,6) (1,8) (2,14) (2,20) (2,3) (3,14) (3,20) (4,21) (4,18) (4,5) (4,17) (4,9) (4,15) (4,10) (5,21) (5,17) (5,9) (5,15) (5,10) (6,16) (6,13) (6,22) (6,7) (6,11) (6,19) (6,8) (7,16) (7,13) (7,22) (7,8) (8,16) (8,13) (8,11) (8,19) (9,18) (9,17) (9,15) (9,10) (10,21) (10,18) (11,16) (11,13) (11,22) (11,19) (12,14) (12,20) (13,16) (13,19) (14,20) (15,21) (15,18) (15,17) (16,22) (17,21) (17,18) (19,22)\nQ: Is there a path between node 1 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1796"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,15) (1,3) (1,20) (2,11) (3,12) (3,6) (3,16) (3,20) (5,14) (5,7) (6,20) (6,21) (7,13) (7,18) (8,14) (8,13) (9,12) (9,16) (9,21) (10,21) (11,17) (12,16) (14,18) (15,16) (15,21) (16,20) (20,21)\nQ: Is there a path between node 11 and node 20?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1797"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,26) (0,15) (0,25) (0,14) (0,7) (0,2) (0,9) (0,5) (1,26) (1,15) (1,25) (1,7) (1,6) (1,2) (1,20) (1,22) (2,25) (2,19) (2,14) (2,4) (3,12) (3,16) (4,15) (4,7) (4,6) (4,8) (5,26) (5,20) (5,8) (5,9) (5,22) (5,13) (6,19) (6,17) (6,7) (6,20) (6,22) (7,19) (7,17) (7,9) (8,19) (9,26) (9,14) (9,24) (11,12) (12,21) (12,18) (12,16) (13,17) (13,22) (14,26) (14,22) (15,19) (15,20) (16,21) (18,23) (19,20) (19,22) (25,26)\nQ: Is there a path between node 12 and node 14?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1798"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,17) (1,5) (1,18) (1,7) (1,22) (1,11) (1,20) (1,4) (1,23) (2,14) (2,10) (2,21) (2,15) (2,16) (2,3) (3,14) (3,10) (3,15) (3,16) (3,6) (3,19) (4,18) (4,7) (4,22) (4,11) (4,20) (4,23) (5,13) (5,7) (5,22) (5,11) (5,20) (5,23) (6,10) (6,21) (6,15) (6,16) (6,9) (6,8) (6,19) (7,13) (7,22) (7,20) (7,23) (8,10) (8,9) (8,19) (9,21) (9,15) (9,19) (10,21) (10,16) (10,19) (11,18) (11,13) (11,22) (11,23) (12,17) (13,22) (13,20) (14,15) (14,16) (14,19) (15,16) (15,19) (16,21) (16,19) (18,20) (18,23) (19,21) (20,22) (20,23) (22,23)\nQ: Is there a path between node 1 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1799"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,24) (0,2) (0,7) (0,15) (0,14) (0,22) (0,10) (0,18) (0,5) (0,9) (0,4) (0,11) (0,8) (0,20) (0,13) (1,2) (1,7) (1,15) (1,14) (1,18) (1,5) (1,16) (1,9) (1,4) (1,11) (1,8) (1,13) (2,24) (2,7) (2,15) (2,14) (2,22) (2,18) (2,16) (2,9) (2,4) (2,11) (2,8) (2,20) (2,23) (3,21) (4,7) (4,14) (4,22) (4,18) (4,16) (4,13) (4,23) (5,24) (5,7) (5,15) (5,14) (5,22) (5,10) (5,18) (5,20) (5,23) (6,12) (7,24) (7,15) (7,14) (7,10) (7,18) (7,16) (7,9) (7,11) (7,8) (7,20) (7,13) (7,23) (8,24) (8,14) (8,10) (8,18) (8,9) (8,13) (8,23) (9,24) (9,15) (9,14) (9,22) (9,10) (9,16) (9,20) (9,23) (10,24) (10,15) (10,14) (10,22) (10,18) (10,16) (10,20) (11,15) (11,14) (11,18) (11,16) (11,20) (11,13) (11,23) (13,24) (13,15) (13,18) (13,16) (13,23) (14,24) (14,15) (14,22) (14,18) (14,16) (14,23) (15,24) (15,22) (15,18) (15,16) (15,20) (15,23) (16,24) (16,20) (16,23) (18,22) (18,20) (18,23) (19,21) (20,22) (22,24) (22,23) (23,24)\nQ: Is there a path between node 23 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1800"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,11) (0,2) (0,7) (0,8) (0,16) (0,15) (1,11) (1,2) (1,7) (1,8) (1,16) (1,15) (1,14) (2,4) (2,11) (2,5) (2,7) (2,12) (2,16) (2,15) (3,13) (3,10) (4,6) (4,5) (4,7) (4,8) (4,12) (4,16) (4,15) (4,14) (5,6) (5,7) (5,8) (5,12) (5,16) (5,14) (6,11) (6,7) (6,8) (6,12) (6,16) (6,15) (6,14) (7,11) (7,8) (7,16) (7,14) (8,11) (8,12) (8,16) (11,12) (11,16) (11,15) (11,14) (12,14) (14,16) (14,15)\nQ: Is there a path between node 3 and node 1?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1801"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,6) (0,11) (0,19) (0,20) (0,1) (0,15) (0,12) (0,7) (0,22) (0,5) (0,21) (0,3) (0,4) (0,18) (0,17) (1,14) (1,6) (1,11) (1,19) (1,20) (1,15) (1,12) (1,7) (1,22) (1,5) (1,21) (1,3) (1,4) (1,18) (1,17) (2,13) (2,10) (2,8) (2,16) (2,9) (3,14) (3,6) (3,11) (3,19) (3,20) (3,15) (3,12) (3,7) (3,22) (3,5) (3,21) (3,4) (3,18) (3,17) (4,14) (4,6) (4,11) (4,19) (4,20) (4,15) (4,12) (4,7) (4,22) (4,5) (4,21) (4,18) (4,17) (5,14) (5,6) (5,11) (5,19) (5,20) (5,15) (5,12) (5,7) (5,22) (5,21) (5,18) (5,17) (6,14) (6,11) (6,19) (6,20) (6,15) (6,12) (6,7) (6,22) (6,21) (6,18) (6,17) (7,14) (7,11) (7,19) (7,20) (7,15) (7,12) (7,22) (7,21) (7,18) (7,17) (8,13) (8,10) (8,16) (8,9) (9,13) (9,10) (9,16) (10,13) (10,16) (11,14) (11,19) (11,20) (11,15) (11,12) (11,22) (11,21) (11,18) (11,17) (12,14) (12,19) (12,20) (12,15) (12,22) (12,21) (12,18) (12,17) (13,16) (14,19) (14,20) (14,15) (14,22) (14,21) (14,18) (14,17) (15,19) (15,20) (15,22) (15,21) (15,18) (15,17) (17,19) (17,20) (17,22) (17,21) (17,18) (18,19) (18,20) (18,22) (18,21) (19,20) (19,22) (19,21) (20,22) (20,21) (21,22)\nQ: Is there a path between node 19 and node 22?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1802"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,7) (0,10) (0,6) (0,2) (0,8) (0,4) (0,1) (1,3) (1,7) (1,10) (1,6) (1,2) (1,8) (1,4) (2,3) (2,7) (2,10) (2,6) (2,8) (2,4) (3,7) (3,10) (3,6) (3,8) (3,4) (4,7) (4,10) (4,6) (4,8) (5,9) (6,7) (6,10) (6,8) (7,10) (7,8) (8,10)\nQ: Is there a path between node 6 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1803"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (1,18) (1,8) (1,4) (2,15) (2,18) (2,11) (2,23) (2,4) (3,12) (3,5) (4,23) (4,25) (5,12) (5,17) (6,22) (6,13) (7,18) (7,23) (7,8) (9,17) (10,19) (10,17) (11,15) (12,24) (14,20) (14,22) (15,18) (16,20) (16,22) (20,22) (21,22) (23,25)\nQ: Is there a path between node 21 and node 5?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1804"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,23) (1,6) (1,19) (1,7) (2,17) (2,24) (2,10) (2,20) (3,22) (3,27) (4,17) (4,15) (5,19) (5,12) (5,25) (6,19) (6,7) (7,18) (7,23) (8,16) (8,13) (9,27) (9,13) (10,21) (10,15) (10,11) (11,17) (11,26) (11,24) (11,14) (12,25) (12,23) (14,17) (14,26) (15,21) (17,26) (17,21) (17,24) (20,21) (20,24) (21,26) (21,24) (23,25)\nQ: Is there a path between node 20 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1805"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,18) (0,17) (0,10) (1,7) (1,24) (1,27) (2,4) (2,8) (2,13) (2,19) (2,27) (3,16) (3,28) (3,9) (4,18) (4,6) (4,10) (4,11) (4,27) (6,20) (6,8) (6,7) (6,27) (7,8) (7,18) (7,17) (7,23) (7,24) (7,10) (7,13) (7,19) (7,11) (7,14) (8,17) (8,22) (8,24) (8,10) (8,11) (10,18) (10,17) (10,12) (10,11) (10,27) (11,17) (11,12) (12,20) (12,18) (12,17) (12,14) (13,20) (13,18) (13,24) (13,27) (13,26) (14,18) (15,28) (15,25) (16,25) (17,20) (17,18) (17,26) (18,22) (18,23) (18,19) (18,27) (19,23) (19,27) (19,26) (20,24) (22,23) (22,24) (22,26) (26,27)\nQ: Is there a path between node 27 and node 12?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1806"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,29) (0,10) (0,18) (0,21) (0,30) (0,28) (0,15) (1,27) (1,24) (1,22) (1,32) (1,14) (1,5) (2,29) (2,10) (2,18) (2,21) (2,19) (2,30) (2,16) (2,28) (2,15) (3,24) (3,13) (3,22) (3,20) (3,5) (4,17) (4,11) (4,6) (4,26) (4,23) (4,31) (4,25) (5,27) (5,13) (5,22) (5,20) (5,32) (5,14) (6,17) (6,9) (6,23) (6,31) (6,25) (7,29) (7,10) (7,18) (7,19) (7,30) (7,16) (7,15) (8,17) (8,11) (8,26) (8,23) (8,31) (9,17) (9,26) (9,23) (9,31) (9,25) (10,29) (10,18) (10,21) (10,30) (10,28) (10,15) (11,17) (11,26) (11,23) (12,27) (12,24) (12,13) (12,22) (12,32) (13,27) (13,24) (13,22) (13,20) (13,32) (13,14) (14,27) (14,22) (14,32) (15,29) (15,18) (15,21) (15,19) (15,28) (16,29) (16,21) (16,19) (16,28) (17,23) (18,29) (18,21) (18,30) (18,28) (19,29) (19,21) (19,30) (19,28) (20,24) (20,22) (20,32) (21,29) (21,30) (21,28) (22,27) (22,24) (22,32) (23,31) (24,27) (25,26) (26,31) (28,30)\nQ: Is there a path between node 26 and node 29?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1807"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,9) (0,8) (0,19) (0,13) (0,11) (1,15) (1,6) (1,3) (1,12) (1,4) (1,2) (1,23) (1,5) (1,16) (1,22) (1,17) (1,18) (1,21) (1,24) (1,25) (2,15) (2,3) (2,4) (2,20) (2,23) (2,22) (2,27) (2,18) (2,21) (2,24) (3,15) (3,4) (3,26) (3,20) (3,23) (3,5) (3,16) (3,14) (3,22) (3,27) (3,18) (3,21) (3,24) (3,25) (4,15) (4,6) (4,12) (4,26) (4,20) (4,5) (4,22) (4,27) (4,17) (4,21) (4,25) (5,15) (5,6) (5,12) (5,20) (5,16) (5,14) (5,22) (5,27) (5,18) (5,21) (5,25) (6,15) (6,12) (6,27) (6,17) (6,21) (6,24) (6,25) (7,19) (7,13) (8,9) (8,19) (8,13) (9,19) (9,10) (10,19) (10,13) (10,11) (11,13) (12,15) (12,26) (12,20) (12,14) (12,22) (12,21) (12,24) (13,19) (14,15) (14,26) (14,20) (14,16) (14,22) (14,17) (14,21) (14,24) (14,25) (15,26) (15,20) (15,23) (15,16) (15,22) (15,17) (15,18) (15,24) (16,26) (16,27) (16,18) (16,25) (17,26) (17,23) (17,18) (17,21) (17,24) (17,25) (18,26) (18,20) (18,22) (18,27) (18,24) (18,25) (20,26) (20,23) (20,22) (20,27) (20,24) (20,25) (21,22) (21,27) (21,24) (21,25) (22,23) (22,27) (22,24) (22,25) (23,27) (23,25) (24,26) (24,27) (25,26) (25,27) (26,27)\nQ: Is there a path between node 15 and node 0?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1808"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (1,24) (1,13) (1,7) (2,24) (2,15) (2,18) (2,8) (2,13) (2,7) (3,23) (3,6) (5,20) (5,14) (6,11) (6,23) (7,12) (7,10) (7,21) (7,8) (7,13) (8,10) (8,15) (8,18) (8,22) (8,13) (9,21) (9,13) (10,12) (10,15) (10,13) (12,24) (13,24) (13,22) (14,20) (15,24) (17,24) (19,20) (21,24)\nQ: Is there a path between node 23 and node 6?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1809"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,8) (1,5) (2,3) (3,5) (3,11) (4,8) (5,9) (5,7) (5,10) (6,11)\nQ: Is there a path between node 6 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1810"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,5) (0,7) (0,2) (0,8) (0,4) (0,9) (0,1) (0,12) (0,3) (0,11) (0,13) (1,10) (1,5) (1,7) (1,2) (1,8) (1,4) (1,9) (1,12) (1,3) (1,11) (1,13) (2,10) (2,5) (2,7) (2,8) (2,4) (2,9) (2,12) (2,3) (2,11) (2,13) (3,10) (3,5) (3,7) (3,8) (3,4) (3,9) (3,12) (3,11) (3,13) (4,10) (4,5) (4,7) (4,8) (4,9) (4,12) (4,11) (4,13) (5,10) (5,7) (5,8) (5,9) (5,12) (5,11) (5,13) (7,10) (7,8) (7,9) (7,12) (7,11) (7,13) (8,10) (8,9) (8,12) (8,11) (8,13) (9,10) (9,12) (9,11) (9,13) (10,12) (10,11) (10,13) (11,12) (11,13) (12,13)\nQ: Is there a path between node 8 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1811"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (1,17) (2,9) (3,16) (5,18) (5,11) (5,21) (6,21) (6,15) (7,19) (7,21) (8,10) (8,12) (8,16) (10,16) (14,23) (15,21) (16,19) (17,20) (18,19) (20,23)\nQ: Is there a path between node 8 and node 12?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1812"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,7) (0,2) (0,8) (1,6) (2,3) (3,6) (3,7) (4,6) (4,5) (5,8) (7,8)\nQ: Is there a path between node 9 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1813"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,31) (0,11) (0,27) (0,18) (1,4) (1,12) (1,31) (1,7) (1,25) (1,8) (1,18) (2,17) (2,14) (2,6) (2,10) (2,19) (3,17) (3,22) (3,9) (4,12) (4,30) (4,31) (4,13) (4,27) (4,18) (5,29) (5,16) (5,22) (5,21) (5,20) (5,28) (5,19) (6,29) (6,9) (6,10) (6,28) (7,11) (7,27) (7,15) (7,18) (8,30) (8,23) (8,11) (9,14) (9,21) (9,10) (11,23) (11,18) (12,30) (12,31) (12,27) (12,25) (12,15) (12,18) (13,23) (13,25) (13,15) (14,29) (14,17) (16,24) (16,17) (16,20) (17,29) (18,30) (18,26) (20,29) (21,24) (22,24) (23,27) (23,25) (25,26) (25,27) (26,31) (27,31) (28,29)\nQ: Is there a path between node 18 and node 30?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1814"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,19) (0,25) (0,2) (0,13) (0,1) (1,17) (1,24) (1,25) (1,11) (2,17) (2,25) (2,16) (2,13) (3,17) (4,23) (4,7) (4,14) (4,8) (5,18) (5,16) (6,18) (6,16) (6,21) (7,14) (7,15) (7,10) (8,23) (8,10) (9,14) (9,10) (10,23) (10,20) (11,17) (11,18) (11,25) (11,16) (11,13) (12,16) (13,17) (13,24) (13,25) (13,21) (14,15) (16,21) (17,19) (17,18) (17,25) (19,25) (19,21) (21,25)\nQ: Is there a path between node 2 and node 21?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1815"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,26) (2,26) (2,30) (2,6) (3,19) (4,29) (4,8) (4,11) (4,9) (5,25) (6,30) (6,19) (6,13) (6,25) (7,23) (7,29) (7,10) (7,28) (7,14) (8,23) (8,15) (8,27) (8,18) (8,11) (8,28) (8,9) (9,23) (9,29) (9,15) (9,18) (9,12) (10,15) (11,29) (11,27) (11,28) (11,14) (12,27) (13,16) (13,26) (14,17) (15,29) (15,21) (15,28) (16,25) (17,23) (17,29) (17,18) (19,20) (19,22) (20,22) (21,27) (21,28) (22,26) (23,29) (23,28) (24,26) (24,30) (25,26) (25,30) (27,28)\nQ: Is there a path between node 28 and node 29?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1816"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,4) (1,5)\nQ: Is there a path between node 0 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1817"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,6) (0,1) (0,7) (0,4) (1,5) (1,6) (1,7) (1,4) (2,3) (4,5) (4,6) (4,7) (5,6) (5,7) (6,7)\nQ: Is there a path between node 4 and node 2?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1818"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,20) (0,27) (0,29) (0,26) (0,17) (0,3) (0,1) (0,16) (1,6) (1,7) (1,20) (1,19) (1,3) (1,33) (1,4) (2,27) (2,34) (2,26) (2,19) (2,17) (2,3) (2,21) (2,4) (3,6) (3,7) (3,11) (3,28) (3,29) (4,6) (4,28) (4,27) (4,29) (4,26) (4,19) (4,33) (4,23) (5,7) (5,11) (5,28) (5,19) (5,33) (5,16) (6,7) (6,28) (6,27) (6,26) (6,21) (7,34) (8,13) (8,12) (8,22) (8,15) (9,24) (9,12) (9,10) (10,25) (11,16) (11,23) (12,32) (12,18) (12,22) (12,15) (13,14) (14,18) (14,15) (15,30) (15,18) (16,27) (16,17) (16,23) (17,29) (17,19) (17,33) (17,23) (18,31) (18,24) (19,28) (19,27) (19,34) (19,29) (19,33) (19,21) (20,21) (21,26) (21,33) (22,30) (22,25) (25,30) (25,31) (26,28) (26,34) (26,29) (27,28) (30,32) (31,32)\nQ: Is there a path between node 26 and node 5?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1819"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,14) (0,10) (0,2) (2,15) (2,20) (2,23) (2,14) (2,17) (2,24) (2,18) (3,21) (4,27) (5,9) (5,22) (6,29) (6,8) (7,29) (7,25) (7,20) (7,17) (7,18) (7,8) (8,23) (8,24) (10,23) (10,18) (11,27) (12,13) (13,21) (14,25) (14,23) (14,17) (14,24) (15,29) (15,25) (15,23) (15,16) (16,29) (16,17) (17,25) (17,23) (17,24) (17,18) (18,29) (20,25) (22,26) (23,25) (24,29) (26,27)\nQ: Is there a path between node 0 and node 10?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1820"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,10) (0,14) (0,20) (0,13) (1,2) (1,8) (1,9) (2,9) (4,10) (4,20) (5,21) (5,17) (5,9) (6,10) (6,14) (6,13) (7,21) (7,22) (8,9) (10,19) (10,18) (10,12) (10,13) (11,16) (11,18) (12,16) (12,19) (12,18) (13,19) (14,19) (16,18) (17,22) (18,19)\nQ: Is there a path between node 17 and node 14?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1821"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,21) (0,7) (0,6) (0,3) (0,17) (0,20) (0,22) (0,16) (0,23) (0,25) (0,27) (1,5) (1,21) (1,4) (1,7) (1,15) (1,18) (1,2) (1,24) (1,20) (1,11) (1,16) (1,25) (1,27) (2,14) (2,5) (2,21) (2,4) (2,15) (2,24) (2,22) (2,11) (2,23) (2,25) (2,27) (3,14) (3,13) (3,21) (3,7) (3,15) (3,6) (3,17) (3,24) (3,22) (3,11) (3,16) (3,23) (4,14) (4,13) (4,5) (4,19) (4,7) (4,18) (4,17) (4,22) (4,11) (4,23) (4,25) (4,27) (5,13) (5,19) (5,15) (5,18) (5,24) (5,20) (5,22) (5,11) (5,23) (5,27) (6,14) (6,21) (6,19) (6,7) (6,15) (6,18) (6,17) (6,24) (6,20) (6,11) (6,16) (6,25) (6,27) (7,14) (7,13) (7,21) (7,19) (7,15) (7,18) (7,17) (7,20) (7,22) (7,11) (7,23) (7,27) (8,30) (8,28) (9,31) (9,10) (9,26) (9,29) (10,31) (10,26) (10,29) (11,13) (11,21) (11,19) (11,15) (11,24) (11,22) (11,25) (11,27) (12,28) (13,14) (13,21) (13,15) (13,18) (13,17) (13,24) (13,20) (13,16) (13,23) (13,25) (13,27) (14,21) (14,19) (14,24) (14,20) (14,22) (14,16) (14,23) (14,25) (15,21) (15,18) (15,17) (15,24) (15,20) (15,22) (15,16) (15,25) (15,27) (16,21) (16,18) (16,17) (16,24) (16,20) (16,22) (16,25) (17,21) (17,19) (17,18) (17,24) (17,20) (17,22) (17,23) (17,25) (17,27) (18,21) (18,24) (18,20) (18,25) (18,27) (19,21) (19,20) (19,22) (19,27) (20,21) (20,24) (20,22) (20,23) (20,27) (21,24) (21,22) (21,25) (21,27) (22,25) (23,25) (23,27) (25,27) (26,31) (26,29) (29,31)\nQ: Is there a path between node 5 and node 23?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1822"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,28) (0,26) (0,7) (0,22) (0,6) (0,1) (0,30) (0,3) (1,16) (1,28) (1,26) (1,22) (1,10) (1,30) (2,4) (2,29) (2,24) (2,14) (2,21) (2,25) (2,13) (2,12) (2,31) (2,19) (2,33) (2,27) (2,23) (2,8) (2,18) (3,16) (3,28) (3,26) (3,9) (3,7) (3,10) (4,29) (4,32) (4,24) (4,21) (4,25) (4,15) (4,12) (4,31) (4,19) (4,33) (4,27) (4,17) (4,23) (4,18) (5,32) (5,14) (5,21) (5,15) (5,12) (5,19) (5,33) (5,27) (5,23) (5,8) (6,28) (6,26) (6,7) (6,22) (6,10) (7,16) (7,9) (7,22) (7,10) (8,29) (8,32) (8,24) (8,21) (8,15) (8,13) (8,33) (8,27) (8,23) (8,18) (9,16) (9,28) (9,26) (9,22) (9,10) (10,28) (10,22) (10,30) (12,29) (12,14) (12,21) (12,25) (12,15) (12,13) (12,31) (12,19) (12,33) (12,17) (12,23) (12,18) (13,20) (13,29) (13,24) (13,21) (13,25) (13,15) (13,31) (13,19) (13,33) (13,27) (13,17) (13,23) (13,18) (14,20) (14,29) (14,32) (14,24) (14,21) (14,15) (14,31) (14,19) (14,33) (14,17) (14,18) (15,20) (15,29) (15,32) (15,24) (15,21) (15,25) (15,31) (15,19) (15,33) (15,27) (15,17) (15,23) (15,18) (16,28) (16,26) (16,22) (16,30) (17,20) (17,29) (17,32) (17,24) (17,21) (17,25) (17,31) (17,19) (17,18) (18,20) (18,29) (18,32) (18,24) (18,21) (18,25) (18,31) (18,19) (18,27) (18,23) (19,32) (19,24) (19,33) (19,27) (19,23) (20,29) (20,32) (20,24) (20,21) (20,25) (20,31) (20,33) (20,27) (20,23) (21,32) (21,24) (21,25) (21,31) (21,33) (21,27) (21,23) (22,26) (22,30) (23,29) (23,32) (23,24) (23,25) (23,31) (23,33) (23,27) (24,32) (24,25) (24,31) (24,27) (25,29) (25,33) (25,27) (26,28) (26,30) (27,29) (27,31) (27,33) (28,30) (29,32) (29,31) (29,33) (31,32) (31,33) (32,33)\nQ: Is there a path between node 19 and node 26?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1823"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,6) (0,4) (1,3) (1,7) (1,2) (2,3) (3,9) (4,6) (5,9) (6,8) (7,9)\nQ: Is there a path between node 3 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1824"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,18) (0,25) (0,19) (0,16) (0,22) (0,8) (0,10) (0,31) (0,13) (0,5) (0,14) (0,24) (0,27) (0,1) (0,15) (0,23) (1,9) (1,30) (1,25) (1,19) (1,16) (1,17) (1,22) (1,8) (1,21) (1,4) (1,31) (1,13) (1,14) (1,24) (1,12) (1,27) (1,15) (2,11) (2,28) (2,29) (2,7) (3,9) (3,18) (3,25) (3,19) (3,16) (3,22) (3,10) (3,4) (3,31) (3,13) (3,5) (3,14) (3,24) (3,12) (3,20) (3,27) (3,15) (3,23) (4,18) (4,30) (4,19) (4,22) (4,8) (4,21) (4,31) (4,5) (4,24) (4,12) (4,27) (4,23) (5,18) (5,30) (5,25) (5,19) (5,17) (5,10) (5,21) (5,31) (5,12) (5,20) (5,15) (5,23) (6,28) (6,29) (6,7) (6,26) (7,28) (8,9) (8,25) (8,19) (8,16) (8,22) (8,10) (8,13) (8,14) (8,24) (8,12) (8,27) (8,15) (8,23) (9,18) (9,30) (9,19) (9,16) (9,17) (9,22) (9,10) (9,31) (9,13) (9,27) (9,15) (9,23) (10,18) (10,30) (10,25) (10,16) (10,22) (10,21) (10,31) (10,14) (10,24) (10,12) (10,20) (10,15) (11,28) (11,26) (12,19) (12,22) (12,21) (12,13) (12,24) (12,15) (12,23) (13,25) (13,19) (13,16) (13,17) (13,22) (13,31) (13,14) (13,27) (14,30) (14,25) (14,16) (14,17) (14,22) (14,31) (14,24) (14,20) (14,15) (14,23) (15,18) (15,30) (15,25) (15,19) (15,16) (15,22) (15,31) (15,24) (16,18) (16,30) (16,22) (16,21) (16,31) (16,20) (16,27) (17,18) (17,30) (17,25) (17,19) (17,22) (17,21) (17,31) (17,24) (17,27) (17,23) (18,30) (18,25) (18,19) (18,22) (18,21) (18,31) (18,24) (18,27) (18,23) (19,30) (19,25) (19,21) (19,24) (19,20) (19,27) (19,23) (20,21) (20,31) (20,24) (20,27) (20,23) (21,25) (21,22) (21,31) (21,24) (21,27) (21,23) (22,30) (22,31) (22,24) (22,23) (23,30) (23,25) (23,24) (23,27) (24,30) (24,25) (24,31) (24,27) (25,30) (25,27) (26,28) (27,30) (27,31) (28,29) (30,31)\nQ: Is there a path between node 22 and node 29?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1825"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,4) (0,11) (0,13) (1,8) (1,21) (1,10) (1,7) (1,2) (2,24) (2,8) (2,9) (2,10) (2,22) (3,5) (3,11) (3,13) (4,15) (4,6) (4,16) (4,11) (5,12) (5,15) (5,19) (5,18) (5,27) (6,19) (6,11) (7,26) (7,23) (7,9) (8,23) (8,9) (8,10) (8,22) (9,25) (9,14) (10,25) (10,17) (10,23) (11,20) (11,27) (12,15) (12,16) (12,18) (14,22) (15,19) (15,27) (16,19) (17,26) (17,24) (17,28) (17,23) (17,22) (19,20) (19,27) (21,26) (21,25) (21,29) (21,22) (22,29) (23,24) (23,29) (26,28)\nQ: Is there a path between node 11 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1826"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,20) (0,17) (0,23) (0,22) (0,1) (0,9) (0,11) (0,14) (0,19) (0,12) (0,18) (0,8) (0,4) (0,16) (0,15) (0,10) (0,6) (1,20) (1,17) (1,23) (1,22) (1,9) (1,11) (1,14) (1,19) (1,12) (1,18) (1,8) (1,4) (1,16) (1,15) (1,10) (1,6) (2,13) (2,5) (2,3) (2,21) (2,7) (3,13) (3,5) (3,21) (3,7) (4,20) (4,17) (4,23) (4,22) (4,9) (4,11) (4,14) (4,19) (4,12) (4,18) (4,8) (4,16) (4,15) (4,10) (4,6) (5,13) (5,21) (5,7) (6,20) (6,17) (6,23) (6,22) (6,9) (6,11) (6,14) (6,19) (6,12) (6,18) (6,8) (6,16) (6,15) (6,10) (7,13) (7,21) (8,20) (8,17) (8,23) (8,22) (8,9) (8,11) (8,14) (8,19) (8,12) (8,18) (8,16) (8,15) (8,10) (9,20) (9,17) (9,23) (9,22) (9,11) (9,14) (9,19) (9,12) (9,18) (9,16) (9,15) (9,10) (10,20) (10,17) (10,23) (10,22) (10,11) (10,14) (10,19) (10,12) (10,18) (10,16) (10,15) (11,20) (11,17) (11,23) (11,22) (11,14) (11,19) (11,12) (11,18) (11,16) (11,15) (12,20) (12,17) (12,23) (12,22) (12,14) (12,19) (12,18) (12,16) (12,15) (13,21) (14,20) (14,17) (14,23) (14,22) (14,19) (14,18) (14,16) (14,15) (15,20) (15,17) (15,23) (15,22) (15,19) (15,18) (15,16) (16,20) (16,17) (16,23) (16,22) (16,19) (16,18) (17,20) (17,23) (17,22) (17,19) (17,18) (18,20) (18,23) (18,22) (18,19) (19,20) (19,23) (19,22) (20,23) (20,22) (22,23)\nQ: Is there a path between node 20 and node 21?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1827"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (1,18) (1,12) (1,15) (1,7) (2,17) (2,3) (3,17) (4,12) (5,17) (5,19) (6,18) (6,10) (6,9) (6,12) (6,16) (7,18) (7,9) (7,13) (7,8) (8,14) (9,18) (9,14) (9,12) (9,13) (10,12) (10,15) (11,17) (12,16) (14,18)\nQ: Is there a path between node 6 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1828"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,4) (0,9) (0,5) (0,13) (1,14) (1,15) (1,12) (1,5) (1,7) (2,4) (2,6) (2,9) (2,12) (2,13) (4,11) (4,6) (4,15) (4,7) (4,8) (4,13) (5,11) (5,10) (5,14) (5,6) (5,9) (5,15) (5,12) (5,7) (5,13) (6,14) (7,14) (7,8) (9,13) (10,14) (12,15)\nQ: Is there a path between node 14 and node 3?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1829"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,5) (0,1) (0,9) (0,3) (0,4) (1,6) (1,5) (1,9) (1,3) (1,4) (2,7) (2,8) (2,10) (3,6) (3,5) (3,9) (3,4) (4,6) (4,5) (4,9) (5,6) (5,9) (6,9) (7,8) (7,10) (8,10)\nQ: Is there a path between node 3 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1830"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,18) (0,1) (0,8) (0,10) (0,11) (0,7) (0,4) (0,2) (0,6) (0,17) (0,14) (1,19) (1,18) (1,8) (1,10) (1,11) (1,7) (1,4) (1,2) (1,6) (1,17) (1,14) (2,19) (2,18) (2,8) (2,10) (2,11) (2,7) (2,4) (2,6) (2,17) (2,14) (3,13) (3,9) (3,15) (4,19) (4,18) (4,8) (4,10) (4,11) (4,7) (4,6) (4,17) (4,14) (5,12) (5,16) (6,19) (6,18) (6,8) (6,10) (6,11) (6,7) (6,17) (6,14) (7,19) (7,18) (7,8) (7,10) (7,11) (7,17) (7,14) (8,19) (8,18) (8,10) (8,11) (8,17) (8,14) (9,13) (9,15) (10,19) (10,18) (10,11) (10,17) (10,14) (11,19) (11,18) (11,17) (11,14) (12,16) (13,15) (14,19) (14,18) (14,17) (17,19) (17,18) (18,19)\nQ: Is there a path between node 17 and node 16?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1831"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,3) (0,4) (1,3) (1,4) (3,4)\nQ: Is there a path between node 3 and node 1?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1832"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,23) (0,4) (1,32) (1,22) (1,34) (1,7) (1,5) (1,28) (1,11) (1,13) (1,30) (1,31) (1,26) (2,12) (2,3) (2,24) (2,15) (2,18) (2,8) (2,20) (2,25) (2,19) (2,17) (2,16) (3,10) (3,24) (3,15) (3,18) (3,8) (3,20) (3,14) (3,19) (3,21) (4,23) (4,6) (5,32) (5,22) (5,7) (5,33) (5,11) (5,13) (5,27) (5,31) (5,26) (6,23) (7,22) (7,34) (7,28) (7,13) (7,27) (7,30) (7,26) (7,29) (8,10) (8,24) (8,15) (8,18) (8,20) (8,14) (8,17) (8,21) (8,16) (9,32) (9,22) (9,34) (9,28) (9,13) (9,27) (9,31) (9,26) (9,29) (10,12) (10,24) (10,15) (10,18) (10,20) (10,25) (10,17) (11,32) (11,22) (11,34) (11,28) (11,13) (11,27) (11,30) (11,31) (11,26) (12,24) (12,25) (12,14) (12,17) (12,21) (12,16) (13,34) (13,33) (13,27) (13,30) (13,31) (13,29) (14,15) (14,18) (14,20) (14,25) (14,19) (14,17) (14,21) (14,16) (15,24) (15,18) (15,20) (15,17) (15,21) (16,24) (16,20) (16,19) (16,17) (17,24) (17,20) (17,21) (18,20) (18,25) (18,19) (20,24) (20,25) (20,21) (21,25) (22,32) (22,28) (22,27) (22,30) (22,31) (22,26) (24,25) (26,34) (26,33) (26,31) (27,34) (27,33) (27,28) (27,30) (27,31) (27,29) (28,32) (28,33) (28,30) (28,31) (28,29) (29,32) (29,33) (30,32) (31,32) (31,34) (32,34) (32,33) (33,34)\nQ: Is there a path between node 21 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1833"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (3,7) (4,6) (5,6)\nQ: Is there a path between node 2 and node 4?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1834"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,17) (0,24) (1,11) (1,9) (1,3) (2,19) (2,29) (2,27) (3,7) (3,20) (4,23) (4,25) (5,17) (6,22) (7,29) (7,27) (7,9) (8,16) (8,30) (8,26) (8,18) (8,31) (9,11) (9,27) (10,13) (10,12) (11,19) (11,27) (12,26) (12,18) (14,28) (15,27) (16,30) (17,23) (18,26) (19,28) (20,29) (21,22) (23,24) (24,25) (27,28) (30,31)\nQ: Is there a path between node 12 and node 19?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1835"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,6) (0,13) (1,6) (1,8) (1,3) (1,4) (2,5) (2,9) (3,12) (3,9) (3,13) (4,6) (4,10) (5,6) (5,9) (6,12) (6,8) (8,9) (9,10) (12,13)\nQ: Is there a path between node 13 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1836"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,21) (0,17) (0,7) (0,29) (1,20) (2,32) (2,6) (2,13) (3,22) (3,23) (3,8) (4,30) (4,31) (6,23) (6,16) (6,32) (7,19) (8,14) (8,23) (8,16) (8,32) (8,13) (9,24) (9,17) (9,29) (13,14) (13,32) (14,16) (14,32) (16,20) (16,28) (17,24) (20,28) (21,29) (24,29) (27,30) (30,31)\nQ: Is there a path between node 23 and node 19?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1837"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,13) (0,2) (0,14) (0,23) (0,8) (0,1) (0,25) (0,27) (0,10) (1,29) (1,13) (1,19) (1,28) (1,23) (1,30) (1,25) (1,24) (2,12) (2,5) (2,14) (2,17) (2,23) (3,7) (3,12) (3,19) (3,23) (3,8) (3,30) (3,25) (3,24) (4,33) (5,20) (5,23) (5,30) (6,15) (6,11) (7,32) (7,17) (7,23) (7,8) (7,10) (8,29) (8,12) (8,32) (8,20) (8,19) (8,17) (8,30) (9,29) (9,28) (9,30) (9,24) (10,13) (10,20) (10,14) (10,22) (11,31) (12,13) (12,23) (12,27) (12,26) (13,29) (13,32) (13,14) (13,28) (13,30) (13,24) (14,17) (14,30) (14,22) (14,27) (15,16) (15,31) (15,33) (17,32) (17,20) (17,19) (17,27) (17,24) (17,26) (18,21) (20,28) (20,30) (20,25) (21,31) (22,32) (22,28) (22,30) (23,28) (23,25) (23,27) (24,29) (24,28) (24,26) (25,32) (26,29) (26,27) (27,32) (27,30) (28,32) (28,30)\nQ: Is there a path between node 9 and node 31?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1838"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,4) (0,18) (0,17) (0,10) (1,7) (1,24) (1,27) (2,4) (2,8) (2,13) (2,19) (2,27) (3,16) (3,28) (3,9) (4,18) (4,6) (4,10) (4,11) (4,27) (6,20) (6,8) (6,7) (6,27) (7,8) (7,18) (7,17) (7,23) (7,24) (7,10) (7,13) (7,19) (7,11) (7,14) (8,17) (8,22) (8,24) (8,10) (8,11) (10,18) (10,17) (10,12) (10,11) (10,27) (11,17) (11,12) (12,20) (12,18) (12,17) (12,14) (13,20) (13,18) (13,24) (13,27) (13,26) (14,18) (15,28) (15,25) (16,25) (17,20) (17,18) (17,26) (18,22) (18,23) (18,19) (18,27) (19,23) (19,27) (19,26) (20,24) (22,23) (22,24) (22,26) (26,27)\nQ: Is there a path between node 1 and node 21?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1839"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,7) (0,3) (0,2) (0,9) (0,8) (1,6) (1,4) (2,7) (2,10) (2,3) (2,8) (2,5) (3,10) (3,9) (3,8) (4,6) (5,7) (5,10) (5,9) (7,8) (8,9)\nQ: Is there a path between node 2 and node 3?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1840"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,3) (0,11) (0,18) (0,7) (0,8) (0,9) (0,1) (0,10) (0,15) (0,17) (0,13) (0,16) (0,19) (0,2) (0,6) (0,5) (0,14) (1,12) (1,3) (1,11) (1,18) (1,7) (1,8) (1,9) (1,10) (1,15) (1,17) (1,13) (1,16) (1,19) (1,2) (1,6) (1,5) (1,14) (2,12) (2,3) (2,11) (2,18) (2,7) (2,8) (2,9) (2,10) (2,15) (2,17) (2,13) (2,16) (2,19) (2,6) (2,5) (2,14) (3,12) (3,11) (3,18) (3,7) (3,8) (3,9) (3,10) (3,15) (3,17) (3,13) (3,16) (3,19) (3,6) (3,5) (3,14) (4,20) (4,21) (5,12) (5,11) (5,18) (5,7) (5,8) (5,9) (5,10) (5,15) (5,17) (5,13) (5,16) (5,19) (5,6) (5,14) (6,12) (6,11) (6,18) (6,7) (6,8) (6,9) (6,10) (6,15) (6,17) (6,13) (6,16) (6,19) (6,14) (7,12) (7,11) (7,18) (7,8) (7,9) (7,10) (7,15) (7,17) (7,13) (7,16) (7,19) (7,14) (8,12) (8,11) (8,18) (8,9) (8,10) (8,15) (8,17) (8,13) (8,16) (8,19) (8,14) (9,12) (9,11) (9,18) (9,10) (9,15) (9,17) (9,13) (9,16) (9,19) (9,14) (10,12) (10,11) (10,18) (10,15) (10,17) (10,13) (10,16) (10,19) (10,14) (11,12) (11,18) (11,15) (11,17) (11,13) (11,16) (11,19) (11,14) (12,18) (12,15) (12,17) (12,13) (12,16) (12,19) (12,14) (13,18) (13,15) (13,17) (13,16) (13,19) (13,14) (14,18) (14,15) (14,17) (14,16) (14,19) (15,18) (15,17) (15,16) (15,19) (16,18) (16,17) (16,19) (17,18) (17,19) (18,19) (20,21)\nQ: Is there a path between node 1 and node 0?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1841"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,8) (1,5) (1,10) (1,8) (2,6) (2,7) (3,9) (3,10) (4,11) (4,8) (6,7) (8,9) (8,10) (11,12)\nQ: Is there a path between node 8 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1842"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,6) (1,2) (3,7) (3,5)\nQ: Is there a path between node 2 and node 7?\nA:", "answer": "The answer is no.", "difficulty": "easy", "doc_id": "1843"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,7) (0,10) (0,6) (0,2) (0,8) (0,4) (0,1) (1,3) (1,7) (1,10) (1,6) (1,2) (1,8) (1,4) (2,3) (2,7) (2,10) (2,6) (2,8) (2,4) (3,7) (3,10) (3,6) (3,8) (3,4) (4,7) (4,10) (4,6) (4,8) (5,9) (6,7) (6,10) (6,8) (7,10) (7,8) (8,10)\nQ: Is there a path between node 5 and node 8?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1844"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,10) (0,17) (0,15) (0,4) (0,12) (0,24) (0,9) (0,3) (0,13) (0,23) (0,7) (0,19) (0,16) (0,6) (0,25) (0,8) (1,10) (1,17) (1,4) (1,12) (1,24) (1,3) (1,13) (1,23) (1,26) (1,22) (1,19) (1,6) (1,14) (1,25) (1,8) (1,20) (2,10) (2,17) (2,11) (2,4) (2,24) (2,9) (2,3) (2,13) (2,23) (2,26) (2,7) (2,22) (2,19) (2,6) (2,14) (2,25) (2,8) (3,10) (3,17) (3,11) (3,15) (3,4) (3,12) (3,24) (3,9) (3,13) (3,26) (3,7) (3,19) (3,16) (3,14) (3,25) (3,8) (3,20) (4,10) (4,17) (4,11) (4,15) (4,12) (4,24) (4,9) (4,7) (4,19) (4,16) (4,6) (4,25) (4,20) (5,18) (6,10) (6,17) (6,15) (6,12) (6,24) (6,9) (6,23) (6,7) (6,16) (6,25) (6,8) (7,10) (7,11) (7,15) (7,12) (7,13) (7,22) (7,19) (7,16) (7,25) (7,8) (7,20) (8,10) (8,17) (8,11) (8,15) (8,12) (8,24) (8,9) (8,23) (8,22) (8,19) (8,16) (8,14) (8,25) (8,20) (9,10) (9,17) (9,11) (9,12) (9,24) (9,13) (9,23) (9,26) (9,22) (9,19) (9,16) (9,20) (10,17) (10,11) (10,15) (10,12) (10,24) (10,13) (10,23) (10,26) (10,19) (10,14) (10,20) (11,15) (11,12) (11,24) (11,13) (11,23) (11,26) (11,19) (11,16) (11,14) (11,20) (12,15) (12,24) (12,23) (12,22) (12,19) (12,16) (12,14) (12,25) (12,20) (13,15) (13,24) (13,23) (13,19) (13,16) (13,14) (13,25) (13,20) (14,17) (14,15) (14,24) (14,23) (14,26) (14,22) (14,19) (14,16) (14,25) (14,20) (15,17) (15,24) (15,23) (15,26) (15,16) (15,20) (16,24) (16,23) (16,26) (16,19) (16,25) (16,20) (17,23) (17,20) (18,21) (19,23) (19,22) (19,25) (19,20) (20,24) (20,23) (20,22) (20,25) (22,26) (22,25) (23,24) (23,26) (23,25) (24,26) (24,25) (25,26)\nQ: Is there a path between node 21 and node 22?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1845"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,22) (0,6) (0,11) (0,10) (0,4) (0,5) (0,9) (0,1) (0,13) (0,21) (0,20) (0,12) (1,22) (1,11) (1,10) (1,5) (1,16) (1,9) (1,13) (1,21) (1,20) (2,8) (2,19) (2,3) (2,18) (2,24) (3,19) (3,17) (3,24) (3,23) (4,22) (4,6) (4,16) (4,9) (4,21) (4,20) (5,22) (5,6) (5,14) (5,11) (5,16) (5,15) (5,9) (5,13) (5,21) (5,20) (6,22) (6,11) (6,10) (6,16) (6,13) (6,21) (6,12) (7,8) (7,17) (7,18) (7,24) (7,23) (8,17) (8,24) (9,14) (9,11) (9,10) (9,16) (9,15) (9,21) (9,20) (9,12) (10,22) (10,14) (10,11) (10,16) (10,15) (10,21) (10,20) (11,22) (11,16) (11,15) (11,20) (12,22) (12,14) (12,15) (12,13) (12,21) (12,20) (13,14) (13,16) (13,15) (13,21) (13,20) (14,22) (14,16) (14,15) (14,21) (15,16) (15,21) (16,22) (16,21) (16,20) (17,19) (17,18) (17,24) (17,23) (18,23) (19,24) (23,24)\nQ: Is there a path between node 17 and node 15?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1846"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (2,8) (2,4) (2,3) (3,8) (5,7) (6,7)\nQ: Is there a path between node 0 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1847"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,12) (0,11) (0,4) (2,10) (2,8) (2,4) (4,6) (4,11) (5,9) (6,7) (6,10) (6,11) (7,8) (8,10) (8,9) (9,12) (10,11)\nQ: Is there a path between node 0 and node 4?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1848"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,5) (0,11) (0,22) (0,30) (0,25) (0,19) (0,12) (0,13) (0,10) (0,29) (1,17) (1,4) (1,18) (1,7) (1,27) (1,2) (1,3) (1,9) (1,23) (1,28) (2,4) (2,21) (2,26) (2,7) (2,27) (2,9) (2,23) (2,28) (3,17) (3,4) (3,21) (3,26) (3,18) (3,7) (3,27) (3,14) (3,9) (3,23) (3,28) (3,24) (4,17) (4,21) (4,26) (4,18) (4,14) (4,9) (4,28) (4,24) (5,11) (5,22) (5,20) (5,25) (5,29) (6,8) (7,21) (7,26) (7,18) (7,27) (7,23) (7,28) (7,24) (9,21) (9,26) (9,18) (9,27) (9,14) (9,23) (9,28) (9,24) (10,11) (10,22) (10,20) (10,30) (10,25) (10,16) (10,19) (10,15) (10,13) (10,29) (11,22) (11,20) (11,30) (11,25) (11,16) (11,19) (11,12) (11,15) (11,13) (11,29) (12,22) (12,20) (12,30) (12,16) (12,15) (12,13) (13,22) (13,20) (13,30) (13,25) (13,16) (13,19) (13,15) (13,29) (14,26) (14,18) (14,23) (14,28) (14,24) (15,22) (15,30) (15,16) (15,19) (15,29) (16,22) (16,30) (16,25) (16,19) (16,29) (17,26) (17,18) (17,27) (17,23) (17,28) (18,21) (18,26) (18,27) (18,24) (19,20) (19,30) (19,25) (19,29) (20,22) (20,25) (20,29) (21,26) (21,27) (21,28) (21,24) (22,30) (22,29) (23,26) (23,27) (23,28) (23,24) (24,27) (24,28) (25,29) (26,27) (27,28) (29,30)\nQ: Is there a path between node 11 and node 27?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1849"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,10) (0,25) (0,16) (0,24) (0,4) (0,8) (0,27) (0,19) (1,5) (1,28) (2,15) (3,12) (3,13) (3,21) (3,24) (3,4) (3,8) (4,26) (4,20) (4,21) (4,11) (4,9) (6,13) (6,14) (6,22) (6,21) (6,7) (6,23) (6,11) (7,12) (7,26) (7,20) (7,17) (7,14) (7,10) (7,25) (7,24) (7,8) (7,11) (7,19) (7,9) (8,25) (8,27) (8,11) (9,17) (9,14) (9,21) (9,23) (9,27) (9,11) (10,26) (10,20) (10,14) (10,25) (10,23) (10,24) (11,13) (11,17) (11,21) (11,25) (11,23) (11,19) (12,20) (12,17) (12,24) (13,26) (13,20) (13,17) (13,22) (13,25) (13,24) (13,19) (14,20) (14,16) (15,28) (15,18) (16,26) (16,21) (16,23) (17,26) (17,22) (17,23) (17,27) (18,28) (19,22) (20,23) (20,24) (20,27) (21,26) (21,27) (23,25) (24,25) (24,27) (25,27)\nQ: Is there a path between node 13 and node 24?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1850"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,3) (0,13) (0,15) (0,7) (1,4) (1,6) (2,9) (2,18) (2,13) (3,12) (4,11) (6,8) (6,17) (7,16) (7,12) (7,13) (7,14) (8,11) (8,17) (8,20) (9,18) (9,21) (9,14) (9,15) (10,12) (12,16) (12,15) (13,18) (13,15) (14,16) (14,21) (15,16) (15,18) (16,18)\nQ: Is there a path between node 10 and node 6?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1851"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,12) (0,7) (0,8) (0,9) (0,13) (0,14) (0,15) (0,5) (1,2) (1,12) (1,16) (1,11) (1,3) (1,6) (1,14) (1,4) (2,12) (2,7) (2,9) (2,13) (2,14) (3,16) (3,11) (3,7) (3,8) (3,14) (3,15) (3,5) (3,4) (4,12) (4,11) (4,8) (4,9) (4,13) (4,14) (4,5) (5,12) (5,16) (5,11) (5,7) (5,8) (5,13) (5,14) (5,15) (6,12) (6,16) (6,11) (6,7) (6,14) (6,15) (7,12) (7,16) (7,11) (7,8) (7,9) (7,13) (8,12) (8,16) (8,11) (8,9) (8,13) (8,14) (9,12) (9,16) (9,11) (9,14) (9,15) (11,12) (11,16) (11,14) (12,13) (12,15) (13,16) (13,15) (14,16)\nQ: Is there a path between node 12 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1852"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,10) (2,9) (2,5) (3,12) (3,14) (3,4) (3,8) (3,18) (4,19) (4,16) (4,11) (5,20) (5,12) (5,14) (5,11) (6,18) (6,16) (7,15) (8,20) (8,12) (8,18) (8,16) (9,20) (9,14) (9,19) (9,11) (11,13) (11,12) (11,18) (11,16) (12,18) (13,19) (13,18) (14,19) (16,20) (18,19)\nQ: Is there a path between node 17 and node 9?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1853"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,20) (0,8) (0,31) (0,22) (1,4) (1,24) (1,19) (1,16) (1,5) (1,2) (1,8) (1,18) (1,27) (2,4) (2,19) (2,12) (2,17) (2,21) (2,31) (2,22) (3,25) (3,20) (3,14) (3,31) (3,22) (3,27) (4,7) (4,21) (4,26) (4,27) (5,11) (5,24) (5,20) (5,19) (5,12) (5,16) (5,17) (5,21) (5,9) (5,22) (6,15) (7,24) (7,20) (7,19) (7,16) (7,29) (7,17) (7,21) (7,14) (7,9) (7,8) (7,18) (7,22) (7,30) (8,20) (8,12) (8,14) (9,20) (9,16) (9,14) (9,18) (9,26) (9,23) (10,15) (11,25) (11,28) (11,20) (11,21) (11,26) (12,28) (12,24) (12,20) (12,29) (12,14) (12,18) (12,26) (12,22) (12,27) (12,23) (14,24) (14,16) (14,18) (14,31) (16,25) (16,26) (16,31) (16,23) (17,31) (17,27) (18,25) (18,28) (18,24) (18,21) (18,26) (18,27) (19,29) (19,21) (19,22) (20,25) (20,21) (20,26) (21,24) (21,29) (21,31) (21,23) (22,29) (22,26) (22,23) (23,25) (23,26) (24,25) (24,26) (24,30) (25,29) (25,31) (26,29) (26,31) (27,28) (27,31) (28,29) (29,31) (29,30) (30,31)\nQ: Is there a path between node 6 and node 29?\nA:", "answer": "The answer is no.", "difficulty": "hard", "doc_id": "1854"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,3) (0,13) (0,2) (0,15) (0,6) (0,17) (0,8) (0,16) (0,18) (0,9) (0,12) (0,11) (1,10) (1,14) (1,7) (1,5) (1,4) (2,3) (2,13) (2,15) (2,6) (2,17) (2,8) (2,16) (2,18) (2,9) (2,12) (2,11) (3,13) (3,15) (3,6) (3,17) (3,8) (3,16) (3,18) (3,9) (3,12) (3,11) (4,10) (4,14) (4,7) (4,5) (5,10) (5,14) (5,7) (6,13) (6,15) (6,17) (6,8) (6,16) (6,18) (6,9) (6,12) (6,11) (7,10) (7,14) (8,13) (8,15) (8,17) (8,16) (8,18) (8,9) (8,12) (8,11) (9,13) (9,15) (9,17) (9,16) (9,18) (9,12) (9,11) (10,14) (11,13) (11,15) (11,17) (11,16) (11,18) (11,12) (12,13) (12,15) (12,17) (12,16) (12,18) (13,15) (13,17) (13,16) (13,18) (15,17) (15,16) (15,18) (16,17) (16,18) (17,18)\nQ: Is there a path between node 10 and node 14?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1855"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (1,21) (1,17) (1,15) (1,2) (1,4) (1,18) (2,8) (2,13) (2,17) (2,15) (2,23) (2,22) (2,4) (2,18) (2,12) (4,21) (4,8) (4,13) (4,15) (4,23) (4,22) (4,18) (4,12) (5,21) (5,8) (5,13) (5,17) (5,15) (5,22) (5,18) (7,14) (7,16) (7,10) (7,11) (7,19) (8,21) (8,17) (8,23) (8,18) (9,14) (9,24) (10,14) (10,24) (10,19) (11,14) (11,16) (11,24) (12,21) (12,13) (12,17) (12,15) (12,23) (12,22) (12,18) (13,21) (13,17) (13,15) (13,23) (13,22) (14,24) (15,21) (15,17) (15,23) (15,22) (15,18) (16,19) (17,21) (17,18) (18,21) (18,23) (21,22) (22,23)\nQ: Is there a path between node 13 and node 21?\nA:", "answer": "The answer is yes.", "difficulty": "medium", "doc_id": "1856"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,19) (0,21) (0,17) (0,7) (0,29) (1,20) (2,32) (2,6) (2,13) (3,22) (3,23) (3,8) (4,30) (4,31) (6,23) (6,16) (6,32) (7,19) (8,14) (8,23) (8,16) (8,32) (8,13) (9,24) (9,17) (9,29) (13,14) (13,32) (14,16) (14,32) (16,20) (16,28) (17,24) (20,28) (21,29) (24,29) (27,30) (30,31)\nQ: Is there a path between node 2 and node 8?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1857"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,16) (0,14) (0,10) (0,24) (0,2) (0,12) (0,19) (0,3) (0,17) (0,25) (0,23) (0,15) (1,18) (1,11) (1,8) (2,14) (2,10) (2,24) (2,7) (2,3) (2,21) (2,25) (2,23) (2,6) (3,14) (3,24) (3,12) (3,19) (3,17) (3,25) (3,23) (3,6) (3,15) (4,18) (4,8) (5,18) (5,11) (5,8) (6,16) (6,14) (6,10) (6,12) (6,7) (6,19) (6,21) (6,25) (6,23) (6,9) (6,15) (7,16) (7,10) (7,24) (7,12) (7,19) (7,17) (7,25) (7,9) (7,15) (8,18) (8,11) (9,16) (9,14) (9,10) (9,24) (9,12) (9,19) (9,17) (9,21) (9,23) (9,15) (10,16) (10,14) (10,19) (10,21) (10,25) (10,23) (10,15) (11,18) (12,16) (12,14) (12,24) (12,19) (12,17) (12,21) (12,25) (12,23) (12,15) (13,20) (14,16) (14,24) (14,17) (14,21) (14,25) (14,23) (14,15) (15,16) (15,24) (15,23) (16,21) (16,25) (16,23) (17,21) (17,23) (19,21) (19,25) (21,24) (21,25) (21,23) (23,25) (24,25)\nQ: Is there a path between node 3 and node 15?\nA:", "answer": "The answer is yes.", "difficulty": "hard", "doc_id": "1858"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,8) (0,5) (0,2) (0,3) (0,10) (0,6) (0,1) (0,4) (0,9) (0,7) (0,12) (1,8) (1,5) (1,2) (1,3) (1,10) (1,6) (1,4) (1,9) (1,7) (1,12) (2,8) (2,5) (2,3) (2,10) (2,6) (2,4) (2,9) (2,7) (2,12) (3,8) (3,5) (3,10) (3,6) (3,4) (3,9) (3,7) (3,12) (4,8) (4,5) (4,10) (4,6) (4,9) (4,7) (4,12) (5,8) (5,10) (5,6) (5,9) (5,7) (5,12) (6,8) (6,10) (6,9) (6,7) (6,12) (7,8) (7,10) (7,9) (7,12) (8,10) (8,9) (8,12) (9,10) (9,12) (10,12) (11,13)\nQ: Is there a path between node 13 and node 10?\nA:", "answer": "The answer is no.", "difficulty": "medium", "doc_id": "1859"}
+{"question": "Determine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (1,2) (3,4) (4,5)\nQ: Is there a path between node 1 and node 4?\nA: Node 1 is in the connected block consisted of node 0, node 1, and node 2.\nNode 4 is in the connected block consisting of node 3, node 4, and node 5. Node 1 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,2) (1,5) (1,2) (1,3) (2,5)\nQ: Is there a path between node 2 and node 3?\nA: Node 2 is connected to node 1, node 1 is connected to node 3. We can follow the path: 2->1->3, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,2) (0,5) (0,6) (1,3) (1,4) (2,5) (2,6) (3,4) (5,6)\nQ: Is there a path between node 5 and node 4?\nA: Node 5 is in the connected block consisted of node 0, node 2, node 5, and node 2.\nNode 4 is in the connected block consisting of node 1, node 3, and node 4. Node 5 and node 4 are not in the same connected block, so the answer is no.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,1) (0,7) (0,6) (1,7) (1,5) (1,6) (5,9) (2,8) (2,4) (2,3) (3,8)\nQ: Is there a path between node 7 and node 9?\nA: Node 7 is connected to node 1, node 1 is connected to node 5, node 5 is connected to node 9.\nWe can follow the path: 7->1->5->9, so the answer is yes.\n\nDetermine if there is a path between two nodes in the graph. Note that (i,j) means that node i and node j are connected with an undirected edge.\nGraph: (0,9) (0,1) (0,2) (0,7) (0,6) (1,2) (1,8) (1,7) (1,4) (1,6) (2,7) (2,4) (2,6) (3,5) (4,9) (4,8) (4,7) (6,9) (6,7) (7,8)\nQ: Is there a path between node 9 and node 7?\nA:", "answer": "The answer is yes.", "difficulty": "easy", "doc_id": "1860"}