{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (24,2) (17,26) (1,8) (30,9) (28,31) (3,31) (25,28) (6,9) (28,4) (0,33) (31,10) (23,32) (12,13) (6,16) (15,14) (24,11) (19,21) (24,20) (12,3) (0,24) (13,22) (19,7) (17,23) (29,18) (28,14) (0,17) (5,27) (26,18) (28,2) (8,30) (16,17) (33,21) (21,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "0"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (22,9) (21,16) (13,7) (18,0) (16,22) (17,7) (3,7) (4,17) (8,3) (2,16) (1,13) (14,9) (24,12) (0,15) (5,3) (10,5) (18,19) (9,23) (5,24) (6,22) (11,12) (12,20) (22,20) (0,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "1"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,2) (5,1) (4,6) (3,2) (1,0) (0,2) (8,6) (5,7) (8,0) (5,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "2"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (1,12) (14,13) (4,19) (11,16) (10,19) (0,3) (6,10) (6,2) (1,0) (7,3) (5,8) (10,0) (10,13) (0,12) (15,14) (2,0) (4,3) (5,18) (16,4) (5,14) (17,7) (0,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "3"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (7,0) (3,5) (8,4) (0,4) (6,7) (6,1) (9,0) (0,2) (4,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "4"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (11,7) (1,16) (11,2) (3,17) (4,5) (11,19) (12,21) (8,3) (20,19) (18,5) (18,6) (9,2) (17,18) (0,15) (12,13) (12,11) (1,19) (4,10) (15,5) (21,3) (14,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "5"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (6,1) (9,5) (3,0) (2,11) (3,7) (3,10) (5,7) (1,5) (8,3) (11,9) (9,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "6"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (7,14) (15,12) (7,16) (0,2) (9,7) (4,11) (14,0) (0,1) (2,8) (6,16) (8,0) (3,12) (1,5) (3,5) (15,11) (10,1) (7,3) (11,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "7"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (10,0) (19,7) (4,27) (5,12) (22,10) (24,0) (14,32) (22,12) (22,7) (8,26) (14,29) (28,25) (0,20) (6,14) (9,24) (2,6) (29,11) (17,29) (1,12) (8,30) (30,23) (26,7) (18,27) (14,28) (14,13) (15,24) (3,20) (14,31) (30,27) (32,9) (16,14) (4,21)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "8"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (10,6) (7,12) (4,7) (2,11) (1,6) (12,3) (8,4) (10,7) (12,11) (3,9) (0,2) (5,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "9"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (10,27) (0,4) (12,25) (22,11) (8,2) (22,9) (21,12) (20,17) (4,28) (13,11) (11,0) (18,16) (15,11) (16,5) (6,17) (18,0) (8,28) (7,26) (3,12) (26,24) (12,1) (23,17) (7,12) (19,1) (27,19) (13,14) (24,17) (5,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "10"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (25,16) (9,7) (25,19) (0,6) (6,23) (21,23) (1,9) (15,11) (19,24) (0,5) (8,1) (16,6) (22,3) (24,14) (15,8) (17,13) (18,9) (18,20) (24,4) (2,12) (18,21) (1,12) (10,20) (13,3) (3,18)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "11"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (13,14) (7,15) (10,11) (5,13) (2,3) (5,1) (0,15) (13,9) (0,13) (9,4) (0,8) (11,9) (3,8) (0,6) (12,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "12"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (17,1) (4,15) (18,11) (10,8) (17,31) (7,2) (10,30) (8,13) (26,30) (27,10) (26,16) (0,2) (10,4) (12,2) (22,24) (14,28) (3,5) (3,30) (0,15) (19,28) (26,9) (24,31) (23,28) (21,2) (20,0) (0,1) (11,22) (7,26) (29,31) (24,2) (0,25) (23,6) (14,17)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "13"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (9,11) (0,8) (8,13) (10,0) (6,10) (9,3) (4,1) (9,5) (12,10) (10,2) (13,7) (10,14) (14,1) (11,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "14"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (5,17) (15,0) (2,20) (19,16) (18,23) (17,4) (11,25) (24,8) (10,17) (4,13) (20,27) (0,19) (21,0) (2,22) (2,0) (12,27) (6,20) (0,3) (26,1) (4,25) (1,0) (25,8) (16,23) (15,14) (6,25) (23,9) (7,16) (19,6) (4,0) (3,24) (1,18)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "15"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (2,10) (4,3) (9,0) (10,6) (7,8) (8,9) (10,8) (5,3) (2,1) (7,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "16"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (3,0) (8,25) (8,5) (20,26) (28,23) (13,6) (9,18) (2,4) (10,14) (9,3) (25,28) (8,4) (2,12) (29,23) (19,2) (10,0) (1,28) (15,17) (16,2) (8,11) (25,21) (19,27) (1,20) (2,0) (0,15) (9,13) (0,1) (3,22) (7,15) (27,9) (23,24) (4,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "17"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (2,5) (6,3) (0,8) (8,2) (8,7) (4,9) (5,1) (8,4) (3,8) (10,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "18"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (10,1) (5,10) (11,7) (0,6) (0,3) (1,7) (9,11) (0,1) (7,2) (5,0) (2,6) (2,0) (4,0) (8,5) (4,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "19"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (14,4) (5,13) (11,2) (7,15) (1,0) (1,14) (3,10) (11,1) (1,12) (3,6) (8,13) (1,16) (9,7) (16,9) (2,0) (16,10) (8,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "20"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (3,0) (3,1) (7,0) (1,10) (0,10) (2,4) (2,0) (11,4) (1,0) (11,10) (7,6) (3,5) (9,0) (4,0) (2,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "21"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (14,8) (6,7) (15,21) (12,17) (7,17) (4,3) (11,18) (9,24) (5,6) (17,20) (18,19) (7,24) (19,2) (18,24) (22,1) (0,6) (10,24) (19,23) (18,21) (10,3) (13,11) (7,14) (16,12) (21,22)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "22"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,5) (0,3) (3,1) (4,6) (2,4) (3,7) (3,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "23"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (16,17) (14,7) (0,15) (3,0) (4,9) (7,1) (6,15) (8,13) (4,11) (17,15) (15,10) (17,8) (17,18) (2,0) (17,5) (7,6) (0,1) (18,11) (3,18) (12,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "24"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (23,18) (21,4) (23,21) (1,9) (13,17) (7,8) (8,0) (21,17) (10,11) (15,16) (5,2) (2,15) (15,8) (0,1) (17,22) (13,20) (14,18) (4,12) (0,10) (6,15) (6,23) (19,11) (3,18)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "25"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,3) (0,9) (1,2) (10,12) (10,5) (10,7) (2,8) (4,3) (4,7) (8,11) (10,2) (9,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "26"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (11,16) (12,14) (10,15) (23,13) (25,22) (7,2) (16,9) (7,0) (0,1) (1,19) (1,6) (27,2) (3,0) (5,4) (14,0) (11,14) (4,21) (23,8) (12,17) (20,25) (11,5) (13,26) (0,2) (24,5) (1,26) (15,27) (13,18) (20,0) (3,8) (17,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "27"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (12,6) (16,15) (11,18) (0,26) (3,28) (25,2) (27,2) (12,27) (4,17) (18,17) (1,28) (18,19) (14,7) (20,7) (25,22) (16,4) (10,20) (30,29) (4,0) (2,5) (25,10) (26,1) (20,26) (24,0) (23,1) (29,17) (9,18) (21,30) (13,28) (1,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "28"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (10,0) (2,21) (9,3) (2,0) (7,12) (8,11) (20,18) (7,16) (18,13) (2,17) (2,6) (4,3) (8,7) (0,4) (0,3) (5,20) (16,19) (21,3) (14,4) (1,13) (0,22) (0,1) (6,7) (15,17) (19,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "29"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (20,10) (15,8) (13,21) (8,2) (15,23) (23,22) (6,14) (18,4) (5,13) (21,17) (21,8) (12,21) (22,3) (3,11) (16,9) (22,18) (14,0) (1,7) (1,23) (21,16) (14,15) (2,10) (19,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "30"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (20,16) (15,11) (11,13) (13,12) (1,21) (30,28) (6,29) (6,12) (16,13) (26,1) (21,19) (3,8) (15,27) (5,19) (13,4) (24,9) (24,31) (4,18) (11,32) (24,8) (23,3) (7,26) (24,25) (28,11) (0,2) (23,17) (30,0) (10,14) (13,22) (14,6) (8,4) (1,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "31"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (4,0) (3,1) (0,1) (4,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "32"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,6) (8,3) (4,7) (5,7) (5,6) (1,0) (1,4) (8,0) (3,0) (2,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "33"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (2,28) (1,30) (21,16) (1,22) (26,10) (7,29) (22,19) (20,26) (13,0) (0,2) (29,24) (14,17) (20,15) (9,4) (25,10) (28,17) (28,13) (16,14) (9,27) (14,12) (7,2) (6,20) (8,6) (17,23) (19,15) (1,0) (14,18) (27,13) (9,3) (0,3) (8,14) (7,11) (5,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "34"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (7,19) (18,10) (21,17) (21,20) (10,11) (1,0) (15,13) (0,2) (22,3) (17,16) (23,6) (20,8) (11,5) (12,22) (3,0) (10,14) (2,15) (7,10) (6,7) (0,15) (4,0) (2,4) (7,9) (1,8) (4,11) (17,2) (3,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "35"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (8,28) (6,13) (8,22) (14,20) (29,24) (11,27) (23,19) (30,15) (22,17) (10,22) (5,18) (12,30) (24,18) (2,11) (23,9) (23,13) (11,14) (4,13) (1,25) (5,21) (16,3) (19,10) (26,21) (1,19) (0,20) (18,12) (2,3) (7,24) (11,10) (15,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "36"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (1,0) (5,6) (9,7) (3,12) (3,0) (4,13) (1,13) (0,2) (10,4) (11,12) (12,8) (7,4) (8,1) (2,4) (6,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "37"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (3,9) (15,20) (22,19) (2,7) (21,10) (1,9) (0,13) (0,2) (8,6) (10,20) (19,15) (0,1) (7,13) (9,14) (14,11) (14,17) (23,13) (14,16) (2,17) (16,4) (24,22) (17,18) (5,7) (8,14) (12,16) (20,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "38"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,4) (8,19) (0,6) (10,20) (1,0) (5,15) (21,18) (3,0) (6,20) (2,17) (17,1) (12,20) (8,18) (14,16) (16,13) (0,2) (13,7) (10,2) (15,9) (7,3) (18,0) (19,11) (9,17) (3,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "39"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (8,4) (1,22) (22,10) (19,5) (2,21) (2,8) (3,10) (0,16) (3,0) (14,21) (11,10) (11,7) (13,5) (20,10) (1,17) (12,15) (6,3) (23,0) (20,13) (10,9) (2,0) (6,12) (0,18) (11,8) (16,4) (1,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "40"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (19,5) (18,21) (16,11) (5,13) (1,18) (19,6) (8,9) (1,17) (10,21) (1,0) (13,20) (15,6) (4,2) (11,2) (12,16) (3,2) (19,8) (5,7) (21,11) (14,9) (12,20)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "41"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (3,1) (4,8) (1,9) (8,10) (3,7) (10,0) (0,2) (3,0) (0,1) (4,5) (2,7) (6,4) (4,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "42"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (13,15) (17,14) (25,27) (26,24) (1,0) (0,23) (1,14) (6,26) (12,3) (18,7) (22,21) (20,24) (24,25) (5,11) (18,16) (23,8) (3,19) (20,17) (22,2) (4,23) (23,11) (2,0) (9,16) (14,10) (10,21) (27,19) (13,7) (15,8) (5,17)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "43"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (15,13) (0,6) (8,9) (10,14) (15,1) (15,5) (2,11) (2,3) (11,8) (4,2) (9,12) (7,11) (8,14) (6,9) (4,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "44"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,2) (8,4) (0,6) (1,4) (2,5) (9,7) (7,0) (6,4) (3,8) (0,2) (0,3) (0,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "45"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (13,11) (15,12) (5,14) (3,2) (1,6) (13,7) (4,14) (13,8) (1,9) (0,2) (6,8) (10,8) (15,1) (9,5) (13,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "46"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (17,23) (9,18) (8,21) (6,0) (5,20) (14,3) (23,1) (15,20) (26,21) (21,29) (0,22) (3,1) (2,21) (4,10) (12,27) (30,31) (3,28) (23,25) (10,5) (1,15) (16,13) (27,31) (24,0) (7,8) (31,6) (30,4) (21,10) (19,23) (16,17) (9,11) (6,18)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "47"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (2,18) (9,17) (12,10) (2,1) (0,15) (17,19) (15,6) (1,13) (5,6) (9,11) (1,14) (9,5) (13,4) (3,14) (4,11) (7,2) (12,1) (16,6) (4,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "48"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (29,18) (10,31) (13,22) (32,23) (19,7) (25,28) (1,8) (26,18) (19,21) (3,0) (0,17) (21,33) (9,30) (14,28) (0,24) (24,2) (16,6) (9,6) (3,12) (33,0) (5,27) (11,24) (16,17) (28,4) (14,15) (17,23) (0,1) (12,13) (28,31) (5,21) (24,20) (26,17) (8,30) (2,0) (3,31) (2,28)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "49"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (4,21) (13,4) (17,27) (7,18) (9,23) (20,7) (5,15) (24,7) (11,25) (23,20) (10,21) (27,22) (1,8) (6,27) (4,5) (4,28) (12,27) (6,23) (0,9) (28,14) (2,17) (21,19) (5,25) (16,20) (8,21) (13,0) (9,3) (26,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "50"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (1,5) (0,4) (3,0) (1,0) (2,0) (1,2) (3,5) (1,4) (0,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "51"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (18,17) (22,0) (11,10) (1,0) (15,18) (8,12) (13,23) (25,13) (8,0) (2,7) (21,11) (3,25) (21,4) (15,8) (2,15) (6,23) (4,16) (9,24) (23,20) (1,14) (24,10) (24,19) (25,15) (6,24) (5,18)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "52"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (19,17) (2,0) (23,0) (23,22) (21,13) (1,14) (6,13) (23,7) (19,9) (3,21) (4,15) (6,8) (0,1) (18,16) (20,5) (22,13) (0,3) (10,17) (12,4) (11,1) (0,4) (23,1) (15,21) (20,7) (19,13) (16,5) (2,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "53"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,2) (7,9) (6,7) (0,5) (8,10) (3,8) (5,4) (4,8) (9,5) (1,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "54"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (16,0) (11,19) (5,22) (17,26) (0,3) (15,19) (13,24) (4,14) (11,18) (12,27) (1,9) (16,13) (11,8) (14,3) (13,12) (25,20) (19,27) (0,1) (23,0) (18,25) (2,0) (2,1) (6,24) (22,15) (19,14) (24,17) (3,21) (21,9) (4,7) (22,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "55"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,0) (3,5) (7,5) (2,4) (6,8) (2,8) (2,1) (5,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "56"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,23) (17,10) (19,16) (10,15) (8,0) (1,0) (0,21) (2,1) (23,12) (20,24) (19,11) (12,18) (9,13) (4,18) (13,20) (12,3) (15,9) (16,7) (22,5) (12,11) (3,20) (5,16) (6,19) (11,1) (7,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "57"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (5,12) (1,3) (9,5) (2,5) (0,10) (1,0) (0,11) (1,13) (0,2) (7,10) (8,6) (11,12) (6,3) (13,0) (5,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "58"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (6,12) (13,2) (5,15) (5,6) (19,3) (18,7) (4,2) (18,14) (5,8) (0,9) (6,10) (5,11) (1,12) (14,17) (14,20) (5,16) (9,4) (15,20) (3,0) (16,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "59"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (13,5) (12,3) (8,11) (12,6) (1,11) (4,9) (2,0) (6,13) (2,4) (3,0) (10,5) (2,13) (9,7) (1,2) (0,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "60"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (22,18) (21,10) (23,14) (4,22) (1,11) (15,7) (17,23) (3,5) (4,1) (24,6) (8,12) (0,15) (23,24) (21,1) (4,20) (4,9) (7,17) (17,3) (13,3) (14,16) (27,16) (12,4) (21,26) (4,7) (25,1) (19,24) (0,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "61"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (9,0) (5,3) (31,7) (20,1) (9,4) (23,5) (29,21) (1,12) (25,30) (30,2) (28,16) (18,9) (27,24) (7,12) (6,24) (29,6) (15,17) (4,22) (31,15) (31,5) (23,26) (11,26) (22,19) (31,16) (10,14) (6,32) (10,15) (19,11) (2,21) (13,22) (29,3) (28,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "62"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (18,6) (2,7) (16,20) (6,19) (20,22) (8,4) (1,13) (11,4) (1,0) (3,14) (15,0) (6,15) (2,0) (2,23) (5,9) (9,11) (24,22) (14,1) (2,1) (6,17) (1,12) (21,5) (17,9) (4,13) (15,20) (12,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "63"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (6,0) (12,9) (14,6) (20,3) (6,21) (4,2) (10,17) (12,0) (25,6) (13,14) (24,20) (19,7) (19,24) (23,22) (16,25) (11,21) (8,22) (1,15) (25,18) (3,5) (20,17) (24,22) (15,8) (20,4) (2,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "64"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (13,23) (17,24) (1,23) (24,21) (24,4) (1,0) (21,3) (15,18) (4,14) (17,11) (22,13) (19,21) (26,6) (13,20) (23,7) (6,8) (6,2) (23,0) (15,1) (25,7) (12,1) (6,27) (22,27) (10,19) (13,9) (16,19) (20,5) (5,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "65"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (12,7) (3,0) (3,2) (2,8) (4,10) (1,0) (9,1) (11,7) (6,2) (10,11) (0,2) (6,7) (0,5) (9,12) (4,0) (10,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "66"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (24,22) (1,20) (21,1) (23,14) (4,8) (17,20) (3,6) (10,24) (7,19) (10,3) (7,16) (24,23) (12,16) (5,13) (18,21) (25,8) (17,16) (1,15) (1,23) (11,17) (2,0) (14,4) (9,26) (9,19) (25,13) (11,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "67"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (6,27) (18,13) (6,17) (19,16) (3,20) (1,13) (19,0) (17,22) (7,16) (26,7) (18,24) (21,3) (0,1) (4,23) (6,2) (14,7) (23,2) (10,0) (23,11) (9,3) (17,0) (8,7) (21,23) (2,25) (4,15) (8,12) (5,20)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "68"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,1) (12,8) (9,10) (0,2) (0,14) (0,7) (8,9) (4,15) (5,6) (12,1) (7,3) (4,13) (5,12) (0,11) (4,14) (7,12) (10,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "69"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (17,1) (6,11) (11,16) (0,3) (8,2) (2,11) (4,5) (5,14) (1,0) (3,17) (7,3) (4,0) (9,4) (12,11) (3,13) (15,0) (3,15) (0,2) (10,12) (3,12) (5,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "70"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (13,6) (20,6) (0,2) (16,6) (3,17) (19,8) (2,4) (9,5) (4,5) (4,7) (1,3) (5,12) (0,3) (18,12) (14,13) (19,4) (14,15) (6,0) (0,1) (6,19) (10,7) (17,4) (20,11) (4,0) (0,21)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "71"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (5,0) (9,1) (2,20) (9,12) (14,19) (11,21) (22,5) (23,3) (3,17) (23,11) (23,24) (8,17) (4,0) (22,2) (9,8) (0,1) (0,2) (15,5) (6,13) (16,14) (23,13) (7,10) (18,15) (7,14) (5,13) (4,16) (22,4) (0,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "72"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (12,1) (8,11) (9,5) (4,12) (5,2) (8,9) (4,5) (11,6) (10,11) (1,0) (3,9) (2,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "73"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (17,27) (29,16) (10,3) (27,28) (25,12) (11,18) (24,13) (7,24) (24,21) (10,14) (27,15) (21,18) (19,18) (24,14) (23,21) (17,7) (26,4) (2,0) (7,6) (1,0) (22,7) (3,0) (0,6) (20,11) (12,17) (8,28) (29,19) (22,1) (5,3) (9,6) (2,19) (26,27)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "74"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (3,0) (5,10) (5,12) (9,7) (15,0) (7,2) (11,5) (5,8) (3,5) (14,6) (4,2) (5,1) (14,8) (11,9) (13,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "75"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,2) (1,7) (5,4) (0,3) (2,0) (0,4) (0,6) (1,0) (7,8) (1,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "76"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (3,13) (7,20) (9,5) (12,1) (22,10) (1,8) (20,3) (3,18) (21,18) (6,21) (18,9) (1,9) (19,16) (10,19) (18,17) (16,6) (15,13) (6,0) (11,15) (12,2) (14,8) (4,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "77"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (29,27) (15,7) (22,9) (10,21) (11,5) (26,21) (0,3) (30,5) (0,4) (12,6) (1,0) (25,4) (4,21) (0,14) (12,24) (8,30) (18,9) (5,4) (28,33) (2,17) (14,15) (20,13) (22,20) (32,0) (5,16) (14,21) (31,1) (3,23) (12,28) (2,0) (23,22) (17,27) (27,6) (20,14) (17,21) (31,27) (19,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "78"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (10,3) (9,4) (15,7) (2,5) (12,3) (2,6) (3,0) (1,15) (13,10) (0,2) (15,11) (14,11) (4,6) (1,10) (0,1) (0,9) (8,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "79"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (1,0) (4,2) (8,5) (1,5) (6,8) (3,2) (12,1) (1,7) (0,9) (11,4) (5,3) (9,1) (10,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "80"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (5,0) (10,21) (14,16) (11,19) (7,21) (14,6) (8,17) (6,13) (11,20) (2,9) (10,9) (1,15) (12,10) (3,1) (18,15) (8,16) (15,17) (19,4) (17,4) (16,0) (14,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "81"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (17,9) (21,24) (6,14) (9,4) (23,18) (10,18) (20,12) (9,24) (15,0) (12,15) (22,11) (19,16) (13,0) (5,23) (1,7) (0,19) (21,10) (22,5) (15,17) (0,7) (20,2) (8,4) (21,14) (3,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "82"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (4,5) (3,7) (8,7) (1,2) (1,7) (7,9) (6,3) (5,3) (0,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "83"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (13,20) (8,17) (10,3) (25,10) (0,1) (23,11) (24,8) (5,7) (19,5) (23,21) (25,6) (2,18) (25,15) (22,20) (2,17) (20,16) (0,14) (13,26) (16,0) (13,18) (11,17) (2,9) (9,12) (26,15) (1,4) (8,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "84"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (5,8) (12,0) (16,14) (3,7) (7,15) (14,5) (6,10) (11,16) (4,13) (1,12) (5,4) (14,10) (4,3) (6,2) (0,10) (0,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "85"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (16,6) (3,15) (12,17) (19,13) (13,12) (12,11) (0,15) (2,5) (3,0) (18,0) (10,15) (8,15) (0,14) (1,4) (4,18) (6,3) (7,3) (14,19) (1,0) (14,9) (2,0) (8,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "86"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (19,15) (12,4) (17,14) (24,22) (20,0) (22,10) (18,21) (22,17) (0,2) (13,22) (20,4) (23,22) (9,11) (9,23) (0,1) (19,3) (0,3) (1,2) (6,23) (0,25) (25,2) (7,12) (10,7) (4,19) (5,11) (19,21) (11,16) (5,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "87"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,5) (6,16) (7,9) (11,4) (14,0) (8,2) (14,7) (17,7) (1,10) (0,1) (0,8) (13,11) (3,7) (16,3) (3,5) (15,11) (15,12) (12,17)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "88"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (20,16) (18,9) (0,1) (8,13) (4,0) (2,18) (15,2) (8,0) (15,12) (9,19) (0,5) (0,2) (0,3) (5,17) (16,6) (3,14) (7,16) (1,8) (3,4) (16,12) (18,11) (6,14) (10,15) (14,5) (13,21)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "89"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,1) (7,5) (0,7) (7,4) (3,6) (3,1) (4,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "90"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (5,3) (8,1) (7,5) (1,4) (8,0) (6,4) (8,5) (1,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "91"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (7,4) (3,20) (20,8) (17,5) (2,20) (9,2) (9,13) (12,16) (16,23) (14,9) (18,19) (21,24) (1,5) (20,21) (10,22) (17,11) (16,19) (8,6) (0,18) (14,15) (20,5) (13,25) (10,21) (15,16) (1,0) (15,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "92"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (17,28) (16,6) (5,21) (10,19) (15,0) (16,17) (30,13) (4,1) (23,18) (19,18) (9,5) (3,14) (14,23) (1,16) (18,25) (11,29) (6,7) (5,23) (17,12) (24,21) (20,9) (15,30) (31,24) (25,8) (19,2) (6,11) (22,4) (25,26) (27,3) (1,13) (12,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "93"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (7,4) (1,16) (14,15) (6,17) (25,22) (12,9) (21,11) (7,5) (22,19) (16,17) (13,17) (18,21) (7,0) (10,20) (23,14) (8,7) (3,5) (24,8) (12,22) (23,17) (17,2) (16,20) (12,11) (8,12) (18,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "94"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (9,2) (10,1) (5,12) (7,3) (14,5) (13,15) (11,1) (8,6) (4,13) (5,8) (13,5) (0,1) (0,5) (2,10) (3,15)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "95"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,2) (0,1) (0,6) (2,6) (0,4) (2,1) (0,3) (1,6) (2,3) (0,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "96"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (2,9) (14,0) (2,0) (4,10) (12,14) (10,11) (14,7) (14,8) (13,10) (13,14) (10,3) (0,1) (6,12) (2,4) (0,4) (0,3) (5,12) (11,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "97"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (25,24) (15,22) (4,6) (0,1) (9,4) (2,5) (11,15) (14,1) (23,13) (1,16) (17,24) (10,1) (20,16) (7,9) (8,22) (3,18) (21,10) (3,10) (19,0) (0,12) (11,19) (7,15) (17,0) (23,25) (6,2) (16,22)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "98"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (5,0) (21,17) (6,23) (18,14) (11,19) (3,18) (4,12) (13,20) (15,6) (1,0) (15,2) (21,4) (22,17) (23,21) (5,2) (23,18) (0,10) (8,7) (11,10) (0,8) (4,0) (15,8) (9,1) (15,16) (3,0) (2,0) (13,17)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "99"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (23,25) (22,19) (23,2) (1,15) (5,27) (19,20) (0,1) (9,29) (5,6) (21,10) (14,3) (31,0) (18,31) (11,7) (7,6) (24,17) (5,12) (19,5) (8,19) (12,2) (4,0) (0,3) (31,6) (2,0) (4,5) (26,20) (8,14) (10,24) (19,16) (13,1) (11,21) (29,5) (28,2) (30,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "100"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (15,2) (18,15) (11,10) (4,17) (24,20) (1,16) (24,12) (26,7) (0,3) (25,3) (21,4) (15,8) (0,2) (13,26) (13,23) (2,9) (0,1) (24,10) (22,11) (6,25) (6,23) (24,0) (19,18) (5,18) (8,14) (15,25) (8,0) (23,21)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "101"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (20,19) (0,26) (12,26) (17,9) (25,17) (0,19) (4,8) (0,14) (6,14) (18,10) (24,9) (24,5) (4,27) (22,15) (23,18) (21,16) (7,0) (3,2) (9,11) (5,23) (7,1) (21,27) (2,20) (10,21) (12,15) (13,22) (25,15)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "102"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,4) (1,5) (12,8) (16,19) (3,5) (27,14) (21,28) (23,6) (13,11) (24,4) (25,5) (15,29) (3,15) (0,1) (5,14) (5,0) (18,19) (21,3) (13,7) (26,9) (10,14) (22,28) (13,15) (2,3) (24,21) (8,19) (1,9) (2,0) (1,20) (17,13) (8,29) (20,6) (0,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "103"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (12,10) (4,22) (11,6) (21,24) (2,19) (25,18) (30,15) (21,5) (29,17) (9,20) (31,13) (23,5) (14,33) (3,27) (23,18) (15,0) (24,32) (8,25) (12,17) (3,14) (26,25) (6,16) (4,1) (18,19) (13,1) (1,16) (19,10) (23,28) (11,30) (5,9) (6,7) (17,16) (32,33)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "104"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,6) (2,9) (8,4) (0,4) (0,3) (7,5) (0,1) (4,1) (2,0) (5,0) (7,0) (7,8) (5,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "105"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,4) (8,2) (0,1) (7,0) (5,8) (6,3) (5,3) (4,5) (1,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "106"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (16,5) (14,3) (6,8) (14,15) (1,12) (6,5) (3,0) (4,2) (14,13) (9,4) (5,17) (10,5) (16,0) (0,9) (6,11) (5,7) (2,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "107"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (16,8) (7,10) (0,8) (2,5) (6,14) (8,9) (1,13) (10,16) (13,2) (15,3) (4,11) (12,14) (0,3) (0,13) (12,1) (11,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "108"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (2,1) (14,0) (0,1) (4,7) (12,2) (8,30) (6,16) (5,11) (19,4) (7,3) (25,14) (6,18) (22,12) (28,6) (18,29) (7,25) (12,9) (22,13) (2,0) (28,26) (10,4) (3,0) (11,6) (27,15) (0,20) (2,15) (23,20) (12,14) (30,15) (16,21) (1,17) (26,12) (15,24)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "109"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (16,12) (0,2) (4,2) (6,0) (15,13) (6,8) (3,12) (14,6) (1,15) (0,7) (13,14) (12,2) (4,11) (10,8) (5,3) (9,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "110"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (5,12) (0,3) (18,6) (4,15) (1,0) (14,10) (12,16) (6,19) (8,5) (13,6) (4,5) (3,19) (14,6) (11,13) (7,9) (17,6) (4,7) (2,17) (0,2) (1,4) (19,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "111"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (15,5) (10,6) (20,17) (6,13) (10,11) (23,8) (25,5) (19,7) (3,14) (15,9) (4,17) (20,21) (7,4) (15,24) (7,12) (17,18) (6,26) (26,0) (8,0) (25,1) (22,19) (0,16) (21,16) (26,25) (9,3) (8,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "112"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (2,0) (16,5) (9,13) (29,12) (25,23) (1,11) (4,0) (1,2) (19,11) (12,22) (19,27) (15,10) (1,0) (11,12) (7,16) (0,27) (0,24) (12,3) (19,6) (14,7) (0,8) (26,18) (15,9) (20,13) (26,5) (3,0) (21,28) (28,20) (3,20) (30,23) (23,28) (18,4) (17,10) (16,29)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "113"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (8,1) (10,6) (2,4) (9,0) (7,0) (2,6) (5,1) (0,12) (5,3) (10,1) (5,9) (11,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "114"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,3) (14,11) (9,7) (1,4) (19,6) (4,16) (6,13) (2,17) (12,17) (5,4) (12,5) (10,20) (7,4) (18,6) (4,19) (6,20) (8,5) (14,13) (19,3) (6,15)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "115"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (4,5) (2,1) (0,10) (16,11) (9,3) (11,3) (2,16) (12,4) (8,2) (6,12) (6,1) (13,14) (7,1) (10,1) (13,15) (2,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "116"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (1,3) (3,5) (0,5) (2,5) (5,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "117"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (2,0) (6,2) (17,0) (10,20) (19,11) (10,1) (21,4) (15,11) (8,9) (0,12) (2,5) (15,16) (15,7) (6,4) (0,3) (19,0) (3,14) (0,1) (16,1) (3,10) (4,17) (16,18) (1,13) (7,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "118"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,5) (8,0) (2,8) (5,6) (4,2) (8,7) (6,1) (3,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "119"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,4) (2,3) (5,2) (2,0) (4,7) (0,6) (8,6) (1,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "120"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (18,13) (2,7) (12,4) (19,7) (6,16) (1,14) (11,3) (17,13) (16,15) (2,1) (10,17) (1,6) (12,3) (8,1) (0,10) (9,2) (13,2) (18,11) (4,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "121"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (4,15) (24,22) (9,25) (4,2) (17,12) (0,1) (23,1) (24,8) (10,9) (21,9) (13,3) (16,17) (0,2) (20,2) (14,23) (6,7) (3,25) (24,5) (16,7) (19,15) (26,5) (3,26) (0,12) (18,12) (8,11) (11,17) (1,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "122"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,1) (5,1) (5,2) (3,0) (2,6) (1,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "123"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,2) (7,5) (2,1) (3,0) (8,3) (1,0) (2,9) (2,0) (5,6) (4,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "124"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (2,8) (9,0) (0,2) (0,3) (4,1) (6,1) (1,0) (9,11) (0,5) (9,2) (8,10) (7,3) (10,3) (6,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "125"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (26,9) (9,19) (13,15) (23,19) (0,3) (11,7) (22,9) (11,1) (14,12) (20,7) (16,22) (21,13) (15,3) (4,21) (10,21) (24,26) (17,8) (10,25) (18,20) (6,13) (0,14) (0,9) (7,8) (23,4) (1,0) (2,15) (7,0) (0,2) (9,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "126"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (13,7) (17,12) (3,5) (0,10) (16,9) (18,20) (12,7) (19,2) (1,16) (17,3) (18,3) (15,7) (20,14) (15,11) (20,8) (8,4) (11,19) (5,1) (6,11) (0,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "127"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (5,0) (8,7) (0,1) (1,6) (9,4) (0,2) (0,4) (6,2) (5,8) (0,3) (6,7) (4,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "128"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (8,5) (11,9) (5,3) (16,11) (5,12) (3,0) (4,2) (5,13) (2,7) (15,8) (7,9) (0,14) (14,6) (1,5) (5,10) (0,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "129"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (21,33) (6,21) (34,5) (8,4) (0,1) (9,20) (9,30) (2,0) (8,3) (32,11) (1,13) (32,25) (18,3) (27,4) (24,14) (12,27) (32,26) (13,14) (10,8) (4,0) (4,1) (18,21) (15,17) (32,31) (6,22) (0,3) (6,15) (28,9) (7,19) (34,17) (10,31) (13,29) (27,30) (10,19) (23,31) (20,0) (2,8) (16,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "130"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (6,19) (20,25) (10,12) (12,1) (0,2) (25,15) (11,4) (0,1) (18,6) (7,2) (1,2) (9,5) (0,15) (22,2) (24,20) (13,1) (11,9) (15,6) (17,25) (4,8) (9,17) (13,4) (1,14) (6,23) (3,0) (0,4) (5,21) (14,3) (16,20)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "131"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,4) (7,10) (19,6) (5,12) (11,13) (16,13) (2,14) (14,9) (11,12) (3,16) (10,6) (8,1) (17,18) (7,20) (5,15) (2,3) (8,14) (4,14) (17,3) (1,20)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "132"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,0) (8,9) (5,1) (4,8) (3,2) (9,6) (6,2) (5,3) (7,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "133"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (28,23) (12,6) (12,19) (20,27) (29,31) (30,7) (31,4) (16,18) (31,11) (30,21) (10,2) (0,11) (15,0) (9,32) (11,14) (3,9) (1,23) (30,5) (8,25) (19,22) (7,8) (24,6) (1,19) (28,32) (27,2) (10,16) (15,22) (22,20) (26,5) (31,5) (18,13) (17,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "134"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (6,10) (11,6) (1,4) (7,10) (2,0) (4,5) (9,7) (7,8) (1,7) (2,9) (1,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "135"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (3,0) (9,4) (0,4) (4,8) (1,0) (2,0) (8,7) (11,3) (7,0) (5,10) (6,8) (6,11) (10,3) (1,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "136"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (14,7) (18,21) (1,13) (6,22) (17,0) (20,22) (27,12) (0,3) (23,0) (12,18) (16,24) (10,3) (16,2) (15,9) (18,26) (4,17) (9,25) (12,20) (16,22) (22,9) (13,12) (24,5) (8,27) (7,3) (19,7) (5,11) (3,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "137"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (9,10) (0,9) (4,8) (5,2) (7,0) (8,3) (7,6) (8,2) (8,1) (0,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "138"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (2,6) (2,12) (3,7) (11,8) (1,3) (10,5) (1,9) (1,0) (2,8) (2,5) (4,10) (9,0) (4,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "139"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (3,9) (2,0) (2,12) (12,8) (7,0) (8,11) (7,8) (0,1) (9,10) (6,7) (5,7) (8,1) (3,2) (12,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "140"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,8) (6,9) (0,4) (5,0) (7,3) (1,9) (10,7) (6,0) (0,1) (9,7) (0,2) (3,0) (7,5) (4,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "141"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (1,0) (5,17) (2,16) (17,23) (2,19) (12,15) (24,26) (4,11) (26,0) (20,8) (19,15) (14,18) (17,25) (3,18) (19,10) (9,4) (15,17) (21,7) (6,22) (8,17) (7,6) (7,1) (18,0) (11,15) (13,20) (15,22) (26,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "142"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (24,11) (22,21) (2,17) (12,21) (6,1) (33,27) (23,22) (6,0) (7,29) (14,26) (15,14) (26,18) (15,12) (32,2) (32,29) (20,27) (16,24) (30,22) (1,19) (32,10) (22,3) (0,25) (2,23) (21,8) (28,15) (5,4) (31,28) (25,13) (27,4) (9,16) (20,0) (30,16) (33,15)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "143"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (30,3) (16,2) (31,0) (1,29) (2,0) (28,5) (26,22) (4,0) (5,0) (14,12) (1,15) (27,8) (18,13) (12,24) (10,7) (29,25) (23,28) (3,0) (11,4) (6,2) (25,13) (6,11) (19,13) (1,26) (17,12) (30,25) (21,9) (5,12) (9,5) (1,0) (27,32) (1,5) (16,14) (17,20) (7,25) (18,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "144"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (2,21) (4,23) (2,13) (0,2) (19,0) (11,8) (24,4) (18,22) (4,26) (8,3) (18,16) (3,10) (1,16) (19,11) (24,0) (16,26) (26,15) (9,10) (1,0) (12,20) (11,5) (3,25) (0,4) (9,13) (18,6) (3,0) (12,11) (7,0) (0,14) (7,17)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "145"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (26,27) (21,7) (24,25) (17,23) (9,8) (17,2) (8,15) (1,21) (18,28) (20,16) (1,0) (29,20) (22,3) (2,5) (0,6) (8,11) (4,23) (11,2) (14,18) (12,18) (15,6) (28,19) (21,20) (9,13) (15,28) (14,25) (10,18) (26,9) (11,22) (1,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "146"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (26,12) (1,2) (18,6) (24,14) (5,11) (11,22) (0,2) (12,21) (12,8) (1,13) (10,6) (26,27) (15,18) (0,14) (17,4) (16,19) (1,0) (14,12) (3,0) (15,23) (16,6) (15,25) (4,7) (2,28) (4,9) (22,20) (7,25) (7,3) (0,20) (2,12) (6,28)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "147"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (17,32) (22,13) (26,6) (16,8) (29,15) (1,26) (8,12) (13,9) (1,27) (8,28) (0,33) (4,15) (25,9) (19,26) (8,20) (17,14) (31,33) (28,14) (13,21) (23,10) (2,0) (20,26) (2,7) (32,11) (0,12) (3,0) (0,1) (5,11) (3,8) (18,29) (30,11) (12,25) (4,6) (12,24) (7,14) (10,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "148"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (8,20) (8,13) (10,5) (18,22) (9,13) (6,4) (1,23) (0,16) (21,22) (4,9) (3,11) (11,20) (17,16) (23,16) (17,2) (3,18) (10,12) (19,8) (15,1) (7,23) (14,18) (10,4) (0,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "149"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (8,4) (13,9) (16,5) (7,17) (2,9) (8,16) (5,11) (10,12) (0,18) (17,2) (13,18) (15,6) (9,14) (15,14) (1,0) (10,16) (5,1) (15,16) (7,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "150"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (1,2) (0,1) (3,6) (0,3) (2,0) (1,7) (5,4) (3,5) (7,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "151"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (11,13) (18,30) (14,10) (11,30) (0,11) (23,28) (7,30) (25,5) (31,28) (12,19) (16,10) (8,7) (0,3) (24,8) (22,15) (17,16) (29,5) (6,12) (31,5) (15,0) (31,27) (1,23) (31,4) (20,26) (1,0) (9,18) (9,3) (20,22) (22,19) (2,27) (6,21) (2,10) (1,19) (2,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "152"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (7,14) (1,0) (0,2) (11,1) (0,11) (10,14) (13,12) (15,2) (9,4) (8,7) (3,15) (16,9) (15,9) (0,7) (9,0) (13,5) (8,13) (7,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "153"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (19,6) (2,0) (4,0) (8,19) (2,11) (16,23) (23,10) (15,21) (11,25) (17,9) (8,9) (7,5) (2,3) (22,6) (20,13) (5,13) (25,14) (12,25) (1,0) (2,4) (12,20) (23,24) (11,16) (19,1) (0,3) (18,21) (5,21) (18,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "154"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (8,1) (4,8) (6,5) (7,4) (0,4) (0,5) (0,2) (8,3) (3,0) (1,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "155"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (10,7) (0,27) (27,24) (14,22) (26,13) (19,9) (10,25) (11,3) (25,17) (2,23) (18,9) (6,9) (15,14) (4,14) (1,17) (9,7) (21,26) (15,7) (16,7) (5,12) (0,1) (6,8) (20,24) (9,26) (10,2) (1,11) (13,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "156"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (28,7) (10,2) (14,5) (3,24) (22,15) (23,4) (10,21) (25,28) (9,6) (19,12) (5,27) (13,10) (2,18) (2,20) (1,2) (14,19) (7,0) (24,13) (19,0) (9,22) (16,8) (8,4) (18,27) (11,27) (21,22) (26,6) (11,17) (27,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "157"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,3) (7,0) (8,6) (6,2) (0,4) (8,0) (5,3) (5,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "158"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (4,7) (11,6) (3,9) (17,12) (7,14) (2,10) (6,3) (20,17) (9,15) (19,8) (6,5) (0,8) (4,17) (20,15) (16,0) (19,13) (18,16) (8,1) (7,10) (0,15)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "159"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (2,10) (8,23) (31,15) (28,22) (17,20) (29,16) (12,17) (23,19) (29,8) (29,15) (13,0) (31,14) (9,31) (30,11) (24,22) (6,0) (21,23) (16,18) (4,15) (7,29) (24,26) (1,2) (2,26) (27,3) (13,10) (11,19) (30,5) (8,27) (2,25) (18,26) (4,20)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "160"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (6,3) (12,17) (12,13) (0,2) (19,14) (13,19) (0,14) (5,2) (0,18) (2,8) (9,14) (15,8) (6,16) (4,1) (15,0) (0,4) (3,0) (0,1) (18,4) (11,12) (7,3) (15,3) (15,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "161"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (4,3) (1,2) (0,5) (5,3) (1,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "162"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (2,3) (6,15) (5,13) (21,10) (19,8) (2,11) (4,2) (5,21) (21,18) (18,1) (13,20) (20,12) (4,0) (12,16) (17,22) (1,0) (0,2) (11,17) (19,6) (3,0) (0,5) (1,19) (11,16) (9,8) (14,9) (7,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "163"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (12,0) (12,5) (0,7) (10,2) (0,14) (4,14) (15,7) (4,10) (3,7) (12,1) (4,16) (10,17) (13,8) (6,5) (8,12) (9,11) (17,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "164"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (5,3) (5,11) (2,1) (0,20) (6,22) (4,0) (4,20) (19,13) (10,7) (0,2) (3,0) (21,10) (7,12) (19,16) (0,1) (22,18) (19,2) (15,21) (11,14) (22,9) (22,19) (22,0) (4,17) (11,9) (12,4) (8,17)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "165"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (25,9) (0,4) (1,7) (25,3) (6,7) (11,8) (16,7) (11,17) (4,15) (26,5) (3,26) (12,0) (3,13) (2,20) (21,9) (24,5) (23,14) (22,24) (0,1) (17,12) (1,23) (12,18) (9,10) (19,15) (0,5) (17,16) (2,4) (24,8) (3,0) (2,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "166"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (11,13) (0,2) (23,2) (25,17) (0,1) (8,14) (26,7) (19,12) (23,12) (3,2) (14,4) (15,24) (13,16) (0,4) (14,23) (6,10) (17,3) (7,10) (24,3) (21,1) (11,22) (1,8) (9,14) (0,3) (6,20) (0,5) (25,16) (5,22) (18,5) (20,21)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "167"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (15,11) (7,6) (5,2) (0,2) (12,18) (11,16) (14,5) (18,1) (4,12) (5,3) (13,14) (6,15) (14,9) (14,10) (7,8) (6,17) (8,14) (0,3) (12,6) (0,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "168"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (5,22) (8,27) (28,8) (13,0) (26,23) (10,4) (31,13) (0,29) (30,13) (15,12) (9,1) (17,25) (6,21) (15,0) (18,30) (7,16) (3,14) (1,29) (22,13) (2,16) (26,28) (24,11) (23,7) (19,15) (15,6) (10,3) (0,8) (8,4) (20,24) (11,17) (24,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "169"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (11,25) (32,10) (5,17) (12,6) (11,21) (16,25) (22,12) (9,28) (16,32) (14,8) (7,10) (13,34) (8,1) (4,32) (11,9) (24,17) (25,31) (11,29) (30,34) (8,0) (24,23) (6,23) (33,2) (27,17) (30,23) (1,18) (15,31) (12,19) (20,2) (3,34) (7,6) (5,0) (26,23) (33,21)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "170"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (13,14) (13,6) (18,12) (0,21) (3,17) (7,4) (19,6) (7,10) (14,15) (0,6) (5,12) (1,3) (4,5) (19,4) (11,20) (17,4) (8,19) (20,6) (5,9) (16,6) (4,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "171"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (23,15) (15,11) (5,24) (24,4) (17,8) (26,21) (25,19) (12,2) (16,4) (18,11) (9,26) (25,12) (12,20) (6,18) (8,25) (9,4) (10,1) (8,1) (14,15) (13,7) (27,0) (16,13) (3,24) (6,16) (17,27) (22,9) (3,19)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "172"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (3,1) (3,10) (7,2) (14,4) (0,10) (11,1) (5,8) (12,13) (9,4) (6,11) (4,7) (13,8) (4,1) (5,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "173"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (19,15) (1,8) (7,0) (19,9) (19,26) (16,24) (5,2) (26,5) (12,20) (0,1) (3,0) (23,14) (20,17) (16,28) (18,26) (2,4) (1,12) (13,0) (2,0) (22,12) (6,21) (14,0) (7,25) (11,9) (8,6) (27,26) (3,17) (20,4) (16,19) (25,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "174"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (23,15) (5,2) (20,8) (6,26) (14,16) (2,0) (19,21) (25,24) (11,25) (25,6) (14,26) (21,4) (14,17) (0,5) (1,18) (11,22) (10,14) (0,1) (5,9) (3,0) (19,26) (23,13) (5,12) (21,3) (14,18) (6,15) (6,7) (4,0) (12,25) (7,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "175"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (6,21) (22,34) (5,32) (18,31) (14,8) (20,19) (1,15) (0,2) (10,21) (7,6) (9,29) (0,3) (1,0) (16,19) (17,24) (23,2) (16,33) (13,1) (23,28) (25,10) (19,5) (6,5) (4,5) (5,30) (27,7) (12,5) (11,33) (24,19) (19,8) (34,21) (20,29) (31,0) (26,11) (12,2) (3,14) (2,31)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "176"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (26,15) (7,12) (23,27) (14,3) (6,10) (16,21) (7,19) (17,18) (4,17) (9,15) (13,6) (0,8) (1,25) (22,19) (2,8) (1,0) (0,26) (9,3) (0,2) (5,15) (24,8) (25,27) (7,4) (11,10) (0,16) (20,21) (26,6) (17,20) (25,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "177"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (30,16) (15,10) (20,0) (14,0) (28,6) (4,23) (17,1) (7,30) (26,13) (19,13) (1,3) (26,5) (12,17) (1,21) (25,13) (29,1) (7,0) (2,8) (23,8) (9,16) (4,5) (15,27) (5,30) (11,18) (11,27) (14,12) (24,25) (14,11) (20,28) (29,22)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "178"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (7,3) (12,10) (12,13) (3,5) (1,8) (9,3) (9,4) (13,11) (7,12) (13,6) (11,2) (5,1) (0,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "179"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,7) (4,0) (5,7) (2,8) (7,3) (3,0) (8,6) (1,0) (4,7) (2,0) (8,1) (3,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "180"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (14,5) (6,2) (7,17) (14,15) (18,5) (13,10) (10,19) (1,12) (7,3) (16,11) (0,9) (4,16) (0,12) (3,4) (0,10) (6,10) (19,4) (14,13) (5,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "181"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (14,3) (23,6) (1,6) (10,16) (9,15) (17,25) (17,10) (17,2) (12,11) (23,24) (15,8) (4,17) (23,18) (5,9) (22,12) (26,14) (0,4) (2,19) (15,25) (27,16) (18,21) (6,12) (7,14) (20,10) (13,7) (15,1) (19,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "182"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (7,10) (2,4) (1,4) (8,7) (6,0) (8,11) (3,5) (4,8) (7,6) (8,9) (3,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "183"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (13,19) (1,0) (22,8) (22,23) (3,13) (18,7) (20,7) (22,12) (31,10) (12,9) (25,13) (17,29) (19,14) (11,9) (17,24) (6,25) (16,27) (21,28) (3,16) (11,30) (11,4) (15,27) (14,21) (29,2) (29,1) (23,26) (24,10) (25,29) (5,7) (0,9) (26,13) (5,29)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "184"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (13,8) (0,5) (9,14) (4,10) (2,11) (2,0) (5,14) (12,10) (3,0) (1,4) (14,2) (2,10) (13,3) (6,10) (0,4) (10,3) (1,0) (7,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "185"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,4) (6,0) (1,0) (5,8) (2,0) (8,2) (5,0) (2,3) (7,1) (4,0) (4,3) (3,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "186"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (13,23) (3,22) (8,19) (0,3) (13,11) (1,32) (15,27) (7,5) (26,25) (6,24) (31,5) (24,16) (0,20) (11,30) (27,28) (12,8) (1,0) (23,31) (27,22) (23,2) (2,29) (26,1) (6,5) (18,4) (1,9) (23,32) (3,13) (0,14) (18,22) (0,2) (28,17) (12,17) (1,21) (14,29) (19,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "187"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (3,0) (5,8) (11,7) (2,7) (11,9) (5,10) (1,10) (7,1) (2,6) (4,0) (4,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "188"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (32,0) (29,21) (29,7) (12,28) (3,9) (21,16) (14,11) (26,31) (4,21) (11,0) (12,14) (19,8) (12,2) (27,8) (7,23) (11,25) (18,8) (20,27) (5,11) (0,1) (30,28) (6,0) (15,28) (19,10) (24,8) (7,10) (29,17) (20,26) (22,14) (3,21) (15,9) (1,25) (13,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "189"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (13,8) (8,7) (7,0) (9,15) (14,10) (7,14) (1,11) (15,3) (9,16) (13,12) (15,2) (4,9) (7,6) (5,13) (0,9) (0,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "190"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (3,9) (10,11) (12,10) (2,14) (14,15) (4,15) (12,6) (15,5) (7,14) (1,6) (7,9) (4,0) (15,1) (6,13) (8,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "191"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,1) (0,8) (7,4) (7,5) (5,6) (3,8) (6,0) (2,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "192"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (4,2) (7,6) (3,7) (5,2) (3,4) (1,4) (4,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "193"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (15,10) (4,0) (12,17) (5,0) (7,16) (3,18) (0,15) (9,13) (12,18) (9,14) (1,2) (8,10) (1,11) (7,6) (11,12) (13,12) (11,16) (5,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "194"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (12,5) (17,1) (9,32) (2,16) (4,33) (5,7) (11,24) (27,12) (13,30) (32,28) (12,14) (32,30) (15,8) (19,7) (20,7) (0,25) (1,31) (21,11) (12,6) (24,29) (12,10) (15,9) (13,14) (11,26) (34,12) (21,20) (0,17) (4,5) (18,22) (15,23) (34,16) (3,20) (16,31) (18,30)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "195"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (8,2) (21,0) (12,6) (16,4) (1,14) (13,27) (30,0) (17,23) (14,17) (20,1) (18,24) (10,24) (19,27) (28,14) (25,6) (4,3) (20,6) (15,31) (7,31) (13,24) (29,1) (30,9) (5,7) (16,1) (28,22) (28,31) (1,26) (11,13) (24,0) (27,1) (8,28)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "196"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (18,16) (8,18) (23,9) (16,1) (21,0) (3,10) (16,7) (12,6) (4,17) (16,11) (20,8) (15,9) (10,9) (12,11) (13,10) (19,4) (6,14) (3,19) (3,5) (8,3) (8,22) (13,21) (1,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "197"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (22,6) (26,1) (24,29) (7,23) (12,14) (0,3) (11,3) (21,8) (15,22) (0,2) (23,29) (24,13) (17,22) (32,5) (18,5) (17,16) (32,15) (10,19) (9,19) (0,28) (26,16) (4,2) (23,14) (21,14) (33,31) (8,11) (25,0) (20,1) (22,31) (0,1) (4,18) (31,23) (9,1) (28,20) (4,0) (4,27) (14,30)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "198"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (3,8) (7,6) (5,6) (0,8) (8,7) (2,5) (7,1) (8,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "199"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (3,2) (29,21) (7,9) (8,1) (11,13) (25,16) (18,24) (9,26) (24,11) (4,14) (23,2) (14,23) (5,22) (0,1) (10,7) (14,15) (12,22) (20,28) (3,0) (19,5) (6,10) (23,12) (3,25) (8,14) (26,29) (3,17) (20,6) (16,13) (27,17) (1,21) (4,0) (0,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "200"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (1,10) (14,11) (17,1) (16,13) (17,12) (5,4) (0,1) (19,14) (12,14) (2,8) (6,16) (15,4) (13,5) (9,13) (11,5) (11,8) (3,1) (15,7) (18,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "201"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (9,5) (6,16) (5,6) (1,14) (15,6) (4,8) (13,1) (1,2) (18,9) (10,12) (2,17) (2,7) (14,3) (4,13) (15,0) (12,1) (4,11) (11,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "202"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (21,24) (15,0) (16,15) (23,7) (24,15) (9,20) (7,10) (3,11) (13,7) (19,2) (4,11) (11,8) (14,22) (2,17) (4,27) (17,20) (26,28) (25,29) (28,12) (10,22) (10,18) (8,5) (6,2) (21,17) (3,26) (10,11) (6,7) (29,2) (27,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "203"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (6,25) (21,0) (5,10) (0,2) (12,25) (2,22) (26,5) (9,17) (29,8) (16,22) (2,11) (19,22) (24,11) (28,0) (14,12) (20,29) (18,25) (15,1) (11,15) (10,14) (16,28) (0,27) (10,13) (17,4) (10,20) (6,7) (20,2) (23,15) (5,3) (9,10) (0,1) (3,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "204"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (20,29) (14,12) (13,18) (6,7) (17,22) (1,15) (13,4) (31,2) (9,32) (23,30) (2,27) (26,9) (18,21) (16,10) (25,28) (4,23) (20,10) (1,8) (3,7) (11,21) (3,16) (10,14) (27,18) (24,0) (9,6) (19,24) (15,0) (24,17) (28,9) (5,24) (1,7) (30,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "205"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (0,3) (2,1) (1,3) (3,4) (1,4) (1,0) (0,4) (2,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "206"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (5,17) (23,0) (23,8) (23,6) (21,10) (25,3) (23,27) (1,0) (24,29) (21,27) (22,16) (11,28) (13,7) (3,16) (14,10) (20,24) (9,26) (13,15) (22,4) (8,15) (12,29) (26,19) (1,14) (24,25) (30,2) (17,14) (18,7) (19,18) (11,5) (20,17) (3,30)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "207"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (20,5) (2,9) (3,20) (24,21) (17,5) (14,9) (6,8) (20,21) (15,14) (13,9) (0,1) (23,16) (13,25) (20,2) (20,8) (22,10) (21,10) (0,18) (16,15) (0,2) (16,12) (19,18) (7,4) (17,11) (16,19) (1,5) (15,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "208"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (4,9) (21,2) (3,5) (23,5) (6,24) (23,26) (8,28) (9,18) (31,7) (26,11) (20,1) (30,25) (16,31) (12,1) (22,19) (4,22) (24,27) (2,28) (30,5) (31,29) (22,13) (6,16) (15,10) (31,15) (21,29) (17,15) (10,14) (9,0) (29,3) (11,19) (12,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "209"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (19,14) (13,24) (17,11) (4,8) (7,27) (0,1) (22,15) (9,22) (12,19) (4,27) (0,7) (21,10) (6,25) (18,2) (2,0) (21,22) (27,18) (16,8) (2,1) (14,5) (0,19) (20,2) (10,2) (4,23) (10,13) (26,5) (11,27) (3,24) (6,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "210"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (13,16) (6,18) (11,18) (1,18) (16,10) (7,17) (3,18) (12,8) (10,1) (2,5) (17,1) (9,17) (8,3) (13,0) (15,14) (5,15) (18,2) (16,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "211"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,4) (1,0) (0,7) (5,1) (2,6) (0,6) (2,1) (3,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "212"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (23,18) (22,2) (27,25) (12,3) (16,27) (9,26) (9,20) (12,23) (21,23) (6,17) (24,28) (11,0) (14,13) (26,3) (19,20) (16,3) (24,4) (24,0) (28,14) (25,1) (2,15) (5,0) (8,10) (22,26) (26,13) (16,17) (10,23) (26,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "213"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (2,4) (6,9) (16,7) (0,12) (1,7) (12,17) (7,5) (2,0) (3,8) (13,2) (17,16) (9,14) (4,11) (9,1) (10,15) (12,3) (15,17)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "214"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (9,6) (15,2) (20,0) (2,23) (7,15) (6,2) (7,21) (23,18) (8,10) (3,22) (14,2) (5,7) (20,18) (16,8) (11,12) (19,17) (1,15) (5,12) (8,4) (10,17) (9,13) (22,20) (24,20) (8,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "215"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,5) (3,4) (2,0) (7,1) (4,1) (7,6) (2,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "216"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (11,33) (10,2) (12,28) (22,19) (29,15) (10,3) (13,23) (4,29) (26,16) (6,32) (9,5) (3,25) (9,17) (32,25) (30,7) (1,18) (21,3) (8,31) (30,28) (24,8) (20,32) (13,0) (23,14) (1,2) (10,27) (3,16) (5,34) (21,17) (23,29) (33,20) (12,14) (14,8) (22,8) (22,32)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "217"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (0,2) (5,2) (4,5) (0,4) (3,1) (3,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "218"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (29,8) (21,23) (5,30) (24,22) (27,3) (26,2) (17,12) (16,18) (32,28) (19,23) (4,15) (2,1) (20,4) (11,19) (29,16) (2,10) (0,13) (2,25) (31,11) (31,9) (0,6) (23,8) (10,13) (26,24) (15,28) (30,22) (18,26) (20,17) (8,27) (29,15) (31,14) (7,29)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "219"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,5) (12,0) (1,4) (6,4) (8,9) (10,7) (3,12) (7,11) (2,9) (4,3) (5,7) (2,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "220"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (17,1) (1,23) (8,26) (10,2) (11,28) (22,25) (18,22) (20,11) (13,9) (5,24) (15,18) (18,24) (4,6) (12,10) (23,25) (24,3) (13,8) (20,8) (4,14) (16,24) (0,17) (25,27) (16,19) (27,21) (27,10) (23,7) (11,3) (4,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "221"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (25,15) (5,21) (1,23) (17,25) (15,6) (6,24) (20,25) (6,18) (9,11) (1,0) (22,2) (2,7) (14,3) (12,10) (20,16) (20,26) (2,26) (12,1) (4,11) (4,13) (9,5) (4,8) (14,1) (15,0) (6,19) (1,13) (9,17)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "222"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (4,15) (14,13) (10,6) (12,2) (17,2) (6,14) (6,8) (2,4) (1,15) (17,7) (0,18) (12,0) (9,0) (5,3) (11,8) (3,12) (13,16) (0,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "223"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,2) (5,8) (9,8) (6,5) (4,2) (2,1) (1,0) (3,0) (5,7) (1,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "224"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (3,0) (5,17) (15,11) (9,15) (17,11) (12,13) (9,1) (10,0) (14,13) (2,0) (16,13) (6,4) (8,3) (1,2) (4,0) (7,11) (14,3) (5,12) (14,4) (1,0) (16,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "225"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (5,24) (24,22) (8,27) (23,1) (16,17) (7,1) (6,7) (23,14) (2,20) (16,7) (12,0) (4,2) (12,17) (25,24) (2,0) (8,3) (10,9) (3,26) (21,9) (12,18) (11,17) (13,3) (26,5) (15,4) (15,19) (8,11) (9,25)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "226"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (9,30) (1,21) (29,21) (15,14) (26,11) (6,29) (20,30) (25,16) (12,23) (18,30) (13,16) (23,14) (25,3) (9,7) (13,11) (17,3) (10,6) (14,4) (22,12) (28,20) (24,5) (1,8) (22,5) (27,17) (3,2) (8,14) (23,2) (10,7) (4,0) (24,19)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "227"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (13,12) (3,11) (11,6) (1,5) (12,11) (2,8) (2,5) (4,12) (10,8) (3,8) (4,9) (8,7) (0,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "228"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (11,10) (10,9) (2,0) (0,1) (4,8) (1,17) (2,8) (0,5) (11,8) (18,10) (7,11) (12,6) (20,13) (15,12) (19,2) (13,5) (10,20) (0,3) (3,10) (3,6) (4,16) (14,21) (16,21)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "229"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,22) (3,0) (17,13) (23,6) (0,1) (2,15) (0,8) (20,23) (10,11) (4,21) (1,12) (21,11) (24,7) (13,23) (17,24) (9,8) (2,0) (18,15) (3,18) (4,14) (5,2) (6,15) (18,16) (10,24) (8,15) (19,24)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "230"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,1) (9,6) (12,20) (13,17) (23,4) (2,0) (1,6) (3,0) (15,19) (14,5) (16,12) (18,21) (2,7) (9,2) (23,13) (17,24) (2,11) (0,4) (4,3) (11,23) (10,23) (5,9) (8,23) (21,12) (16,22) (17,15) (10,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "231"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (2,0) (3,0) (3,6) (2,8) (0,9) (7,10) (8,10) (1,2) (4,7) (4,3) (9,8) (5,10) (11,2) (4,0) (1,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "232"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (8,4) (26,13) (24,23) (16,28) (31,2) (6,5) (4,31) (2,5) (9,21) (19,6) (20,17) (16,1) (30,6) (25,15) (31,7) (18,3) (18,22) (28,11) (15,26) (29,10) (33,1) (8,18) (13,9) (29,20) (0,1) (32,27) (4,25) (0,7) (34,8) (32,22) (17,24) (24,28) (8,12) (20,14) (7,28)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "233"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (29,19) (12,1) (1,28) (24,14) (16,10) (14,28) (8,26) (0,20) (1,27) (11,19) (32,2) (18,22) (23,14) (29,3) (25,19) (13,32) (0,1) (21,30) (24,6) (30,7) (21,11) (20,18) (32,22) (28,15) (9,28) (24,11) (0,17) (5,21) (15,31) (10,9) (13,4) (4,8) (27,22)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "234"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,1) (2,0) (4,8) (1,8) (5,0) (4,9) (3,10) (8,6) (3,6) (0,7) (8,7) (4,0) (0,3) (5,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "235"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (4,11) (4,6) (8,2) (12,0) (8,3) (13,5) (5,7) (1,2) (4,9) (1,13) (10,0) (10,7) (0,1) (13,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "236"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (8,4) (0,2) (5,9) (15,6) (4,0) (3,14) (3,0) (2,17) (4,11) (1,0) (6,5) (6,16) (13,1) (0,15) (18,9) (1,2) (1,14) (4,13) (12,10) (1,12) (7,2) (11,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "237"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (4,15) (1,0) (2,15) (5,8) (7,1) (3,0) (14,6) (10,11) (13,17) (13,6) (10,0) (0,5) (15,8) (0,4) (0,8) (12,11) (4,9) (15,17) (0,2) (17,16) (2,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "238"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (22,18) (0,16) (14,3) (13,12) (13,17) (8,21) (16,13) (23,12) (2,1) (19,11) (15,19) (20,15) (11,7) (5,22) (21,0) (6,4) (9,1) (19,17) (22,9) (4,14) (3,10) (18,11) (14,19)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "239"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (8,12) (18,7) (10,2) (1,12) (17,9) (20,5) (17,0) (4,14) (4,19) (18,12) (6,5) (12,11) (7,0) (9,15) (13,18) (8,16) (5,10) (0,14) (10,4) (3,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "240"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (4,14) (0,8) (13,6) (18,11) (15,16) (17,3) (10,0) (10,11) (9,8) (12,1) (0,3) (7,2) (17,19) (20,3) (17,13) (15,6) (8,15) (5,18) (4,18) (1,0) (2,15) (0,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "241"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (13,6) (4,2) (11,5) (8,2) (0,9) (0,14) (0,1) (7,12) (9,4) (3,5) (2,12) (4,6) (11,10) (3,0) (8,1) (0,2) (13,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "242"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (7,3) (5,1) (3,0) (5,7) (2,0) (4,2) (10,8) (1,0) (7,0) (5,4) (1,8) (6,10) (3,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "243"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (5,15) (2,0) (1,9) (3,17) (8,9) (19,16) (5,13) (6,13) (14,7) (2,11) (14,13) (9,12) (15,3) (14,20) (14,18) (5,11) (7,10) (8,17) (16,4) (2,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "244"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (5,1) (6,3) (2,11) (5,12) (11,10) (4,2) (2,3) (7,11) (1,9) (4,8) (0,1) (1,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "245"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (9,12) (8,3) (1,5) (15,13) (2,13) (4,14) (3,14) (12,14) (11,6) (1,4) (14,7) (2,0) (2,1) (10,9) (11,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "246"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (10,2) (12,20) (16,3) (12,3) (15,23) (18,0) (6,22) (23,9) (6,23) (7,23) (8,0) (13,3) (5,10) (14,0) (1,0) (18,6) (2,22) (20,17) (13,14) (16,21) (17,4) (16,11) (9,19)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "247"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (2,1) (0,4) (7,10) (7,14) (0,14) (8,4) (0,15) (9,6) (11,12) (9,10) (11,3) (2,5) (5,11) (4,12) (7,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "248"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (9,22) (5,11) (5,24) (3,7) (3,10) (6,22) (1,13) (16,25) (12,18) (20,22) (13,12) (17,4) (2,16) (15,9) (12,24) (14,7) (0,23) (3,5) (20,12) (8,27) (28,24) (21,18) (27,18) (17,0) (16,22) (9,26) (7,19) (3,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "249"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,8) (3,0) (7,0) (4,3) (1,0) (2,4) (1,5) (2,0) (9,0) (0,4) (7,3) (2,6) (3,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "250"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (4,7) (8,10) (9,2) (10,9) (1,7) (11,3) (3,10) (5,8) (1,0) (0,6) (3,0) (4,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "251"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,5) (9,7) (6,1) (4,5) (6,11) (10,7) (6,12) (9,5) (8,3) (2,1) (4,8) (8,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "252"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (16,24) (5,21) (30,20) (32,33) (14,7) (31,23) (4,12) (12,26) (26,13) (2,25) (8,5) (17,0) (30,5) (20,25) (13,24) (12,28) (21,11) (10,15) (3,24) (0,34) (14,8) (6,11) (13,9) (11,29) (16,15) (33,18) (31,27) (9,29) (5,22) (33,5) (17,2) (19,34) (1,25) (23,24)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "253"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (9,13) (11,2) (0,19) (20,0) (22,2) (12,24) (25,5) (5,10) (12,14) (9,10) (7,6) (10,20) (15,11) (0,16) (6,25) (1,15) (25,17) (22,18) (5,3) (23,11) (4,17) (15,21) (14,10) (26,2) (8,10) (22,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "254"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (13,4) (17,22) (28,8) (22,4) (7,26) (10,21) (25,4) (14,24) (13,21) (28,19) (16,15) (20,10) (12,1) (2,0) (19,5) (6,2) (1,0) (5,14) (21,23) (5,9) (13,14) (0,27) (7,30) (27,3) (6,10) (20,11) (22,3) (12,0) (29,10) (24,16) (4,30) (18,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "255"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (13,12) (8,11) (11,14) (17,10) (17,7) (17,0) (12,1) (1,19) (20,16) (18,19) (1,0) (0,11) (9,11) (0,4) (12,3) (15,12) (0,2) (7,12) (4,17) (3,0) (13,6) (16,5) (2,8) (7,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "256"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (21,3) (11,6) (9,7) (0,2) (11,0) (18,17) (0,16) (10,7) (2,20) (0,1) (8,19) (14,20) (1,17) (14,15) (18,13) (8,11) (1,12) (13,5) (3,10) (15,21) (22,9) (6,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "257"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (4,0) (5,3) (5,1) (2,1) (4,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "258"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,2) (4,8) (0,1) (2,3) (0,5) (3,5) (1,2) (6,4) (2,4) (0,3) (0,4) (7,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "259"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (9,16) (1,15) (4,22) (2,6) (4,19) (11,20) (21,18) (13,23) (14,22) (8,12) (5,7) (6,0) (5,16) (12,24) (17,0) (8,23) (0,1) (25,1) (11,25) (11,22) (10,14) (3,10) (11,8) (21,7) (3,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "260"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (15,7) (24,6) (4,9) (22,23) (25,21) (16,22) (3,17) (11,1) (0,15) (19,4) (24,18) (5,3) (10,21) (4,12) (12,8) (4,7) (0,2) (1,21) (3,13) (20,4) (14,26) (17,23) (14,23) (1,4) (7,17) (24,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "261"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (13,16) (17,3) (24,11) (1,21) (5,22) (14,15) (3,2) (20,6) (10,7) (19,5) (23,14) (3,25) (7,9) (12,23) (23,2) (10,6) (8,1) (17,26) (4,14) (25,16) (13,11) (0,4) (14,8) (24,18) (27,9) (12,22) (20,21)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "262"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (2,3) (10,6) (17,22) (17,3) (19,11) (23,12) (14,4) (21,20) (16,13) (8,14) (22,5) (1,21) (14,7) (24,9) (4,0) (23,2) (24,10) (15,5) (11,13) (3,16) (1,8) (20,6) (14,23) (12,18)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "263"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (8,3) (10,0) (3,7) (0,1) (3,1) (3,6) (0,9) (0,5) (9,6) (4,2) (6,4) (0,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "264"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (6,3) (4,5) (0,3) (7,3) (0,1) (4,0) (5,2) (0,5) (2,0) (1,7) (2,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "265"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (10,26) (1,23) (24,25) (17,0) (1,14) (22,8) (10,21) (10,3) (9,7) (11,19) (13,23) (15,7) (2,5) (15,11) (6,4) (22,16) (1,16) (0,12) (2,6) (9,4) (20,16) (25,26) (22,15) (17,24) (0,19) (18,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "266"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (2,0) (3,2) (12,9) (7,11) (4,1) (6,9) (1,15) (11,8) (2,4) (0,1) (10,14) (2,11) (5,15) (6,0) (13,15) (14,8) (8,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "267"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (22,1) (19,15) (8,6) (7,2) (20,25) (7,11) (5,16) (10,26) (21,16) (13,0) (17,2) (13,26) (1,27) (27,9) (22,19) (14,17) (12,14) (14,18) (15,20) (9,3) (24,10) (9,4) (17,23) (13,7) (8,14) (6,20) (16,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "268"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (1,13) (2,17) (0,2) (12,7) (2,6) (19,16) (21,19) (9,3) (20,5) (17,15) (7,16) (10,0) (8,11) (21,3) (7,8) (13,18) (4,3) (0,1) (20,18) (7,6) (14,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "269"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (4,3) (2,0) (3,0) (1,4) (2,5) (0,5) (1,0) (1,2) (4,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "270"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (1,7) (0,6) (1,3) (4,5) (1,0) (0,4) (0,2) (7,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "271"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (2,4) (0,3) (1,0) (1,7) (7,4) (9,3) (0,2) (5,0) (5,6) (4,0) (5,9) (8,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "272"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,0) (0,7) (5,2) (0,3) (5,9) (8,5) (4,9) (0,2) (3,8) (6,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "273"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (10,1) (25,11) (10,19) (13,29) (29,6) (2,7) (4,9) (5,29) (4,7) (14,5) (20,28) (16,22) (8,1) (27,17) (25,28) (0,12) (21,17) (23,3) (28,13) (29,23) (0,19) (3,18) (26,2) (23,21) (8,7) (11,24) (15,14) (20,22) (19,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "274"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (12,15) (26,12) (19,15) (17,25) (24,26) (2,19) (7,6) (15,22) (8,17) (11,4) (3,18) (4,9) (7,21) (16,2) (0,18) (22,6) (5,17) (11,15) (10,19) (7,1) (15,17) (23,17) (8,20) (18,14) (13,20) (26,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "275"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (18,3) (0,4) (18,9) (16,6) (9,5) (21,19) (0,6) (3,17) (19,16) (20,7) (1,11) (1,9) (15,18) (14,13) (2,12) (20,6) (13,3) (0,2) (1,8) (1,0) (12,8) (15,10) (18,21)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "276"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,2) (18,9) (16,8) (23,5) (18,2) (20,0) (14,15) (0,3) (1,10) (4,5) (23,13) (22,12) (15,17) (24,4) (21,4) (8,7) (12,1) (6,9) (1,0) (20,7) (7,1) (14,10) (9,3) (4,11) (19,5) (13,0) (21,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "277"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (4,0) (22,17) (15,2) (22,19) (24,2) (22,25) (0,1) (0,11) (9,8) (3,0) (10,14) (1,4) (10,21) (23,4) (3,23) (0,8) (20,17) (15,16) (12,8) (12,24) (18,20) (19,16) (7,3) (22,10) (11,3) (24,13) (17,6) (6,5) (0,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "278"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,3) (0,3) (5,0) (7,3) (6,3) (2,4) (6,9) (6,4) (8,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "279"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (8,2) (19,1) (17,0) (22,6) (18,22) (0,11) (18,16) (1,12) (13,8) (12,17) (11,10) (11,9) (17,4) (17,13) (20,7) (7,5) (5,16) (12,7) (15,11) (19,21) (14,12) (3,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "280"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,4) (7,6) (5,6) (3,7) (1,7) (2,0) (4,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "281"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (17,23) (31,13) (0,30) (3,0) (22,13) (7,26) (19,21) (24,8) (14,10) (25,24) (24,11) (16,20) (9,1) (12,13) (4,13) (3,8) (9,24) (16,13) (11,15) (19,5) (4,0) (12,6) (2,0) (6,14) (29,6) (0,1) (18,4) (26,1) (28,30) (11,28) (8,4) (23,3) (1,21) (27,15)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "282"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (16,7) (2,0) (11,12) (19,4) (0,3) (1,0) (5,16) (14,10) (9,15) (11,1) (19,11) (10,15) (20,13) (0,5) (18,0) (6,0) (9,13) (12,17) (18,3) (20,12) (2,1) (16,19) (8,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "283"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (16,22) (2,11) (16,11) (9,2) (13,0) (25,17) (1,3) (1,0) (10,19) (23,12) (7,25) (20,14) (11,24) (10,15) (6,11) (7,20) (4,17) (13,12) (9,21) (15,2) (17,19) (8,19) (2,5) (19,18) (3,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "284"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (14,4) (2,3) (21,1) (13,16) (11,13) (14,23) (5,15) (12,23) (11,19) (14,7) (6,10) (4,0) (1,8) (17,3) (18,12) (20,21) (1,0) (2,0) (3,16) (24,9) (8,14) (24,10) (5,22) (20,6) (22,17) (23,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "285"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,16) (4,13) (2,1) (1,0) (2,10) (0,14) (7,4) (10,13) (2,11) (12,4) (9,6) (15,6) (14,5) (5,2) (4,0) (0,2) (10,9) (3,8) (8,11) (0,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "286"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (12,11) (16,13) (2,3) (10,7) (19,7) (8,1) (17,18) (14,2) (5,15) (14,4) (12,5) (3,16) (6,10) (6,1) (0,4) (9,14) (14,8) (13,11) (3,17)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "287"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (14,11) (0,3) (5,17) (11,9) (10,20) (7,12) (13,18) (1,16) (12,19) (9,6) (13,8) (2,13) (4,12) (16,10) (15,8) (17,3) (7,0) (4,20) (1,0) (2,0) (16,8) (9,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "288"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (28,20) (20,27) (6,8) (7,14) (32,25) (18,32) (21,24) (6,17) (9,21) (22,12) (28,13) (29,4) (17,26) (19,1) (16,11) (31,24) (9,2) (23,5) (12,4) (0,17) (12,30) (13,22) (0,15) (19,5) (7,23) (12,3) (5,11) (16,31) (20,10) (27,26) (17,1) (30,18)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "289"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (2,17) (24,25) (2,4) (3,5) (23,18) (14,13) (20,15) (18,6) (1,0) (14,3) (14,12) (0,14) (25,28) (26,16) (29,10) (27,1) (22,27) (11,24) (15,16) (28,29) (0,3) (19,25) (0,2) (17,25) (14,9) (16,21) (20,19) (9,4) (8,27) (7,17) (5,6) (27,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "290"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,16) (6,2) (5,4) (2,7) (3,0) (20,8) (5,18) (5,13) (12,16) (9,10) (8,17) (15,0) (18,1) (5,11) (14,5) (3,5) (20,15) (7,14) (15,19) (9,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "291"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (8,7) (0,1) (2,1) (3,0) (6,2) (3,4) (0,11) (9,8) (0,2) (6,5) (10,1) (3,6) (8,11) (0,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "292"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (1,0) (11,8) (2,3) (10,7) (0,2) (11,3) (0,3) (2,10) (6,9) (2,9) (7,12) (2,4) (1,11) (8,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "293"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (13,3) (11,6) (2,6) (10,12) (4,0) (7,5) (1,8) (2,1) (2,0) (1,7) (12,9) (8,3) (0,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "294"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (12,9) (13,10) (9,11) (8,3) (7,5) (1,0) (0,9) (5,8) (0,3) (5,2) (4,7) (10,6) (4,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "295"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (15,17) (3,9) (1,9) (13,10) (14,9) (16,4) (17,14) (7,13) (5,7) (18,8) (8,14) (17,2) (11,16) (6,14) (2,7) (10,16) (0,13) (12,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "296"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (11,9) (7,13) (13,12) (2,4) (0,8) (5,12) (6,11) (3,11) (10,11) (10,8) (9,1) (4,5) (0,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "297"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (19,9) (6,14) (29,24) (31,21) (18,31) (29,7) (25,24) (17,22) (8,27) (1,29) (26,12) (16,17) (5,15) (16,5) (8,12) (9,12) (30,10) (3,31) (3,19) (11,2) (13,22) (28,0) (27,4) (26,17) (31,28) (22,20) (19,1) (29,10) (0,1) (23,1) (30,2) (20,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "298"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (3,1) (3,0) (3,7) (0,1) (6,3) (2,0) (4,2) (6,4) (6,8) (0,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "299"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (18,20) (19,16) (13,1) (2,0) (1,0) (10,0) (3,4) (6,7) (6,2) (15,17) (8,7) (0,22) (20,5) (21,3) (19,0) (13,18) (8,11) (9,3) (14,4) (2,17) (2,21) (3,0) (12,7) (16,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "300"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (19,10) (20,16) (1,16) (17,14) (2,0) (10,18) (11,12) (12,9) (17,13) (8,12) (4,7) (7,0) (18,21) (6,17) (16,17) (21,8) (3,5) (5,7) (15,14) (11,20) (8,7) (2,17) (0,1) (0,3) (0,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "301"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (16,1) (15,10) (2,7) (10,5) (1,8) (4,7) (4,6) (0,3) (3,14) (14,0) (2,0) (12,5) (2,11) (8,7) (13,5) (1,13) (1,0) (9,0) (3,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "302"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (16,0) (6,11) (8,19) (20,12) (15,13) (4,0) (4,5) (18,16) (19,17) (19,11) (9,1) (0,3) (17,13) (2,0) (3,7) (0,14) (4,14) (10,19) (2,1) (0,1) (11,18) (15,9) (3,14) (13,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "303"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (4,28) (6,10) (8,17) (14,3) (18,5) (5,4) (11,23) (1,0) (10,26) (15,26) (15,12) (25,19) (7,11) (23,27) (0,2) (21,9) (9,10) (16,1) (13,17) (26,2) (21,4) (12,16) (9,7) (28,0) (24,22) (21,14) (19,0) (24,26) (0,17) (14,20)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "304"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (9,3) (4,5) (0,3) (10,5) (6,0) (2,8) (5,1) (0,8) (1,6) (9,7) (11,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "305"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (9,17) (21,1) (26,9) (15,5) (20,33) (4,29) (11,2) (2,0) (20,11) (17,8) (13,27) (26,4) (13,31) (5,19) (9,3) (16,32) (27,4) (12,31) (25,0) (4,1) (0,3) (30,24) (1,0) (30,8) (7,19) (17,6) (23,21) (28,18) (19,2) (14,16) (22,16) (0,7) (2,3) (7,18) (22,20) (10,26)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "306"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (7,0) (14,10) (9,4) (11,1) (13,5) (9,16) (15,3) (7,8) (6,7) (15,2) (13,8) (9,0) (14,7) (11,0) (13,12) (9,15)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "307"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (10,7) (1,17) (13,11) (18,14) (15,14) (5,6) (9,13) (16,9) (14,3) (2,19) (15,7) (1,21) (4,12) (9,6) (20,9) (11,0) (12,7) (7,9) (10,17) (8,1) (10,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "308"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (1,3) (1,0) (0,5) (5,1) (2,0) (7,5) (5,2) (3,6) (4,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "309"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (9,10) (0,2) (6,7) (0,9) (8,1) (2,5) (3,8) (2,8) (4,8) (0,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "310"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,2) (6,4) (1,0) (1,5) (9,7) (8,1) (5,0) (5,7) (3,6) (1,6) (0,10) (10,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "311"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,14) (2,0) (27,4) (1,12) (4,23) (10,12) (17,9) (2,10) (22,15) (24,20) (9,16) (12,27) (24,25) (23,28) (18,0) (6,5) (11,18) (8,12) (22,18) (0,26) (14,4) (7,21) (19,23) (26,21) (3,7) (0,1) (28,5) (24,7) (28,13) (17,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "312"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (8,14) (7,20) (16,19) (15,13) (9,1) (20,3) (0,6) (1,0) (15,11) (9,18) (2,12) (21,6) (0,4) (6,16) (21,18) (18,3) (13,3) (10,19) (8,1) (10,22) (1,12) (17,18) (9,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "313"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (14,8) (8,1) (9,11) (3,5) (2,1) (8,0) (5,12) (14,6) (6,5) (4,9) (13,10) (9,7) (1,4) (13,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "314"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (6,2) (1,14) (3,6) (2,0) (0,1) (5,6) (4,13) (4,0) (11,8) (1,3) (11,1) (2,12) (8,7) (3,0) (8,9) (13,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "315"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (15,18) (2,0) (23,13) (15,5) (12,9) (10,7) (5,13) (14,7) (6,13) (3,23) (14,16) (4,16) (0,1) (5,22) (14,19) (4,0) (11,21) (8,9) (22,2) (8,17) (3,17) (20,2) (23,11) (4,22) (9,1) (3,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "316"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (24,11) (8,7) (16,0) (18,6) (31,4) (20,6) (18,13) (21,29) (1,14) (23,10) (0,3) (20,25) (17,20) (0,6) (25,24) (0,1) (10,30) (7,14) (5,33) (4,0) (9,11) (7,32) (2,18) (32,26) (6,4) (17,32) (19,24) (12,14) (15,1) (2,33) (3,26) (7,10) (22,4) (18,21) (27,19) (0,2) (28,22)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "317"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (28,15) (23,9) (17,23) (3,10) (4,34) (2,13) (29,8) (31,8) (27,5) (23,7) (4,6) (30,22) (15,20) (0,3) (27,12) (1,4) (12,0) (7,20) (8,6) (16,26) (21,28) (16,25) (34,32) (3,1) (4,0) (11,12) (0,1) (30,4) (2,1) (34,33) (14,17) (18,1) (6,11) (19,24) (2,0) (26,34) (15,34) (11,19)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "318"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (6,27) (32,7) (3,11) (15,1) (2,31) (13,5) (19,32) (2,17) (20,32) (8,9) (15,22) (30,13) (29,0) (10,21) (1,18) (12,26) (23,24) (8,3) (27,14) (0,2) (13,8) (30,16) (29,20) (1,30) (25,26) (1,12) (14,9) (23,15) (10,27) (33,20) (18,7) (4,12) (24,28)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "319"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (7,1) (11,9) (2,3) (7,10) (7,11) (2,0) (9,5) (5,4) (3,11) (2,6) (8,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "320"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (16,10) (9,20) (11,16) (20,5) (7,3) (8,4) (1,5) (16,17) (15,16) (0,2) (20,19) (6,15) (14,15) (14,9) (20,2) (18,0) (7,20) (5,12) (19,13) (8,17) (0,1) (10,18)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "321"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (14,3) (16,5) (11,6) (14,13) (0,2) (16,0) (0,3) (5,10) (5,7) (5,17) (12,2) (0,9) (5,6) (0,1) (12,1) (9,4) (2,4) (15,14) (6,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "322"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,11) (9,13) (5,4) (4,9) (1,12) (1,0) (13,3) (3,11) (0,15) (3,0) (2,10) (6,10) (1,8) (4,7) (0,2) (10,8) (11,8) (14,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "323"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (16,0) (8,14) (5,16) (2,14) (13,6) (20,1) (1,10) (4,15) (20,19) (18,6) (11,17) (16,4) (12,7) (8,11) (7,9) (6,19) (20,9) (4,1) (14,0) (3,18)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "324"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (2,0) (32,5) (8,5) (6,11) (20,30) (21,5) (1,25) (20,25) (14,7) (13,26) (33,31) (16,24) (11,21) (9,13) (27,12) (11,29) (0,17) (31,22) (12,26) (24,23) (23,28) (1,0) (33,0) (9,29) (13,24) (30,5) (2,25) (16,15) (33,18) (8,14) (12,4) (15,10) (3,24) (2,17) (5,19)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "325"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (23,13) (25,7) (19,21) (27,6) (3,21) (8,6) (20,5) (6,26) (4,14) (7,23) (0,23) (10,19) (17,24) (15,1) (12,1) (17,11) (19,16) (6,2) (13,22) (16,5) (9,13) (22,27) (23,1) (13,20) (21,24) (18,15) (4,24)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "326"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,4) (8,3) (4,1) (2,5) (8,0) (0,6) (4,6) (1,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "327"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,14) (31,22) (1,18) (7,24) (28,6) (4,18) (8,1) (15,16) (13,25) (16,20) (10,14) (4,29) (24,11) (17,4) (27,29) (23,0) (1,11) (22,21) (0,20) (12,2) (12,9) (13,3) (0,2) (23,26) (19,32) (32,25) (22,27) (25,6) (19,17) (6,33) (27,16) (5,16) (27,30) (12,34)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "328"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (9,3) (0,1) (1,11) (2,10) (4,2) (5,8) (11,10) (0,4) (11,7) (6,9) (2,0) (3,2) (8,2) (0,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "329"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (3,0) (0,16) (32,23) (28,3) (19,16) (30,12) (2,7) (29,23) (21,32) (21,4) (5,15) (7,20) (12,25) (11,15) (2,0) (19,13) (30,17) (24,16) (12,15) (27,7) (29,18) (10,15) (31,9) (31,8) (6,12) (1,0) (31,12) (11,1) (10,28) (22,18) (11,14) (0,21) (26,16) (11,20) (13,31)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "330"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (29,0) (7,21) (12,28) (15,1) (18,10) (6,23) (15,9) (22,10) (11,28) (20,12) (13,30) (2,19) (14,7) (14,4) (17,5) (6,1) (14,19) (28,6) (12,24) (23,29) (25,15) (27,28) (16,15) (25,17) (14,17) (8,9) (3,4) (26,29) (23,18) (30,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "331"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (13,18) (9,17) (0,18) (19,9) (29,10) (7,3) (4,28) (0,26) (27,24) (29,23) (2,10) (7,21) (8,17) (7,24) (6,5) (12,1) (22,24) (0,14) (15,28) (12,27) (5,28) (20,23) (4,23) (26,21) (16,22) (8,12) (11,12) (25,18) (4,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "332"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (3,6) (5,8) (0,4) (8,0) (1,8) (10,8) (1,7) (10,2) (3,9) (6,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "333"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (22,20) (14,25) (1,0) (31,5) (21,19) (30,6) (9,30) (10,22) (5,14) (29,12) (16,6) (7,27) (25,26) (0,24) (4,11) (15,27) (10,2) (15,0) (8,6) (23,24) (1,9) (23,13) (2,18) (0,2) (19,30) (4,23) (16,31) (28,9) (20,17) (27,29) (17,21) (1,23) (3,26)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "334"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (10,13) (2,1) (11,9) (4,1) (3,5) (8,0) (9,4) (6,5) (8,14) (1,8) (12,5) (9,7) (6,13) (14,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "335"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (8,20) (12,18) (5,10) (4,0) (0,12) (14,11) (21,19) (30,28) (16,4) (2,0) (0,21) (0,1) (27,22) (15,24) (2,8) (29,7) (7,17) (15,8) (3,0) (3,21) (21,9) (23,11) (22,26) (5,11) (27,19) (25,14) (4,19) (1,15) (4,14) (0,17) (11,13) (16,6) (20,25) (28,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "336"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (8,3) (5,7) (7,9) (0,7) (4,7) (8,6) (8,1) (3,2) (2,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "337"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (4,5) (0,1) (5,3) (17,8) (0,2) (1,18) (5,14) (0,3) (0,5) (5,13) (15,0) (16,12) (9,10) (7,2) (5,8) (5,11) (18,15) (0,4) (14,7) (6,2) (0,16) (11,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "338"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (13,9) (12,4) (2,7) (0,11) (9,6) (14,3) (1,13) (9,12) (2,10) (5,6) (17,9) (9,10) (16,14) (14,15) (15,7) (7,11) (8,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "339"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (11,8) (8,17) (14,6) (19,9) (0,13) (11,2) (11,0) (5,0) (0,4) (3,20) (18,5) (8,4) (10,12) (6,1) (15,0) (7,6) (12,7) (2,0) (0,3) (18,12) (9,2) (0,1) (16,20)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "340"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (4,21) (14,12) (6,13) (0,7) (0,1) (15,13) (8,17) (15,3) (9,10) (8,7) (10,21) (16,22) (7,11) (7,19) (22,23) (1,11) (4,23) (9,0) (15,2) (9,5) (21,13) (18,20) (14,0) (20,9) (0,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "341"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (6,8) (4,8) (10,5) (10,3) (4,9) (0,7) (0,2) (3,6) (7,8) (8,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "342"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (12,2) (14,12) (15,0) (11,9) (6,4) (10,7) (10,15) (15,1) (8,0) (14,10) (11,13) (5,3) (6,9) (10,5) (2,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "343"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,3) (6,5) (7,1) (8,2) (0,3) (8,4) (0,1) (8,7) (5,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "344"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (3,16) (24,5) (3,34) (10,16) (0,2) (29,9) (2,27) (32,7) (13,18) (12,21) (7,6) (21,24) (3,11) (24,0) (8,1) (7,1) (14,10) (28,9) (4,23) (9,6) (19,14) (4,13) (20,10) (15,0) (17,25) (15,1) (30,8) (24,17) (26,28) (11,9) (18,27) (1,0) (33,2) (18,22) (30,23) (31,20)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "345"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (24,14) (28,26) (19,32) (3,0) (29,15) (31,26) (0,6) (4,0) (26,29) (20,14) (7,12) (20,22) (23,16) (15,11) (25,13) (2,10) (3,9) (7,21) (3,1) (14,29) (18,22) (0,2) (16,22) (17,21) (1,0) (31,5) (17,25) (30,14) (13,22) (9,23) (5,0) (19,27) (8,15) (5,32) (4,13) (10,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "346"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (19,9) (7,20) (18,8) (0,6) (8,27) (21,14) (24,30) (2,31) (31,6) (0,2) (18,1) (15,12) (29,11) (0,15) (29,16) (9,2) (21,23) (16,20) (12,27) (32,18) (5,0) (1,0) (31,4) (28,2) (14,8) (25,22) (23,17) (25,2) (10,12) (29,9) (3,2) (31,13) (30,18) (26,32)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "347"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (3,10) (6,0) (2,1) (9,7) (7,4) (3,12) (13,3) (7,1) (11,0) (6,2) (1,0) (8,13) (10,0) (13,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "348"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (14,4) (12,3) (11,13) (11,15) (2,0) (9,14) (5,2) (14,5) (5,1) (0,1) (15,6) (12,8) (7,8) (14,6) (14,10) (7,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "349"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (11,6) (10,7) (9,2) (0,2) (4,5) (4,1) (1,7) (1,3) (6,10) (7,8) (7,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "350"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (4,1) (7,0) (4,6) (1,3) (6,0) (3,2) (5,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "351"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (17,18) (3,16) (0,14) (10,8) (16,2) (8,13) (11,5) (1,17) (17,5) (14,10) (15,11) (1,3) (13,7) (12,15) (3,4) (6,18) (7,9) (17,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "352"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (4,14) (16,12) (2,11) (5,2) (4,13) (11,14) (13,7) (9,13) (1,0) (6,10) (3,1) (3,5) (13,16) (14,8) (15,10) (10,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "353"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (19,13) (4,25) (25,22) (29,32) (22,5) (6,1) (28,14) (21,26) (9,18) (10,2) (26,18) (30,13) (29,10) (6,31) (20,7) (6,13) (17,28) (24,6) (24,4) (19,9) (2,0) (4,16) (12,28) (32,23) (20,15) (9,12) (8,26) (27,11) (4,3) (9,20) (23,16) (27,26)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "354"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (12,19) (13,2) (12,18) (20,13) (17,6) (3,0) (5,2) (9,18) (4,11) (16,12) (25,8) (23,17) (8,24) (28,27) (16,14) (19,1) (23,15) (10,11) (7,14) (28,26) (21,0) (25,1) (25,15) (3,22) (10,8) (0,17) (13,21) (0,26)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "355"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,6) (8,0) (7,5) (2,4) (3,2) (8,3) (4,1) (1,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "356"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (8,7) (10,29) (27,0) (2,5) (26,4) (18,21) (6,16) (0,2) (19,13) (4,12) (3,29) (33,4) (13,22) (17,21) (4,23) (25,17) (26,16) (1,9) (30,26) (9,14) (9,32) (21,19) (5,25) (20,3) (8,21) (9,15) (11,22) (20,5) (1,0) (14,28) (34,32) (30,5) (31,29) (0,8) (24,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "357"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,6) (6,10) (3,6) (8,1) (1,9) (10,15) (13,9) (1,11) (0,1) (2,12) (0,4) (9,5) (7,15) (3,13) (14,3) (12,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "358"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (3,9) (4,13) (12,13) (11,4) (1,0) (1,14) (8,1) (10,7) (4,7) (12,3) (14,6) (12,8) (6,5) (4,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "359"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,2) (4,16) (17,14) (14,9) (1,9) (17,2) (2,7) (1,0) (13,0) (7,13) (15,14) (7,5) (6,20) (17,16) (10,18) (14,8) (13,19) (16,12) (3,9) (8,6) (10,20) (14,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "360"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (3,17) (10,25) (0,13) (25,16) (5,2) (4,2) (3,0) (20,12) (6,18) (0,14) (22,14) (16,19) (19,15) (7,0) (2,0) (23,16) (8,6) (11,9) (19,9) (12,21) (12,1) (1,0) (7,24) (1,8) (4,20) (19,5) (17,20)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "361"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (2,0) (11,8) (19,16) (4,0) (12,11) (9,18) (1,0) (14,6) (0,3) (1,19) (6,0) (18,17) (3,2) (19,14) (4,6) (17,12) (13,17) (18,7) (10,7) (5,7) (14,18) (7,15) (3,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "362"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (21,10) (14,17) (21,16) (13,14) (10,0) (10,13) (2,0) (6,2) (0,11) (5,8) (16,12) (12,1) (19,5) (14,5) (20,7) (19,4) (20,9) (4,18) (15,0) (10,6) (7,3) (4,3) (1,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "363"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (15,14) (7,10) (15,21) (14,19) (6,0) (3,10) (18,8) (0,3) (21,7) (11,0) (9,1) (4,0) (0,13) (11,6) (17,16) (18,12) (3,20) (0,1) (17,1) (13,5) (5,0) (6,4) (2,0) (20,2) (8,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "364"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,7) (0,18) (1,0) (8,15) (13,0) (4,3) (9,11) (8,3) (5,2) (19,13) (11,12) (17,8) (17,1) (14,19) (17,13) (0,16) (13,9) (6,13) (15,10) (5,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "365"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (11,5) (2,11) (17,8) (10,7) (14,17) (8,9) (16,4) (15,3) (3,13) (2,0) (5,18) (0,3) (15,5) (1,9) (9,12) (6,13) (0,1) (7,14) (16,14) (2,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "366"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,4) (19,0) (15,8) (1,17) (19,6) (17,5) (16,19) (4,10) (21,20) (7,16) (13,4) (16,18) (20,6) (0,12) (20,3) (14,2) (9,17) (8,6) (22,3) (20,2) (18,1) (11,15)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "367"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (6,5) (1,4) (15,14) (19,27) (1,25) (7,17) (7,3) (27,10) (27,21) (3,0) (9,13) (2,20) (6,8) (30,17) (26,14) (5,18) (24,14) (29,0) (0,10) (5,22) (13,21) (26,12) (1,0) (13,23) (1,2) (16,8) (6,21) (17,9) (2,0) (15,11) (5,31) (17,28) (14,28) (1,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "368"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,3) (5,6) (4,8) (2,7) (5,1) (4,12) (0,9) (0,6) (12,11) (3,7) (4,3) (10,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "369"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (16,12) (6,15) (0,12) (4,2) (12,1) (5,7) (17,16) (17,2) (18,15) (7,4) (2,19) (11,7) (8,14) (19,13) (8,12) (10,5) (9,19) (3,6) (6,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "370"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (18,15) (15,11) (21,19) (2,5) (24,13) (17,0) (13,23) (8,5) (9,20) (11,14) (25,28) (25,11) (0,23) (17,1) (3,4) (9,6) (21,16) (26,19) (13,9) (7,13) (17,8) (26,3) (13,11) (26,0) (27,10) (27,14) (8,22) (0,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "371"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (5,2) (4,1) (6,3) (0,4) (3,0) (5,7) (0,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "372"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (10,14) (1,0) (7,3) (3,4) (7,15) (5,8) (0,9) (0,10) (14,5) (12,0) (13,4) (16,14) (2,6) (5,4) (2,0) (16,11) (12,1) (10,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "373"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (9,10) (14,16) (1,6) (1,5) (3,2) (17,11) (9,8) (7,5) (8,6) (11,2) (12,16) (5,13) (17,14) (12,13) (0,1) (11,15) (4,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "374"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (10,7) (7,1) (5,4) (2,8) (4,9) (5,3) (3,8) (7,0) (2,6) (0,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "375"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (21,27) (5,6) (8,16) (0,10) (17,28) (24,33) (21,6) (23,13) (31,0) (10,27) (1,4) (2,0) (5,18) (9,13) (0,1) (9,17) (15,14) (15,11) (1,2) (25,14) (12,1) (14,26) (20,2) (21,13) (8,6) (1,30) (12,26) (27,19) (22,5) (32,17) (3,7) (17,7) (3,0) (32,29) (5,24) (28,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "376"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,2) (13,16) (1,28) (11,21) (24,22) (29,21) (24,4) (3,19) (15,0) (7,4) (12,1) (15,4) (22,25) (23,27) (9,12) (13,6) (3,5) (10,4) (14,16) (20,7) (4,26) (30,6) (1,4) (3,17) (30,18) (23,17) (21,1) (24,8) (17,7) (23,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "377"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (13,3) (2,6) (8,3) (5,7) (2,0) (1,0) (6,11) (0,3) (12,9) (5,0) (8,1) (10,0) (1,2) (7,1) (4,0) (10,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "378"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (6,13) (11,4) (6,5) (12,4) (0,6) (7,2) (0,9) (4,8) (4,3) (3,10) (5,1) (13,12) (3,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "379"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (4,20) (22,17) (25,22) (12,7) (14,17) (12,4) (16,11) (18,21) (4,19) (19,15) (22,24) (6,23) (7,10) (22,23) (11,5) (9,11) (3,19) (22,13) (26,10) (23,9) (2,25) (0,20) (25,27) (8,5) (22,0) (2,1) (19,21)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "380"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (12,24) (8,29) (0,26) (0,2) (25,14) (33,13) (28,9) (14,23) (10,33) (4,20) (29,11) (14,6) (14,19) (3,0) (2,16) (30,12) (17,21) (16,21) (15,28) (31,23) (8,22) (2,26) (22,23) (18,1) (33,28) (18,27) (32,5) (32,14) (27,10) (25,28) (0,1) (8,7) (3,18) (30,7) (29,4) (7,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "381"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (7,30) (15,21) (2,7) (18,3) (5,1) (15,16) (12,13) (10,2) (9,1) (25,20) (16,26) (13,1) (18,0) (30,4) (17,15) (23,29) (27,13) (26,22) (5,25) (19,18) (11,1) (14,26) (30,28) (6,14) (11,23) (8,20) (15,10) (4,27) (24,8) (6,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "382"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (14,20) (11,9) (18,9) (17,1) (14,25) (8,14) (13,9) (18,2) (0,3) (6,5) (15,0) (25,6) (7,23) (23,8) (16,6) (4,6) (20,10) (24,19) (13,19) (12,11) (12,21) (1,6) (22,25) (15,6) (18,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "383"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (5,7) (2,6) (5,0) (7,1) (7,0) (4,0) (3,0) (7,3) (5,6) (2,0) (1,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "384"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (5,21) (20,18) (22,18) (10,9) (21,11) (13,32) (25,22) (1,28) (1,0) (13,4) (19,31) (2,0) (32,2) (16,1) (24,14) (30,12) (29,3) (22,27) (7,24) (14,28) (17,10) (15,33) (30,8) (11,19) (34,6) (18,34) (24,11) (28,15) (1,27) (9,28) (29,19) (4,8) (23,0) (26,14) (21,32) (0,20)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "385"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (4,21) (30,13) (19,6) (18,8) (22,14) (3,2) (23,8) (25,10) (16,32) (12,30) (9,26) (0,24) (20,13) (4,29) (19,11) (32,5) (9,19) (6,8) (6,31) (31,7) (17,32) (26,1) (27,20) (16,25) (28,30) (16,2) (21,30) (24,18) (6,22) (13,15) (22,27) (28,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "386"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (4,7) (8,16) (1,3) (0,5) (5,15) (8,6) (14,8) (11,15) (3,10) (9,14) (2,14) (10,15) (5,12) (6,7) (13,9) (15,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "387"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (14,9) (2,16) (13,15) (0,18) (17,9) (11,3) (18,4) (0,11) (12,1) (6,12) (5,1) (10,1) (15,2) (17,0) (11,1) (2,0) (7,11) (6,15) (13,8) (0,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "388"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (14,9) (5,6) (14,7) (8,1) (2,7) (9,11) (2,15) (13,15) (0,3) (4,12) (7,10) (3,14) (2,0) (6,9) (0,1) (12,9) (0,11) (1,13) (0,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "389"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (4,8) (15,6) (24,11) (18,30) (3,14) (1,29) (30,13) (26,28) (3,10) (25,17) (8,28) (11,17) (22,5) (2,16) (10,24) (15,0) (29,0) (4,10) (8,0) (26,23) (13,22) (24,20) (23,7) (13,31) (15,12) (19,15) (7,16) (8,27) (1,9) (13,0) (6,21)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "390"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,24) (4,23) (17,12) (11,5) (24,25) (11,8) (16,1) (2,20) (21,18) (0,19) (7,15) (4,16) (19,11) (0,14) (4,24) (3,8) (1,0) (16,18) (18,6) (9,10) (0,7) (13,9) (11,12) (10,3) (3,22) (2,13) (2,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "391"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (10,8) (23,10) (4,24) (16,27) (26,3) (23,18) (20,9) (26,7) (3,16) (0,2) (1,0) (17,16) (24,28) (28,14) (0,3) (9,26) (4,0) (20,19) (23,12) (12,3) (0,24) (0,5) (11,0) (26,13) (2,15) (22,2) (14,13) (27,25) (22,26) (23,21) (1,25) (17,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "392"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (8,7) (13,18) (10,0) (6,28) (19,16) (6,17) (11,23) (3,20) (2,24) (7,16) (1,0) (0,19) (1,13) (21,3) (23,21) (0,2) (28,22) (17,23) (5,20) (27,7) (9,3) (26,2) (0,17) (8,12) (2,6) (25,18) (15,4) (7,14) (23,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "393"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (12,8) (24,17) (19,7) (20,8) (6,16) (25,0) (16,22) (6,18) (19,6) (30,11) (4,24) (24,14) (28,29) (27,22) (10,0) (26,29) (21,16) (11,4) (25,9) (11,16) (14,26) (19,1) (8,2) (15,26) (26,0) (6,2) (10,3) (4,13) (5,16) (23,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "394"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (16,2) (2,20) (6,22) (11,14) (12,20) (12,7) (10,17) (18,3) (9,5) (28,7) (9,22) (29,0) (10,16) (4,26) (19,27) (13,25) (21,22) (21,26) (4,14) (6,19) (1,3) (25,12) (23,21) (8,29) (24,10) (21,13) (4,3) (14,15) (8,24)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "395"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (2,12) (15,17) (20,10) (8,9) (10,5) (12,14) (9,10) (0,13) (2,11) (16,0) (6,7) (20,0) (11,18) (5,3) (6,10) (16,21) (5,19) (1,15) (10,14) (17,4) (11,15)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "396"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (9,16) (20,16) (12,28) (20,19) (0,2) (7,12) (7,2) (25,5) (4,24) (17,6) (6,27) (6,13) (26,30) (1,26) (14,16) (9,11) (31,25) (4,23) (1,6) (20,21) (25,27) (29,7) (22,12) (19,1) (6,4) (8,22) (3,12) (10,18) (29,24) (18,17) (15,26)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "397"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (7,20) (6,11) (11,0) (1,0) (12,18) (13,0) (2,20) (16,17) (8,18) (17,1) (19,14) (14,15) (0,2) (9,1) (3,15) (10,7) (10,3) (6,4) (8,11) (5,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "398"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,0) (6,1) (6,2) (11,2) (9,5) (14,12) (17,10) (8,2) (2,0) (7,5) (4,3) (17,11) (0,3) (15,9) (12,10) (13,12) (16,15) (12,16) (9,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "399"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (24,21) (3,10) (8,22) (6,23) (4,14) (3,22) (18,15) (14,9) (7,12) (5,0) (17,20) (19,5) (5,25) (21,2) (8,6) (6,7) (15,13) (11,10) (16,10) (3,1) (15,9) (20,15) (27,26) (8,14) (5,27) (16,21) (25,24)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "400"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (29,20) (1,22) (10,2) (18,1) (15,1) (6,28) (20,4) (3,17) (6,1) (3,12) (0,7) (30,9) (14,16) (10,25) (19,23) (8,23) (16,0) (22,8) (2,22) (28,27) (16,5) (12,13) (9,31) (15,9) (12,5) (26,24) (11,9) (2,0) (0,1) (20,27) (9,12) (12,24) (29,21)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "401"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (25,7) (5,1) (29,19) (0,4) (22,16) (10,31) (4,7) (17,13) (14,20) (15,28) (28,16) (3,15) (0,1) (9,10) (32,24) (2,0) (0,3) (13,24) (27,25) (30,17) (23,16) (7,21) (22,20) (29,14) (2,6) (26,25) (8,16) (18,19) (0,10) (21,1) (4,12) (9,23) (17,6) (18,11) (17,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "402"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,2) (10,0) (3,4) (6,3) (7,8) (6,2) (8,9) (0,4) (5,6) (1,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "403"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (10,11) (0,3) (6,8) (5,2) (15,3) (11,12) (0,12) (12,7) (12,8) (13,10) (7,5) (7,4) (14,8) (7,1) (9,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "404"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (26,12) (18,27) (9,2) (14,20) (21,19) (11,25) (20,7) (4,17) (0,1) (27,14) (28,19) (16,23) (11,24) (11,2) (2,5) (7,25) (29,10) (13,12) (17,19) (6,11) (29,16) (3,1) (29,17) (0,13) (27,3) (15,2) (9,22) (8,19) (15,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "405"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (11,21) (17,20) (6,14) (23,22) (18,25) (22,26) (3,20) (27,6) (4,2) (8,22) (19,24) (25,24) (27,2) (5,3) (26,13) (19,7) (12,9) (16,25) (8,15) (10,17) (0,12) (6,21) (15,1) (14,13) (20,24) (6,0) (4,20)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "406"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (19,4) (24,21) (13,3) (23,17) (6,24) (0,2) (0,15) (25,23) (8,12) (24,16) (3,17) (4,12) (7,14) (1,22) (4,9) (15,22) (11,1) (1,4) (4,7) (23,20) (10,21) (5,3) (21,1) (4,18) (17,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "407"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,28) (15,19) (9,23) (11,7) (3,7) (31,20) (26,4) (10,9) (5,29) (18,24) (0,30) (27,11) (16,27) (13,17) (22,11) (14,28) (18,2) (26,8) (32,14) (6,31) (1,4) (29,19) (13,2) (17,12) (0,23) (2,10) (26,28) (2,0) (17,21) (31,25) (0,1) (6,7) (10,25) (15,25)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "408"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (8,6) (14,8) (18,5) (2,0) (2,14) (8,3) (10,16) (9,14) (15,12) (16,20) (15,17) (1,3) (15,5) (3,0) (7,11) (9,15) (5,0) (13,20) (6,19) (1,0) (4,10) (3,10) (6,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "409"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (6,25) (1,18) (14,10) (23,19) (6,15) (21,3) (20,14) (13,27) (16,25) (2,5) (28,12) (25,27) (6,7) (19,26) (5,12) (22,8) (24,11) (15,26) (8,7) (9,5) (14,21) (11,25) (0,2) (1,0) (4,21) (26,14) (12,6) (18,14) (23,17)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "410"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (3,6) (3,4) (1,0) (8,4) (4,1) (2,9) (8,5) (7,4) (1,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "411"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (3,0) (3,6) (10,9) (5,11) (7,8) (1,0) (11,0) (0,2) (6,11) (4,11) (1,8) (9,1) (7,2) (9,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "412"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (14,6) (24,17) (20,15) (10,22) (19,24) (8,17) (9,16) (17,16) (21,4) (12,9) (7,6) (3,15) (7,20) (6,24) (22,18) (4,2) (5,13) (21,3) (17,11) (17,0) (16,23) (1,10) (22,13) (4,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "413"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (11,16) (19,13) (6,15) (4,8) (14,15) (16,19) (22,20) (18,0) (17,16) (7,3) (9,21) (18,10) (7,20) (17,8) (2,20) (1,5) (14,9) (21,20) (12,5) (10,21) (16,15) (5,20)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "414"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (9,21) (8,11) (2,0) (23,13) (10,22) (0,1) (0,3) (13,24) (22,5) (22,18) (19,11) (24,6) (14,19) (18,11) (24,17) (15,20) (0,16) (12,3) (1,2) (14,4) (21,0) (16,13) (7,4) (1,9) (17,19) (15,19) (14,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "415"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (8,7) (2,18) (0,10) (13,5) (3,0) (13,2) (8,4) (9,1) (9,3) (2,8) (1,0) (4,0) (2,0) (11,9) (1,2) (14,15) (16,9) (17,3) (15,6) (12,10) (15,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "416"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (20,28) (20,13) (24,0) (19,11) (13,9) (23,25) (2,0) (0,8) (11,1) (3,0) (27,0) (23,28) (2,1) (29,16) (10,17) (19,27) (12,11) (3,20) (12,22) (30,23) (0,1) (21,28) (12,29) (5,26) (3,12) (19,6) (14,7) (5,16) (26,18) (9,15) (7,16) (18,4) (15,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "417"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,3) (0,5) (0,2) (1,5) (5,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "418"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (11,10) (11,4) (12,19) (12,16) (17,23) (10,8) (13,2) (26,27) (24,8) (14,16) (13,20) (5,2) (19,1) (7,14) (17,6) (25,15) (0,3) (26,0) (0,1) (15,23) (18,12) (0,21) (25,8) (0,17) (9,18) (25,1) (3,22) (21,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "419"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (5,2) (8,3) (6,5) (5,7) (0,3) (7,8) (1,0) (0,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "420"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (11,4) (12,15) (0,8) (3,0) (1,12) (0,2) (8,10) (13,2) (8,17) (6,17) (11,16) (16,3) (4,0) (0,1) (1,13) (12,14) (9,10) (0,13) (5,2) (7,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "421"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (14,6) (19,3) (5,12) (17,6) (4,7) (8,5) (15,4) (18,6) (14,10) (13,11) (4,19) (0,3) (13,6) (6,19) (17,2) (4,5) (1,4) (12,16) (9,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "422"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (3,0) (1,4) (3,2) (0,2) (2,1) (1,0) (4,3) (4,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "423"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (18,5) (22,8) (11,14) (1,25) (17,22) (2,3) (28,8) (30,15) (20,14) (2,11) (15,9) (3,16) (30,12) (23,9) (1,19) (21,5) (11,27) (0,20) (13,23) (26,21) (11,10) (2,0) (7,24) (13,6) (4,13) (12,18) (3,0) (19,23) (24,18) (10,19) (10,22) (24,29) (0,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "424"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (6,10) (3,7) (12,8) (16,15) (0,2) (12,0) (14,15) (1,11) (0,14) (6,13) (16,7) (7,4) (4,9) (4,2) (1,2) (0,1) (12,6) (5,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "425"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (5,1) (4,0) (5,0) (0,2) (4,1) (1,0) (4,2) (3,4) (0,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "426"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (8,6) (7,5) (8,5) (4,5) (8,2) (6,1) (0,4) (3,6) (6,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "427"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (15,14) (7,1) (2,25) (18,26) (24,22) (6,26) (3,11) (5,26) (9,23) (20,1) (11,8) (2,17) (20,25) (11,27) (11,0) (17,21) (19,21) (24,29) (0,1) (13,1) (10,13) (15,29) (24,28) (16,9) (12,1) (12,6) (22,25) (18,4) (24,0) (23,15)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "428"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (7,12) (2,8) (11,10) (14,1) (7,13) (1,12) (11,0) (12,0) (5,7) (12,3) (11,8) (15,5) (9,12) (11,6) (13,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "429"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (9,3) (7,0) (1,10) (4,3) (5,10) (11,2) (1,6) (0,2) (13,11) (0,11) (10,11) (1,0) (3,2) (4,8) (12,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "430"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (2,6) (1,2) (2,7) (0,1) (7,9) (0,3) (3,2) (8,4) (2,0) (9,5) (8,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "431"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (16,15) (18,4) (14,4) (0,8) (17,19) (9,8) (2,15) (13,17) (1,12) (5,18) (10,11) (1,0) (15,6) (7,2) (20,3) (3,17) (18,11) (10,0) (13,6) (8,15)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "432"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (16,8) (15,26) (4,8) (22,26) (6,9) (8,11) (17,10) (2,26) (12,24) (26,11) (7,15) (21,17) (2,6) (22,3) (20,0) (2,23) (1,0) (13,9) (2,0) (18,20) (8,10) (27,18) (7,5) (20,23) (26,19) (25,7) (14,2) (1,15) (12,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "433"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,12) (7,15) (0,19) (5,2) (15,21) (10,3) (0,17) (15,11) (9,4) (9,7) (22,16) (11,19) (2,6) (0,1) (1,13) (16,1) (6,4) (1,10) (10,20) (17,22) (8,22) (14,3) (18,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "434"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (11,12) (4,7) (1,11) (11,15) (16,5) (8,15) (10,7) (12,16) (0,3) (1,2) (13,12) (5,0) (9,10) (14,0) (13,9) (16,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "435"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (31,29) (27,28) (9,17) (5,15) (20,13) (31,19) (11,6) (4,0) (2,13) (12,14) (0,1) (10,20) (21,20) (23,32) (0,3) (19,4) (13,8) (12,10) (22,29) (7,24) (21,4) (9,18) (25,10) (1,7) (11,10) (33,1) (5,16) (16,10) (24,3) (28,19) (18,0) (33,4) (28,0) (0,2) (31,26) (2,23) (30,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "436"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (22,16) (0,3) (25,18) (2,22) (3,5) (10,20) (25,12) (0,1) (0,27) (2,11) (10,9) (15,11) (0,2) (28,0) (2,20) (8,29) (17,9) (28,16) (1,15) (5,26) (14,12) (7,6) (10,13) (10,14) (24,11) (25,6) (0,21) (22,19) (5,10) (29,20) (17,4) (15,23)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "437"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (22,19) (1,10) (9,21) (4,18) (19,6) (0,14) (9,7) (11,21) (2,14) (17,6) (8,11) (6,20) (1,20) (16,4) (14,8) (5,16) (18,3) (7,12) (13,20) (4,1) (16,0) (15,21)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "438"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (9,17) (15,25) (20,16) (6,15) (25,17) (2,26) (15,0) (9,11) (0,1) (5,9) (4,11) (1,14) (1,12) (8,4) (6,18) (25,20) (26,20) (7,2) (12,10) (13,1) (3,14) (5,21) (13,4) (2,0) (6,19) (2,22) (6,24) (1,23)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "439"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,2) (10,8) (7,1) (11,8) (4,1) (5,9) (3,6) (10,5) (4,12) (12,11) (8,3) (11,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "440"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (2,0) (23,21) (0,6) (3,0) (13,11) (11,18) (24,10) (3,4) (22,17) (14,25) (6,7) (18,21) (17,7) (5,6) (2,19) (12,20) (1,0) (12,17) (1,22) (7,15) (14,8) (18,14) (10,3) (24,19) (19,18) (7,24) (16,21) (9,24)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "441"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (23,7) (12,28) (17,2) (15,16) (9,20) (26,28) (17,20) (19,2) (10,11) (17,21) (5,8) (0,15) (24,15) (13,7) (1,0) (11,3) (18,10) (26,3) (29,25) (0,3) (2,0) (4,27) (4,11) (27,1) (24,21) (6,7) (22,10) (22,14) (29,2) (6,2) (10,7) (11,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "442"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (11,0) (2,9) (2,7) (10,2) (11,3) (12,10) (6,4) (9,6) (13,5) (3,2) (8,3) (1,10) (1,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "443"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (9,6) (1,19) (14,0) (5,8) (9,4) (20,2) (10,21) (16,6) (14,2) (1,7) (2,12) (14,3) (9,18) (0,1) (7,21) (12,13) (11,2) (21,20) (21,15) (9,19) (15,8) (17,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "444"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (8,12) (2,1) (4,7) (2,6) (5,1) (9,6) (1,8) (3,0) (10,11) (12,7) (0,2) (0,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "445"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (1,2) (4,5) (7,5) (3,2) (3,5) (4,6) (0,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "446"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,1) (13,9) (14,19) (8,2) (11,5) (0,18) (7,15) (13,16) (17,12) (8,11) (14,11) (10,1) (17,1) (1,3) (4,0) (6,16) (0,2) (4,5) (12,14) (5,13) (0,3) (4,15)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "447"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (26,12) (16,23) (15,10) (6,11) (28,19) (0,13) (1,0) (29,17) (19,8) (27,3) (29,10) (2,15) (11,24) (19,17) (20,7) (25,7) (3,1) (25,11) (20,14) (4,17) (5,2) (27,18) (9,2) (22,9) (14,27) (11,2) (19,21) (16,29) (13,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "448"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (31,33) (9,13) (26,12) (16,15) (32,5) (26,13) (0,33) (10,15) (20,25) (1,25) (22,31) (14,8) (18,33) (5,19) (20,30) (12,27) (4,12) (17,0) (24,13) (24,16) (25,2) (21,11) (0,1) (6,11) (29,9) (2,0) (2,17) (30,5) (11,29) (23,28) (7,14) (24,23) (21,5) (5,8) (24,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "449"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (3,1) (0,2) (2,6) (5,1) (3,7) (0,9) (4,3) (0,1) (2,4) (8,0) (0,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "450"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (18,3) (6,22) (20,12) (2,16) (11,4) (19,8) (9,4) (23,17) (22,15) (14,18) (10,19) (6,7) (21,7) (17,5) (15,11) (12,15) (17,24) (17,15) (20,13) (19,2) (0,15) (25,20) (1,7) (0,18) (8,17)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "451"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (14,8) (13,17) (18,5) (4,21) (13,27) (19,4) (24,10) (23,27) (24,12) (1,0) (15,25) (9,2) (11,10) (8,0) (25,3) (17,28) (25,6) (23,22) (11,26) (18,15) (21,24) (23,6) (15,8) (1,16) (26,7) (20,18) (0,24) (15,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "452"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (21,3) (2,16) (10,14) (4,8) (20,22) (13,9) (9,18) (10,0) (5,8) (24,23) (15,7) (3,0) (12,2) (1,19) (11,8) (13,6) (15,17) (9,23) (1,20) (9,3) (2,19) (23,8) (4,2) (15,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "453"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (15,21) (19,6) (21,24) (6,20) (26,14) (22,11) (10,1) (9,7) (12,7) (14,2) (6,17) (16,0) (1,20) (16,23) (3,18) (19,26) (8,11) (14,24) (9,21) (8,23) (1,4) (13,20) (5,16) (18,4) (25,0) (23,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "454"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (2,11) (3,9) (12,7) (1,5) (3,7) (1,6) (3,8) (5,12) (12,10) (11,5) (0,3) (4,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "455"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (1,9) (0,1) (6,11) (7,11) (0,2) (6,2) (3,6) (0,10) (5,7) (12,4) (0,3) (1,8) (5,1) (11,10) (5,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "456"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (1,22) (18,14) (12,15) (10,3) (22,14) (2,19) (11,7) (9,11) (5,6) (19,18) (21,13) (10,18) (21,19) (14,8) (21,7) (6,0) (7,17) (12,17) (3,4) (0,1) (6,7) (17,16) (20,18)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "457"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (20,24) (33,13) (11,14) (22,17) (10,32) (28,9) (3,5) (15,4) (23,16) (5,30) (23,14) (1,12) (8,1) (21,6) (33,2) (27,4) (24,3) (32,27) (7,22) (22,0) (24,1) (9,33) (31,23) (21,26) (9,0) (29,6) (6,17) (3,16) (24,18) (13,20) (19,25) (19,10) (19,18)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "458"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (17,4) (21,0) (17,9) (0,1) (17,18) (15,18) (4,14) (9,16) (13,16) (2,10) (2,3) (4,0) (20,1) (6,1) (18,8) (19,1) (12,7) (23,16) (5,12) (18,11) (20,10) (7,20) (2,22)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "459"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (3,9) (24,7) (10,20) (21,18) (14,6) (14,12) (4,17) (16,14) (0,16) (24,22) (2,23) (27,15) (9,1) (17,24) (24,27) (11,23) (17,26) (1,15) (22,8) (19,11) (16,8) (15,25) (29,5) (26,10) (19,4) (21,6) (13,0) (29,12) (23,28)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "460"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (13,18) (1,4) (23,20) (23,27) (5,0) (7,8) (28,11) (2,18) (0,16) (26,13) (2,0) (3,0) (20,16) (0,24) (10,3) (25,10) (12,29) (17,2) (15,26) (1,0) (15,30) (29,14) (9,21) (9,28) (20,13) (25,19) (30,6) (2,22) (8,29) (17,8) (25,5) (0,4) (11,17) (5,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "461"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (15,13) (2,0) (8,14) (5,0) (12,5) (15,2) (11,5) (3,0) (10,9) (4,18) (1,5) (3,6) (13,1) (15,18) (16,7) (9,6) (0,1) (4,0) (3,16) (9,17) (17,4) (5,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "462"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (11,8) (17,4) (8,9) (16,15) (18,4) (0,2) (15,3) (2,11) (18,5) (2,1) (14,9) (17,2) (18,13) (0,6) (11,10) (15,8) (7,9) (3,0) (0,1) (14,12) (6,18)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "463"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (18,4) (13,17) (2,6) (11,4) (1,16) (4,7) (3,6) (7,0) (14,1) (0,6) (7,16) (13,6) (5,13) (12,15) (10,1) (9,17) (8,13) (5,15)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "464"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (6,18) (13,14) (2,10) (14,0) (0,1) (0,8) (5,10) (23,9) (3,16) (15,23) (7,23) (16,11) (3,12) (23,6) (22,6) (21,16) (13,3) (20,17) (17,4) (19,9) (12,20) (18,0) (2,22)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "465"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (11,2) (17,27) (25,24) (9,18) (17,28) (29,0) (29,8) (28,3) (26,11) (28,14) (12,29) (15,7) (5,18) (20,4) (1,19) (19,21) (25,5) (3,21) (12,22) (3,23) (16,2) (4,5) (27,6) (23,10) (3,15) (11,12) (11,13) (19,26) (18,1) (29,30)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "466"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (13,9) (5,4) (0,5) (5,11) (0,1) (8,4) (3,8) (6,8) (6,1) (10,7) (9,7) (6,9) (12,6) (1,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "467"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (10,0) (3,10) (27,22) (16,5) (6,19) (29,11) (26,14) (20,8) (2,0) (2,6) (24,14) (8,2) (22,16) (0,3) (26,15) (12,8) (7,19) (18,6) (4,29) (16,11) (26,28) (1,0) (26,0) (13,4) (25,0) (19,1) (4,24) (17,24) (1,23) (16,21) (9,25) (16,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "468"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (5,17) (4,8) (17,24) (30,19) (28,11) (16,32) (8,1) (11,25) (25,16) (32,3) (11,21) (9,11) (21,31) (6,23) (2,33) (18,2) (7,6) (6,12) (23,30) (8,0) (23,22) (17,26) (10,7) (10,32) (23,24) (14,1) (15,12) (5,0) (33,19) (9,27) (29,25) (31,13) (12,20)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "469"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (13,25) (7,27) (19,14) (13,3) (5,29) (7,33) (17,24) (4,11) (19,13) (22,12) (18,32) (29,2) (28,5) (31,21) (20,7) (24,10) (3,16) (16,30) (29,1) (9,11) (14,21) (13,26) (27,15) (8,22) (0,1) (10,7) (23,26) (12,9) (0,9) (22,23) (29,17) (25,6) (32,11) (29,25)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "470"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (4,7) (1,0) (2,11) (7,2) (1,8) (8,7) (0,14) (14,3) (1,10) (13,5) (6,4) (5,10) (9,0) (15,13) (3,11) (12,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "471"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (17,10) (0,21) (19,18) (4,0) (6,1) (21,17) (13,11) (19,2) (1,0) (22,13) (17,9) (20,16) (4,14) (14,17) (11,7) (14,12) (5,3) (16,10) (4,13) (3,0) (10,8) (13,15) (14,18) (5,2) (3,1) (0,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "472"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (22,2) (10,8) (16,3) (17,16) (4,24) (17,6) (26,7) (25,1) (12,3) (15,2) (12,23) (13,25) (23,10) (20,19) (5,0) (14,26) (9,26) (0,11) (22,26) (24,0) (16,24) (26,3) (18,23) (14,13) (23,21) (9,20)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "473"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (4,0) (3,0) (13,12) (3,8) (14,28) (25,23) (7,5) (8,14) (30,0) (29,12) (15,13) (13,26) (30,21) (1,0) (21,28) (27,5) (25,21) (9,2) (18,7) (13,31) (25,10) (14,19) (15,23) (11,9) (7,1) (17,8) (6,7) (9,22) (0,2) (3,2) (25,1) (24,26) (16,2) (20,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "474"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (6,12) (0,5) (8,6) (11,5) (1,0) (4,8) (7,9) (6,9) (8,3) (2,0) (6,1) (0,3) (4,5) (7,10) (0,4) (2,1) (13,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "475"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (12,17) (3,15) (24,5) (1,4) (13,12) (3,8) (9,15) (22,0) (6,18) (6,3) (19,24) (20,16) (0,15) (20,12) (24,21) (24,10) (14,15) (23,0) (19,13) (7,2) (4,18) (11,14) (22,24) (2,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "476"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,1) (4,7) (7,8) (13,1) (2,4) (9,3) (6,5) (0,2) (12,13) (12,0) (3,14) (10,3) (3,11) (8,9) (1,4) (5,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "477"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (6,2) (2,5) (3,0) (0,4) (5,0) (1,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "478"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,8) (7,10) (0,10) (4,6) (5,1) (10,2) (4,10) (2,9) (0,1) (3,2) (9,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "479"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (13,1) (2,9) (6,4) (5,13) (3,8) (2,10) (7,2) (10,12) (11,0) (10,1) (6,9) (3,2) (11,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "480"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (4,7) (5,8) (5,2) (9,12) (1,0) (7,5) (3,8) (13,14) (6,10) (9,0) (3,0) (13,10) (4,6) (0,4) (2,0) (9,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "481"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (13,1) (4,8) (14,3) (15,0) (2,0) (5,6) (10,1) (5,9) (0,3) (2,1) (15,13) (12,6) (9,2) (2,7) (0,1) (12,4) (14,6) (1,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "482"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (2,8) (2,7) (1,6) (0,7) (5,1) (3,5) (4,1) (2,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "483"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (16,23) (13,30) (2,10) (6,13) (26,18) (28,17) (0,2) (12,9) (13,19) (22,25) (11,27) (20,9) (3,4) (4,25) (32,29) (7,20) (32,23) (19,9) (1,6) (15,20) (26,8) (18,9) (21,26) (24,4) (4,16) (6,24) (10,29) (12,28) (14,28) (5,22) (26,27) (6,31)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "484"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (7,21) (3,0) (6,17) (0,2) (23,0) (3,12) (22,12) (4,0) (16,33) (17,26) (7,23) (1,19) (18,34) (19,5) (22,13) (24,5) (0,17) (20,28) (34,14) (30,12) (32,31) (1,0) (18,30) (11,5) (1,17) (26,27) (20,15) (9,6) (27,20) (28,13) (12,4) (8,34) (32,4) (21,10) (29,31) (25,24) (11,16) (9,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "485"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,2) (4,5) (3,4) (6,3) (0,6) (1,0) (5,0) (1,2) (3,0) (4,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "486"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (9,1) (10,11) (2,4) (5,4) (12,5) (0,8) (11,9) (3,11) (11,6) (8,10) (1,0) (7,12) (0,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "487"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (12,5) (0,11) (2,8) (3,12) (10,11) (7,1) (4,5) (3,7) (5,8) (4,9) (0,12) (2,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "488"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (11,12) (1,15) (9,15) (17,4) (14,3) (12,6) (14,21) (7,13) (5,9) (4,0) (17,15) (6,20) (6,1) (17,22) (10,16) (7,14) (14,19) (2,19) (12,18) (18,10) (15,8) (17,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "489"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (10,5) (9,6) (1,4) (2,4) (4,3) (8,2) (2,0) (0,4) (1,0) (3,0) (9,7) (3,7) (7,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "490"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (6,3) (15,0) (24,16) (1,4) (8,3) (8,2) (11,15) (24,28) (12,13) (12,20) (23,6) (3,0) (12,26) (15,14) (27,5) (9,24) (28,25) (19,24) (18,20) (0,2) (13,19) (26,27) (21,25) (3,15) (0,1) (22,29) (7,25) (0,22) (24,0) (17,14) (4,18) (10,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "491"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (24,25) (8,27) (16,17) (19,9) (4,27) (30,2) (5,15) (20,6) (1,29) (22,20) (23,1) (10,29) (31,3) (12,8) (13,22) (21,31) (11,2) (26,17) (7,29) (14,6) (19,3) (30,10) (5,16) (12,26) (31,18) (0,28) (19,1) (29,24) (9,12) (22,17) (31,28)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "492"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,13) (12,11) (7,9) (7,5) (0,1) (14,15) (6,1) (3,1) (4,0) (14,8) (4,1) (11,8) (9,6) (14,2) (4,10) (6,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "493"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (9,6) (15,8) (18,1) (2,17) (4,10) (2,15) (1,0) (1,7) (2,0) (11,8) (14,3) (10,19) (6,16) (2,13) (4,7) (19,9) (9,5) (2,12) (14,0) (12,14) (9,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "494"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (2,9) (1,14) (3,12) (7,19) (10,0) (11,3) (17,13) (11,18) (2,7) (6,16) (18,13) (1,2) (15,16) (4,5) (6,1) (1,8) (4,12) (13,2) (10,17)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "495"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (2,0) (22,28) (15,31) (17,14) (6,25) (3,4) (19,27) (31,28) (7,5) (33,31) (28,8) (1,0) (3,0) (30,0) (14,28) (14,32) (2,8) (24,10) (6,20) (7,31) (1,27) (4,0) (23,17) (4,16) (16,1) (11,13) (27,13) (24,0) (1,29) (1,20) (26,1) (0,21) (24,18) (12,6) (1,33) (30,9) (24,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "496"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (8,2) (12,1) (18,0) (7,12) (11,0) (11,10) (4,17) (12,14) (17,20) (7,5) (12,17) (9,11) (22,6) (0,23) (1,19) (18,16) (11,15) (13,17) (22,19) (3,12) (13,8) (21,7) (16,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "497"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,16) (19,16) (0,1) (4,0) (20,17) (12,17) (8,1) (10,7) (0,3) (9,15) (10,2) (18,21) (4,7) (15,21) (11,6) (0,8) (17,4) (5,6) (19,13) (2,0) (15,0) (3,6) (8,20) (3,9) (14,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "498"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,16) (9,11) (2,8) (8,15) (17,8) (11,16) (15,11) (14,15) (13,8) (0,14) (3,12) (4,13) (7,15) (10,3) (14,5) (10,2) (6,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "499"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,7) (10,3) (13,18) (6,15) (5,7) (12,15) (3,9) (11,5) (14,1) (17,0) (8,9) (8,13) (13,11) (12,4) (2,6) (4,1) (12,17) (6,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "500"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (5,6) (7,9) (11,3) (0,8) (1,4) (3,1) (2,9) (0,4) (4,10) (2,3) (8,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "501"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (8,5) (7,2) (1,5) (7,6) (0,1) (7,4) (1,2) (3,4) (9,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "502"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,26) (3,10) (16,11) (8,2) (10,0) (6,2) (27,24) (26,4) (0,4) (19,7) (6,17) (22,25) (5,16) (19,1) (15,24) (18,8) (6,16) (13,4) (20,16) (2,0) (23,0) (16,22) (24,14) (8,12) (1,21) (3,0) (9,25) (1,0) (6,19) (26,11) (26,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "503"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,2) (12,4) (20,8) (0,3) (0,12) (10,4) (14,16) (20,19) (5,16) (13,11) (21,19) (15,1) (19,14) (9,11) (0,21) (0,17) (18,7) (1,0) (17,7) (11,15) (8,15) (6,21) (8,2) (0,4) (3,21)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "504"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (13,12) (11,7) (4,2) (16,9) (5,11) (1,3) (0,3) (8,2) (2,16) (6,9) (14,3) (2,0) (12,15) (11,10) (0,4) (0,1) (7,14) (13,0) (2,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "505"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (24,2) (12,17) (13,18) (6,18) (29,20) (21,2) (23,9) (3,15) (8,4) (26,14) (7,3) (5,22) (21,0) (24,4) (27,10) (30,10) (5,17) (28,27) (0,11) (8,7) (23,21) (13,14) (15,10) (5,26) (19,11) (24,6) (28,29) (25,10) (16,8) (29,1) (31,17)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "506"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (3,30) (0,20) (6,23) (25,0) (10,30) (13,8) (22,11) (24,22) (9,26) (15,4) (26,30) (10,4) (14,17) (18,11) (10,27) (26,16) (17,31) (21,2) (17,1) (5,3) (19,28) (31,24) (8,10) (7,26) (2,12) (2,24) (28,14) (15,0) (23,28) (29,31) (2,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "507"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (18,9) (6,13) (23,25) (15,7) (23,26) (17,15) (16,2) (9,3) (15,0) (24,20) (0,10) (19,1) (5,8) (2,19) (25,21) (9,13) (1,20) (0,3) (10,14) (4,8) (12,2) (3,22) (8,25) (11,8) (4,2) (23,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "508"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (2,10) (6,2) (9,7) (7,10) (2,0) (2,1) (5,9) (3,2) (0,1) (3,8) (8,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "509"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,1) (6,3) (2,9) (1,4) (8,5) (9,1) (7,4) (4,8) (4,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "510"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (7,8) (16,14) (15,11) (21,3) (6,12) (20,6) (6,7) (4,21) (1,18) (14,13) (0,2) (5,12) (5,9) (2,5) (19,18) (14,17) (14,8) (19,11) (14,10) (6,15) (21,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "511"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (10,7) (19,8) (21,15) (0,1) (4,6) (8,11) (3,21) (16,0) (2,0) (6,11) (0,11) (17,18) (3,10) (14,15) (18,13) (13,5) (14,20) (20,2) (9,7) (22,9) (1,12) (1,17)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "512"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (24,8) (24,12) (14,21) (21,2) (21,12) (6,20) (13,23) (16,10) (0,3) (18,2) (1,19) (9,20) (5,24) (19,14) (17,23) (3,8) (0,1) (4,22) (8,15) (3,23) (9,14) (9,16) (22,12) (7,8) (7,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "513"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (7,3) (27,4) (13,3) (20,27) (19,16) (5,9) (16,25) (27,0) (14,3) (14,28) (28,18) (10,8) (3,11) (9,17) (14,5) (19,29) (26,29) (24,14) (10,5) (8,16) (8,27) (2,16) (11,6) (19,1) (15,25) (23,25) (21,29) (10,12) (6,22)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "514"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,6) (0,1) (3,6) (7,5) (0,2) (0,4) (7,8) (8,0) (4,7) (9,5) (3,0) (1,7) (2,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "515"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (11,3) (9,15) (13,16) (20,12) (10,2) (3,7) (18,8) (6,18) (23,6) (22,0) (18,0) (6,21) (17,1) (10,20) (5,15) (14,16) (8,20) (7,17) (22,13) (9,17) (0,4) (2,19) (19,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "516"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (3,0) (11,4) (2,4) (5,1) (0,4) (3,7) (11,10) (12,1) (3,6) (0,1) (7,0) (8,2) (11,0) (0,2) (9,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "517"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (2,17) (6,15) (29,14) (24,0) (0,30) (25,4) (28,14) (5,21) (20,23) (18,10) (23,27) (3,0) (6,12) (9,23) (5,13) (9,22) (22,1) (25,29) (4,19) (2,22) (24,18) (26,8) (12,7) (11,5) (26,24) (16,21) (20,3) (6,5) (14,27) (22,21)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "518"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,9) (1,3) (8,0) (7,2) (0,6) (8,5) (4,0) (3,0) (3,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "519"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (12,11) (3,2) (7,12) (0,15) (14,13) (14,7) (8,14) (1,6) (5,6) (10,4) (0,3) (6,7) (7,10) (9,11) (3,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "520"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (17,7) (4,3) (3,0) (27,10) (25,23) (4,30) (6,5) (7,8) (1,0) (22,1) (4,31) (13,30) (24,7) (10,3) (14,26) (0,31) (6,10) (19,10) (12,5) (20,2) (11,9) (21,13) (30,14) (2,0) (16,9) (7,2) (22,15) (25,13) (21,18) (28,18) (32,5) (11,25) (18,29) (22,23) (7,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "521"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (13,0) (2,18) (11,21) (12,21) (1,20) (3,14) (12,5) (19,22) (16,15) (14,19) (0,10) (9,8) (23,22) (4,8) (2,10) (19,17) (5,22) (11,7) (1,0) (2,0) (1,23) (17,10) (0,3) (6,19) (5,4) (16,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "522"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (6,5) (2,0) (3,10) (7,11) (13,11) (1,5) (9,8) (3,12) (2,7) (2,9) (3,11) (1,2) (14,5) (4,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "523"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (27,16) (0,32) (19,31) (14,9) (11,1) (16,13) (25,10) (4,18) (20,0) (32,25) (0,12) (27,22) (13,2) (8,12) (21,23) (7,1) (18,1) (15,11) (29,27) (16,3) (6,30) (22,14) (17,19) (0,23) (0,1) (17,4) (5,24) (4,29) (27,26) (24,6) (25,6) (22,28) (16,20)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "524"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,5) (4,9) (15,13) (12,10) (16,4) (14,11) (16,6) (8,15) (9,17) (15,6) (18,11) (12,9) (7,16) (12,0) (18,3) (3,4) (8,1) (2,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "525"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (14,9) (5,3) (5,6) (17,1) (2,17) (14,0) (16,13) (10,16) (14,8) (12,6) (3,14) (0,1) (18,11) (7,14) (17,19) (18,5) (19,15) (4,9) (4,2) (16,15)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "526"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (1,13) (0,1) (7,2) (2,1) (5,9) (4,13) (2,21) (0,2) (8,4) (6,19) (17,6) (6,15) (12,1) (6,18) (20,5) (16,20) (12,10) (3,14) (1,14) (9,11) (9,17) (22,15) (0,15) (11,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "527"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (6,7) (15,0) (11,3) (11,10) (3,15) (10,16) (5,11) (15,8) (11,4) (13,10) (4,2) (2,7) (1,8) (7,14) (9,10) (2,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "528"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (2,6) (5,0) (6,0) (2,0) (1,6) (0,4) (0,3) (1,0) (1,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "529"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (22,13) (0,19) (22,15) (2,7) (1,22) (11,25) (2,24) (0,9) (5,14) (5,19) (21,17) (18,20) (14,12) (17,5) (7,8) (23,13) (7,4) (11,20) (19,10) (23,3) (23,21) (1,26) (6,4) (25,10) (8,1) (3,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "530"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (12,5) (3,9) (8,1) (15,0) (2,6) (7,5) (9,2) (6,4) (10,8) (16,7) (2,8) (17,13) (15,17) (11,8) (11,12) (10,14) (15,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "531"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (3,9) (0,9) (5,10) (10,2) (7,4) (6,5) (8,2) (1,7) (5,0) (2,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "532"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (17,4) (2,15) (9,11) (17,9) (18,21) (13,1) (3,18) (21,16) (7,15) (3,15) (20,23) (6,9) (0,4) (8,19) (10,16) (5,14) (5,8) (15,13) (4,3) (12,5) (1,5) (6,22) (2,20)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "533"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (12,0) (7,8) (4,1) (11,3) (8,9) (5,6) (9,12) (4,7) (1,3) (0,4) (3,5) (10,3) (2,4) (2,0) (1,0) (0,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "534"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (3,14) (2,11) (3,11) (1,0) (7,2) (4,6) (2,0) (5,12) (4,7) (5,13) (5,10) (1,16) (13,1) (8,7) (15,10) (0,9) (0,14) (1,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "535"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (22,15) (4,18) (24,6) (3,5) (21,1) (20,23) (13,3) (23,21) (4,9) (0,2) (8,12) (4,12) (19,4) (1,11) (1,4) (22,1) (0,15) (17,7) (4,7) (10,21) (14,7) (24,16) (17,24) (17,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "536"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,2) (0,8) (7,1) (9,3) (5,6) (6,3) (0,1) (0,4) (8,10) (3,0) (5,8) (8,1) (2,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "537"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,3) (7,3) (2,4) (0,4) (1,4) (3,5) (6,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "538"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (7,8) (0,2) (4,1) (13,12) (3,11) (3,9) (3,14) (0,12) (10,3) (4,2) (5,6) (13,1) (7,4) (5,3) (9,8) (3,0) (1,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "539"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,4) (0,2) (9,0) (2,4) (6,7) (8,6) (0,1) (3,1) (3,0) (4,5) (9,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "540"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (11,3) (1,7) (5,7) (2,6) (3,10) (4,7) (1,0) (2,1) (6,0) (3,9) (0,10) (8,0) (0,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "541"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (18,4) (12,16) (20,7) (5,8) (20,9) (10,21) (0,11) (10,13) (19,4) (19,5) (14,5) (1,12) (4,3) (6,2) (15,0) (17,14) (0,10) (21,16) (10,6) (7,3) (13,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "542"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,3) (7,5) (5,6) (8,2) (3,7) (7,1) (8,4) (8,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "543"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (1,3) (5,0) (1,0) (2,4) (10,9) (11,0) (8,3) (3,6) (0,9) (3,7) (6,4) (6,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "544"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (2,7) (6,7) (1,5) (6,8) (9,1) (4,9) (0,8) (3,0) (4,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "545"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (13,7) (0,3) (4,2) (0,4) (0,5) (3,6) (4,14) (4,1) (5,11) (7,6) (4,8) (9,1) (4,10) (7,0) (12,1) (1,0) (2,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "546"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (15,11) (13,19) (32,12) (1,11) (18,22) (30,10) (31,12) (13,31) (29,11) (20,33) (10,15) (31,8) (20,7) (16,0) (16,24) (17,30) (18,29) (4,21) (16,27) (14,11) (6,12) (25,34) (28,7) (28,3) (2,7) (19,16) (9,31) (21,25) (23,33) (26,12) (5,15) (21,0) (23,32) (15,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "547"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (9,18) (16,12) (0,3) (4,11) (18,1) (15,21) (21,13) (20,3) (0,8) (12,17) (17,6) (1,13) (0,19) (2,5) (11,10) (14,16) (12,19) (14,7) (10,8) (15,8) (2,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "548"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (2,10) (18,13) (4,21) (17,9) (16,9) (0,20) (5,6) (21,7) (14,4) (14,0) (19,7) (4,10) (18,12) (7,3) (8,17) (22,5) (22,15) (0,18) (5,10) (12,8) (1,12) (12,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "549"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (24,7) (0,4) (23,20) (3,0) (13,4) (15,5) (14,28) (2,0) (21,8) (18,7) (26,2) (17,27) (9,23) (27,6) (27,22) (2,17) (20,7) (4,5) (21,19) (20,16) (21,10) (0,9) (11,25) (0,13) (4,28) (9,3) (0,1) (23,6) (25,5) (1,8) (12,27) (21,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "550"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (21,17) (19,4) (1,0) (11,23) (14,6) (27,15) (8,22) (16,8) (23,26) (16,14) (10,26) (17,4) (0,9) (23,2) (21,12) (7,1) (11,19) (25,24) (13,10) (24,22) (15,20) (6,18) (0,16) (17,24) (9,3) (24,5) (1,15) (27,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "551"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,14) (11,5) (13,5) (19,20) (9,11) (8,2) (11,14) (10,13) (1,0) (22,7) (14,12) (0,20) (0,7) (15,8) (12,17) (4,16) (1,17) (21,1) (5,4) (6,16) (1,15) (1,3) (18,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "552"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,1) (8,12) (7,15) (3,13) (0,3) (5,0) (8,1) (11,1) (9,5) (0,2) (0,6) (0,4) (1,9) (3,6) (10,15) (3,14) (6,16) (9,13) (16,10) (2,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "553"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (6,17) (9,11) (11,8) (16,7) (18,2) (2,0) (0,17) (5,11) (15,12) (9,4) (14,2) (3,5) (1,0) (14,0) (1,2) (7,14) (10,7) (4,12) (4,0) (13,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "554"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (5,2) (2,8) (8,4) (0,7) (1,8) (3,8) (7,6) (2,0) (9,0) (10,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "555"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (6,1) (6,14) (0,6) (2,6) (1,5) (9,13) (12,8) (11,10) (8,14) (3,9) (12,7) (13,14) (3,15) (6,4) (11,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "556"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,11) (3,11) (8,13) (23,9) (10,1) (16,21) (25,24) (12,6) (15,6) (1,12) (4,18) (20,1) (0,24) (15,19) (22,21) (7,11) (2,17) (22,24) (20,25) (11,23) (14,9) (13,15) (17,18) (5,1) (2,25)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "557"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (10,11) (20,1) (12,23) (10,19) (18,28) (1,19) (18,5) (13,3) (14,11) (22,10) (0,20) (26,11) (2,11) (5,21) (21,25) (15,9) (9,23) (24,18) (27,8) (22,8) (16,22) (24,15) (24,7) (13,6) (14,17) (3,2) (23,19) (13,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "558"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,1) (7,11) (4,8) (0,2) (7,12) (3,12) (7,1) (2,9) (1,0) (12,5) (12,9) (10,7) (4,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "559"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (15,8) (19,18) (20,8) (0,17) (3,21) (16,14) (2,8) (10,4) (19,22) (12,4) (21,6) (11,15) (16,5) (0,1) (11,9) (7,20) (0,21) (19,21) (15,1) (0,12) (11,13) (14,22) (17,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "560"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (23,24) (6,30) (20,17) (28,24) (6,5) (24,17) (14,20) (10,29) (7,31) (31,2) (4,25) (13,26) (27,32) (31,4) (9,13) (26,15) (16,1) (29,20) (0,7) (22,32) (11,28) (28,16) (7,28) (18,22) (18,8) (6,19) (9,21) (25,15) (8,12) (3,18) (1,8) (4,33) (2,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "561"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (24,12) (29,0) (17,25) (15,16) (30,2) (7,21) (6,28) (30,13) (15,25) (17,5) (18,10) (28,11) (14,7) (28,12) (28,27) (2,19) (8,9) (23,29) (12,20) (14,17) (23,18) (4,14) (3,4) (10,22) (23,6) (15,9) (26,29) (1,15) (19,14) (6,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "562"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (19,6) (13,20) (4,5) (0,30) (27,26) (5,16) (7,15) (21,14) (20,22) (0,2) (2,17) (12,24) (1,31) (3,0) (9,22) (15,14) (14,20) (25,21) (14,0) (22,23) (8,30) (21,4) (27,17) (27,6) (31,6) (10,21) (1,0) (4,12) (18,9) (29,27) (28,5) (23,3) (17,21) (11,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "563"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (11,12) (6,9) (13,0) (9,7) (14,15) (11,8) (5,7) (4,0) (4,10) (14,8) (1,4) (1,6) (14,2) (3,1) (14,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "564"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (3,10) (4,5) (7,11) (5,16) (0,4) (2,0) (7,9) (20,4) (3,0) (16,1) (6,17) (0,15) (12,13) (11,19) (17,8) (9,4) (15,12) (9,10) (0,10) (18,0) (2,14) (0,1) (14,17) (19,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "565"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (17,19) (11,13) (15,5) (14,4) (17,3) (3,2) (0,4) (16,3) (18,12) (22,5) (14,2) (21,20) (13,16) (1,8) (22,7) (6,10) (14,9) (14,8) (12,11) (6,20) (1,21) (7,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "566"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (7,0) (9,0) (8,18) (13,27) (7,8) (11,1) (10,26) (9,19) (20,7) (2,15) (11,7) (4,23) (4,21) (20,22) (21,10) (22,17) (9,24) (19,23) (15,13) (0,28) (0,14) (9,5) (3,15) (14,12) (25,9) (21,16) (13,6) (27,26)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "567"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (15,0) (6,1) (7,3) (1,16) (0,1) (2,10) (6,8) (7,13) (0,2) (5,15) (2,11) (0,6) (16,12) (9,14) (8,10) (0,4) (13,9) (3,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "568"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (7,4) (1,12) (6,3) (15,2) (14,17) (8,11) (12,8) (7,5) (16,2) (4,2) (10,7) (16,12) (13,6) (6,15) (12,0) (5,9) (17,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "569"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (7,13) (10,18) (25,15) (16,10) (6,1) (1,0) (0,2) (17,4) (23,21) (23,18) (14,7) (6,22) (19,14) (15,8) (20,12) (12,11) (0,4) (25,17) (9,5) (6,12) (2,19) (24,14) (15,1) (17,2) (17,23) (14,3) (9,15)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "570"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (26,20) (3,22) (27,23) (2,12) (20,1) (0,15) (2,19) (18,9) (9,27) (19,1) (16,2) (15,17) (23,25) (24,23) (4,8) (6,13) (0,3) (25,8) (15,7) (8,11) (21,25) (2,4) (8,5) (10,0) (9,13) (9,3) (14,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "571"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,3) (0,2) (2,6) (1,0) (3,0) (5,3) (8,2) (0,5) (3,2) (4,0) (2,4) (4,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "572"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,0) (4,8) (9,2) (8,7) (0,3) (5,7) (0,2) (5,6) (4,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "573"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (10,6) (16,1) (23,11) (24,26) (22,24) (14,3) (19,0) (5,18) (4,21) (27,4) (11,7) (15,26) (15,12) (16,12) (26,2) (26,23) (21,14) (19,25) (14,20) (10,9) (7,9) (13,17) (5,4) (17,8) (10,0) (17,0) (9,21)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "574"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (4,3) (2,0) (4,1) (3,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "575"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (12,11) (0,2) (9,10) (7,1) (3,12) (10,2) (7,14) (7,9) (9,5) (0,4) (12,4) (1,8) (0,13) (13,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "576"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (4,14) (0,16) (3,7) (1,2) (3,14) (0,14) (18,11) (17,13) (9,1) (9,15) (18,16) (8,19) (12,13) (19,11) (5,4) (0,1) (19,10) (11,6) (20,12) (0,2) (17,19) (3,0) (15,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "577"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (1,0) (29,15) (6,14) (29,17) (16,21) (14,0) (13,21) (1,7) (8,30) (11,26) (28,3) (11,3) (14,27) (15,18) (12,16) (25,22) (18,4) (21,28) (19,21) (20,21) (23,27) (5,13) (28,22) (8,24) (26,27) (10,29) (2,24) (24,9) (23,1) (2,29) (10,22)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "578"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (1,18) (9,14) (11,18) (14,10) (5,3) (12,2) (5,12) (15,6) (7,6) (19,17) (5,4) (7,8) (6,19) (14,16) (0,2) (8,14) (6,12) (20,2) (15,11) (14,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "579"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (14,3) (14,10) (5,3) (24,5) (14,0) (2,4) (8,14) (18,25) (22,25) (13,6) (11,16) (24,7) (15,16) (21,16) (20,26) (20,15) (19,23) (9,4) (20,22) (1,17) (12,18) (9,14) (2,17) (25,17) (25,19) (5,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "580"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (15,10) (9,2) (17,19) (3,14) (19,18) (15,2) (20,7) (22,16) (13,12) (23,12) (14,20) (9,21) (11,6) (24,11) (4,0) (4,17) (11,16) (13,0) (17,25) (19,10) (1,0) (5,2) (2,11) (25,7) (3,1) (19,8) (0,2) (3,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "581"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,1) (1,9) (0,22) (17,32) (26,8) (5,9) (12,30) (26,28) (27,24) (14,29) (16,13) (4,9) (0,23) (10,18) (4,25) (19,33) (15,20) (2,14) (3,10) (7,31) (18,11) (26,27) (31,21) (26,6) (0,15) (32,27) (30,14) (23,1) (2,21) (11,32) (0,2) (28,2) (7,23) (5,33) (13,30)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "582"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (19,0) (6,2) (21,15) (12,0) (3,10) (16,18) (7,9) (6,4) (1,16) (9,4) (1,10) (11,19) (11,15) (13,1) (22,17) (7,15) (17,0) (10,20) (22,16) (8,22) (14,3) (5,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "583"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (10,3) (5,13) (3,0) (1,0) (11,2) (11,1) (16,15) (17,1) (3,6) (17,9) (7,17) (10,16) (4,14) (16,7) (13,8) (12,1) (0,2) (8,4) (1,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "584"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (23,1) (11,17) (8,24) (1,0) (31,7) (33,30) (29,11) (15,16) (27,1) (21,4) (9,15) (28,33) (19,3) (13,0) (16,6) (2,4) (8,19) (13,20) (4,23) (22,10) (32,29) (12,28) (18,14) (30,20) (5,27) (29,13) (23,8) (18,33) (7,24) (26,32) (10,26) (25,29) (6,31)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "585"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (13,1) (5,17) (19,0) (10,18) (9,0) (10,19) (11,2) (12,14) (4,6) (3,20) (13,17) (15,3) (8,7) (7,2) (11,16) (19,5) (5,14) (8,1) (20,1) (4,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "586"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (11,0) (13,10) (23,4) (3,22) (18,21) (0,10) (6,2) (24,15) (20,9) (0,17) (13,14) (12,1) (8,5) (22,16) (14,20) (5,19) (4,19) (25,21) (7,24) (4,22) (10,21) (16,12) (5,14) (6,10) (7,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "587"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (11,7) (0,21) (26,20) (1,4) (14,25) (17,25) (3,25) (8,10) (5,6) (13,21) (23,16) (13,18) (14,18) (10,16) (17,24) (12,17) (15,13) (5,2) (3,1) (10,17) (19,14) (25,9) (11,25) (14,26) (2,19) (22,26)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "588"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (14,11) (9,16) (14,23) (3,8) (17,0) (13,20) (11,13) (11,25) (8,19) (9,5) (13,9) (3,4) (17,8) (25,24) (0,7) (19,18) (0,23) (0,21) (1,17) (12,15) (5,2) (15,11) (6,13) (10,21) (13,22)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "589"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (23,14) (9,27) (27,11) (5,20) (30,11) (24,9) (23,10) (27,13) (17,15) (15,14) (3,0) (1,19) (22,6) (24,8) (24,20) (21,25) (3,1) (18,24) (26,16) (12,18) (2,0) (25,17) (6,31) (16,8) (2,23) (7,30) (14,4) (8,29) (9,28) (10,1) (31,25) (0,1) (27,23)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "590"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (8,10) (0,1) (10,2) (6,5) (0,5) (4,9) (0,2) (4,1) (0,8) (3,2) (7,0) (3,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "591"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,8) (0,7) (4,3) (1,7) (8,4) (2,3) (2,9) (0,1) (0,2) (5,9) (3,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "592"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (16,1) (0,3) (0,2) (21,19) (17,3) (18,13) (0,4) (12,7) (2,13) (9,11) (11,6) (0,1) (16,8) (10,16) (5,9) (0,7) (21,12) (10,20) (15,8) (13,8) (14,21) (12,20) (9,4) (17,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "593"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (29,25) (16,21) (26,10) (1,11) (0,14) (6,13) (15,13) (26,28) (9,27) (15,2) (24,9) (20,7) (22,20) (0,9) (10,21) (23,19) (0,25) (9,5) (12,14) (9,19) (3,15) (7,0) (4,21) (7,11) (8,7) (22,17) (18,8) (23,4) (13,27) (0,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "594"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (8,20) (17,29) (16,9) (7,3) (14,0) (30,29) (18,8) (18,24) (25,17) (18,6) (6,27) (13,22) (24,9) (0,24) (4,30) (15,21) (13,26) (7,22) (23,16) (11,3) (1,29) (19,2) (20,10) (19,11) (12,17) (28,0) (6,1) (1,0) (20,15) (27,5) (2,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "595"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (11,10) (3,7) (5,7) (0,7) (5,1) (6,4) (4,8) (6,0) (9,3) (2,7) (10,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "596"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (1,8) (3,13) (11,13) (2,3) (2,14) (1,6) (14,4) (16,6) (7,14) (12,16) (0,4) (5,12) (10,11) (9,5) (8,14) (15,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "597"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (22,21) (16,14) (20,14) (5,23) (8,9) (23,11) (5,15) (14,12) (10,7) (19,15) (25,7) (0,2) (8,25) (5,25) (18,17) (1,9) (16,4) (2,22) (24,2) (22,11) (9,13) (25,4) (3,17) (13,6) (23,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "598"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (9,11) (8,21) (16,26) (15,22) (0,3) (20,27) (25,10) (6,9) (4,25) (5,9) (17,19) (13,2) (7,12) (26,12) (5,24) (22,3) (23,24) (20,10) (7,0) (18,22) (16,25) (13,8) (1,16) (21,17) (13,23) (27,8) (11,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "599"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (6,2) (8,4) (0,1) (10,7) (5,9) (7,9) (3,2) (2,1) (8,3) (2,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "600"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (5,2) (24,8) (32,31) (18,22) (16,7) (33,32) (33,6) (15,2) (30,9) (1,33) (26,6) (1,0) (29,7) (33,4) (20,16) (3,27) (25,12) (28,17) (13,15) (20,3) (34,19) (20,21) (9,19) (13,8) (3,26) (9,14) (28,11) (1,23) (18,10) (29,12) (22,17) (21,14) (20,11) (29,0) (3,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "601"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (7,10) (0,4) (2,5) (6,8) (0,9) (4,5) (0,1) (0,2) (6,3) (5,0) (0,10) (3,0) (1,3) (5,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "602"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (5,8) (10,7) (10,11) (1,4) (7,2) (2,12) (10,1) (7,3) (3,9) (7,6) (5,3) (2,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "603"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (10,3) (14,6) (2,3) (3,13) (4,1) (11,6) (9,8) (12,2) (5,6) (3,7) (0,6) (4,11) (9,2) (12,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "604"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,12) (0,1) (21,17) (6,3) (8,23) (15,6) (19,15) (13,23) (8,14) (7,4) (4,2) (16,12) (21,16) (17,2) (23,22) (5,10) (7,11) (22,20) (1,12) (12,18) (6,13) (2,19) (19,9) (5,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "605"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (3,28) (0,2) (25,23) (0,3) (18,9) (7,8) (21,26) (4,10) (1,3) (20,5) (0,6) (31,27) (29,21) (23,19) (6,18) (14,3) (22,0) (5,10) (10,21) (17,16) (12,27) (16,13) (2,21) (0,1) (30,4) (20,15) (11,9) (1,23) (4,0) (15,1) (0,24) (6,31) (17,23) (31,30) (21,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "606"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (1,10) (0,1) (11,4) (7,2) (7,1) (7,11) (9,11) (4,0) (2,6) (5,8) (0,3) (5,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "607"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (3,8) (4,0) (3,4) (9,5) (1,0) (6,0) (9,7) (8,1) (2,4) (9,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "608"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (17,0) (8,1) (9,2) (14,5) (15,16) (15,2) (14,6) (10,5) (8,15) (11,9) (12,13) (16,7) (3,4) (3,0) (14,3) (16,12) (6,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "609"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (7,1) (15,8) (2,13) (15,2) (14,0) (4,22) (18,2) (2,12) (21,7) (3,14) (9,19) (1,0) (6,9) (19,1) (9,20) (21,11) (3,0) (2,0) (12,14) (8,10) (4,0) (4,21) (20,2) (5,9) (6,17) (16,21)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "610"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,4) (7,5) (2,8) (6,7) (1,7) (1,0) (8,6) (0,2) (3,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "611"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (23,0) (15,8) (13,7) (17,14) (14,1) (16,7) (10,19) (22,24) (11,5) (14,10) (17,5) (21,11) (6,16) (4,23) (12,18) (18,21) (23,8) (3,9) (22,2) (3,19) (20,17) (24,23) (20,24) (15,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "612"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (25,8) (26,16) (32,3) (6,27) (9,13) (9,16) (22,10) (6,17) (23,12) (14,6) (18,11) (19,20) (1,6) (29,24) (17,21) (4,24) (20,18) (7,2) (30,12) (28,4) (20,22) (32,25) (7,12) (16,15) (7,29) (2,0) (6,4) (1,26) (19,1) (5,12) (26,31) (27,25)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "613"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (26,24) (17,10) (21,0) (26,16) (25,29) (9,29) (13,27) (19,2) (11,7) (25,15) (10,8) (0,1) (23,14) (16,10) (0,3) (25,19) (18,14) (13,22) (28,17) (13,18) (21,17) (11,29) (1,4) (5,6) (25,3) (0,2) (12,27) (25,17) (14,26) (27,20) (5,2) (3,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "614"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (29,4) (12,1) (29,10) (7,3) (26,21) (4,28) (9,19) (21,7) (27,24) (28,15) (0,18) (14,0) (18,13) (5,6) (22,16) (2,10) (4,23) (8,17) (26,0) (8,12) (9,17) (7,24) (12,27) (23,20) (11,12) (25,18) (30,23) (14,30) (28,5) (24,22)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "615"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (3,4) (3,7) (2,5) (2,8) (3,2) (6,3) (1,6) (6,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "616"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (10,9) (12,5) (3,10) (11,1) (13,5) (6,12) (13,10) (12,7) (2,4) (2,8) (11,0) (13,1) (0,1) (4,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "617"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (4,8) (8,1) (4,7) (3,6) (5,8) (0,2) (7,0) (9,3) (8,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "618"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,7) (0,1) (3,0) (4,5) (5,3) (2,1) (0,7) (2,8) (3,6) (0,2) (8,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "619"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (10,6) (17,0) (21,18) (7,3) (21,10) (11,0) (8,5) (21,13) (14,5) (23,4) (20,14) (5,19) (24,7) (4,19) (16,12) (2,6) (22,16) (10,25) (15,24) (10,0) (26,13) (20,9) (22,4) (22,3) (14,13) (12,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "620"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (26,17) (5,22) (8,31) (13,33) (12,1) (10,3) (0,13) (8,4) (7,23) (2,16) (34,10) (23,6) (27,26) (33,9) (28,30) (10,24) (18,7) (0,15) (13,25) (20,15) (24,11) (24,21) (8,0) (14,15) (22,34) (28,8) (19,30) (13,10) (1,29) (29,4) (17,11) (6,15) (3,16) (0,32)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "621"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (3,11) (8,13) (12,10) (11,4) (8,10) (0,3) (2,9) (12,15) (6,9) (7,12) (5,9) (8,5) (13,14) (7,0) (13,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "622"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (12,10) (7,0) (8,6) (3,0) (15,0) (2,3) (4,6) (8,14) (9,1) (0,4) (16,12) (16,14) (14,7) (9,5) (11,13) (11,4) (9,13) (2,0) (0,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "623"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (1,2) (9,3) (10,1) (11,5) (2,4) (6,5) (1,0) (6,2) (11,7) (9,5) (8,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "624"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (11,0) (11,9) (11,4) (3,0) (1,0) (2,6) (2,4) (5,1) (3,8) (0,10) (7,3) (0,7) (1,3) (2,0) (4,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "625"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (8,4) (17,3) (20,1) (15,11) (10,22) (26,13) (0,16) (7,27) (0,3) (28,1) (23,14) (18,23) (15,27) (7,24) (5,3) (12,7) (2,19) (25,20) (1,0) (24,14) (9,25) (29,3) (26,0) (2,0) (23,6) (16,22) (21,29) (4,0) (17,12) (28,11) (26,5) (11,8) (19,20)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "626"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (3,4) (5,2) (0,2) (0,1) (7,4) (2,4) (2,6) (1,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "627"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (2,14) (8,0) (4,9) (15,12) (17,14) (6,0) (3,2) (16,10) (9,5) (5,10) (12,13) (7,1) (4,7) (9,15) (0,11) (17,5) (0,15)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "628"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (7,13) (0,16) (6,3) (12,17) (1,8) (15,0) (7,10) (8,0) (18,15) (15,9) (16,14) (2,10) (17,4) (11,6) (4,7) (3,9) (5,6) (8,17)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "629"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (8,3) (1,0) (1,8) (8,4) (4,6) (0,5) (5,7) (2,0) (6,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "630"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (2,1) (4,1) (3,2) (0,4) (6,5) (5,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "631"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (22,16) (2,15) (20,7) (0,7) (12,14) (10,9) (7,8) (22,9) (15,13) (20,18) (4,21) (3,15) (9,0) (24,19) (0,14) (5,9) (13,21) (8,17) (6,13) (10,21) (11,1) (23,4) (19,23) (11,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "632"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (5,13) (11,10) (6,3) (4,2) (16,7) (22,26) (19,11) (20,15) (9,27) (1,4) (7,17) (14,5) (15,13) (5,9) (22,25) (0,6) (26,15) (11,22) (14,8) (23,15) (21,4) (2,11) (3,23) (24,0) (28,19) (22,18) (23,7) (12,19)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "633"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (6,33) (12,34) (0,3) (2,12) (28,6) (23,0) (30,27) (27,22) (5,0) (16,15) (13,3) (0,14) (1,18) (16,20) (31,22) (16,5) (27,16) (10,14) (22,21) (1,0) (23,26) (27,29) (8,1) (9,12) (20,0) (4,18) (24,11) (4,29) (25,32) (1,11) (17,4) (24,7) (25,6) (2,0) (17,19) (19,32) (25,13) (4,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "634"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (17,14) (2,6) (13,10) (21,16) (4,3) (3,7) (2,0) (10,6) (4,18) (20,9) (1,12) (11,0) (0,1) (14,5) (10,0) (8,5) (0,3) (13,14) (19,4) (5,19) (0,15) (16,12) (10,21) (20,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "635"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (19,18) (21,23) (25,24) (27,22) (22,2) (24,20) (13,7) (7,18) (8,15) (14,1) (9,16) (13,15) (27,24) (14,10) (0,23) (3,28) (16,19) (21,10) (3,25) (17,14) (3,12) (26,11) (26,6) (23,4) (17,20) (8,23) (5,11) (5,17)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "636"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (9,10) (1,3) (10,0) (4,0) (0,3) (0,1) (2,7) (5,8) (0,8) (2,0) (3,2) (6,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "637"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (27,14) (31,1) (9,25) (15,2) (34,20) (30,33) (30,29) (10,28) (7,8) (19,21) (19,26) (12,13) (22,24) (30,12) (2,1) (20,11) (6,5) (9,22) (5,3) (32,22) (3,26) (24,8) (5,23) (11,18) (12,19) (29,1) (10,2) (24,11) (29,4) (13,17) (28,14) (16,3) (0,31) (29,20)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "638"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (30,12) (28,27) (11,9) (32,14) (5,25) (23,10) (6,17) (5,14) (27,5) (15,24) (19,30) (17,20) (17,29) (22,8) (2,30) (21,25) (21,31) (3,32) (24,0) (3,13) (1,3) (29,13) (4,12) (0,9) (0,16) (14,22) (7,33) (32,4) (23,26) (18,23) (9,28) (21,10) (33,1) (34,28)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "639"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (11,26) (3,28) (11,2) (0,29) (11,13) (11,12) (5,25) (15,7) (28,14) (5,18) (2,0) (20,4) (18,1) (29,8) (15,3) (4,5) (25,24) (2,16) (21,19) (28,17) (0,1) (23,3) (27,17) (26,19) (29,12) (1,19) (23,10) (6,27) (12,22) (21,3) (18,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "640"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (5,23) (12,1) (6,29) (22,4) (15,17) (22,13) (19,11) (20,9) (0,9) (33,5) (10,14) (7,12) (2,21) (2,31) (1,22) (28,23) (30,26) (0,3) (32,16) (9,4) (3,29) (25,31) (29,21) (1,0) (26,11) (3,5) (31,16) (4,0) (0,2) (6,24) (31,18) (24,30) (6,7) (8,28) (15,7) (27,19) (15,34) (15,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "641"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (11,7) (5,16) (18,4) (15,14) (12,16) (3,6) (1,5) (16,9) (1,8) (8,4) (2,19) (14,0) (20,7) (17,11) (0,1) (5,19) (14,6) (10,15) (0,3) (11,13) (0,2) (11,1) (0,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "642"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (1,17) (16,21) (11,15) (1,0) (15,8) (23,18) (14,2) (16,5) (9,17) (16,19) (0,2) (3,0) (6,8) (22,20) (19,0) (20,6) (13,4) (18,1) (0,12) (17,3) (23,7) (4,0) (23,20) (20,2) (6,19) (4,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "643"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (13,20) (7,6) (15,11) (17,23) (7,1) (17,5) (18,0) (22,15) (19,8) (0,15) (18,14) (2,16) (7,21) (19,10) (20,25) (3,18) (17,8) (12,15) (15,17) (17,24) (9,4) (12,20) (22,6) (2,19) (4,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "644"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (12,11) (15,18) (4,3) (0,1) (18,3) (9,10) (3,10) (6,18) (16,1) (17,16) (2,11) (0,12) (0,3) (16,4) (14,7) (0,8) (13,2) (9,13) (2,0) (0,7) (11,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "645"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (19,16) (6,18) (25,15) (3,7) (0,20) (8,12) (15,23) (4,9) (14,24) (20,22) (14,12) (12,2) (12,26) (11,5) (2,15) (14,0) (4,17) (6,28) (15,29) (7,25) (10,6) (7,4) (1,13) (21,12) (18,27) (11,22) (2,1) (28,26) (6,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "646"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (14,18) (1,22) (3,22) (9,8) (4,17) (19,11) (20,14) (21,7) (11,2) (9,18) (15,8) (15,21) (2,17) (1,4) (10,18) (20,16) (9,13) (6,0) (12,18) (2,5) (11,8) (15,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "647"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (5,3) (3,4) (6,7) (7,3) (0,3) (8,0) (6,9) (2,3) (9,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "648"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (7,16) (8,23) (8,1) (27,24) (16,22) (1,0) (12,15) (13,11) (24,25) (6,16) (17,11) (18,2) (2,0) (12,16) (13,0) (0,26) (20,5) (0,4) (15,10) (3,4) (18,9) (9,21) (18,19) (14,3) (14,6) (0,3) (5,14) (8,13) (2,15) (27,17)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "649"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (9,19) (17,19) (23,22) (23,7) (20,5) (15,4) (13,19) (16,18) (7,20) (0,23) (10,17) (4,12) (22,13) (2,6) (15,21) (6,13) (23,1) (13,21) (1,14) (16,5) (21,3) (1,11) (8,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "650"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (5,4) (7,1) (1,2) (15,13) (16,13) (13,2) (3,10) (11,1) (12,4) (17,2) (1,6) (3,11) (2,8) (10,0) (6,14) (9,17) (16,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "651"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (11,8) (6,23) (4,9) (0,5) (4,3) (18,14) (13,6) (21,7) (10,15) (23,1) (15,18) (19,18) (10,17) (16,3) (20,5) (10,4) (2,3) (12,20) (22,2) (8,21) (13,14) (13,0) (21,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "652"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (6,2) (0,5) (4,0) (11,7) (3,2) (5,10) (4,10) (8,2) (0,2) (7,10) (1,0) (6,7) (0,3) (1,9) (9,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "653"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,6) (7,11) (19,4) (11,22) (6,2) (10,3) (23,13) (8,12) (25,8) (7,23) (15,1) (11,8) (0,17) (3,24) (5,7) (11,21) (4,27) (25,1) (21,18) (22,14) (5,16) (16,9) (10,14) (12,26) (22,20) (1,0) (7,27)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "654"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,1) (2,4) (2,3) (4,1) (8,2) (7,1) (1,9) (6,4) (3,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "655"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,2) (4,7) (6,4) (0,9) (3,12) (6,12) (4,9) (3,0) (1,11) (10,13) (8,5) (5,2) (2,13) (8,6) (0,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "656"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (1,9) (11,6) (9,3) (0,3) (0,10) (7,3) (10,8) (6,7) (3,4) (5,11) (3,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "657"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (9,1) (10,8) (16,2) (5,14) (7,12) (11,4) (16,10) (13,6) (14,10) (3,15) (0,3) (17,7) (4,3) (12,2) (13,12) (9,14) (6,4) (8,18)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "658"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (12,15) (26,24) (1,3) (17,21) (9,11) (31,7) (13,29) (26,4) (31,0) (3,6) (15,25) (24,22) (27,15) (14,17) (10,0) (20,30) (17,4) (23,19) (18,1) (20,10) (10,25) (11,31) (13,18) (1,0) (31,23) (5,8) (16,27) (18,11) (21,2) (7,28) (0,5) (25,22)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "659"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (18,14) (6,7) (0,6) (18,10) (4,3) (3,10) (12,15) (11,7) (11,9) (22,14) (22,1) (6,5) (13,21) (7,21) (20,18) (17,7) (12,17) (19,2) (8,14) (21,19) (18,19) (17,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "660"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (17,6) (11,4) (24,30) (0,4) (33,3) (33,2) (12,30) (9,19) (0,1) (1,2) (29,0) (10,34) (32,19) (31,18) (13,4) (14,15) (5,21) (31,0) (7,33) (5,28) (3,22) (6,20) (1,16) (21,7) (9,13) (27,8) (12,28) (26,34) (31,15) (2,0) (10,7) (0,3) (18,12) (32,2) (23,25) (0,23) (21,20) (33,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "661"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (21,31) (21,0) (12,15) (31,9) (7,27) (30,17) (29,18) (25,12) (20,7) (30,13) (19,16) (18,22) (15,10) (24,16) (11,1) (8,31) (3,28) (12,31) (15,11) (5,15) (11,20) (29,23) (11,14) (0,1) (16,0) (21,4) (13,19) (28,10) (16,26) (7,2) (12,23) (12,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "662"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (13,17) (18,12) (15,14) (16,21) (3,6) (22,1) (9,5) (7,2) (10,13) (16,12) (4,6) (2,11) (0,2) (2,9) (8,5) (20,17) (17,15) (21,11) (9,4) (19,12) (20,1) (10,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "663"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (20,23) (28,24) (8,24) (1,0) (28,19) (31,7) (7,13) (21,3) (15,27) (6,21) (16,18) (7,9) (8,1) (12,0) (25,2) (28,27) (21,16) (12,11) (22,9) (29,12) (5,11) (4,29) (1,9) (27,0) (2,30) (7,10) (15,14) (22,30) (10,23) (2,0) (17,30) (5,3) (6,26)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "664"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (27,14) (15,6) (25,29) (9,22) (5,21) (16,21) (8,26) (10,18) (6,5) (24,18) (23,27) (24,0) (12,6) (7,12) (1,22) (20,23) (2,17) (14,28) (3,0) (11,5) (29,14) (22,2) (20,3) (5,13) (26,24) (22,21) (19,4) (25,4) (23,9) (0,30)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "665"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (7,4) (6,18) (22,21) (12,0) (2,14) (13,27) (23,19) (4,24) (13,23) (21,16) (5,10) (6,15) (5,7) (2,17) (15,26) (19,18) (17,22) (25,6) (6,3) (12,24) (1,0) (8,23) (19,2) (12,16) (1,12) (29,28) (25,28) (7,11) (8,20) (19,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "666"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (21,0) (22,2) (13,12) (0,3) (4,11) (11,16) (7,19) (9,5) (17,26) (15,22) (24,1) (0,27) (16,12) (19,14) (8,6) (18,24) (15,28) (8,14) (28,10) (18,9) (13,9) (14,28) (23,4) (25,0) (26,7) (23,6) (20,2) (3,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "667"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (6,2) (3,9) (15,17) (19,0) (3,4) (7,12) (13,18) (2,21) (18,20) (6,7) (0,22) (8,11) (7,8) (17,2) (5,20) (10,0) (21,3) (13,1) (19,16) (7,16) (0,1) (14,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "668"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (14,3) (8,16) (16,1) (7,3) (14,5) (13,6) (5,10) (14,15) (17,16) (3,2) (10,8) (12,9) (5,9) (3,11) (19,0) (8,19) (14,18) (10,4) (6,11) (0,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "669"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (6,3) (0,2) (0,6) (1,0) (4,3) (5,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "670"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (12,5) (9,13) (20,22) (30,12) (1,6) (3,32) (26,16) (18,20) (2,0) (9,16) (24,29) (7,29) (11,18) (23,12) (15,16) (6,4) (6,14) (32,25) (24,4) (27,25) (26,1) (20,19) (8,25) (12,7) (31,26) (19,1) (4,28) (7,2) (27,6) (10,22) (17,21) (17,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "671"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (7,2) (1,0) (33,5) (22,23) (11,9) (7,24) (0,2) (21,13) (28,18) (4,32) (21,31) (29,18) (25,23) (19,10) (12,5) (34,18) (27,10) (9,16) (18,5) (1,22) (14,26) (31,0) (3,10) (25,13) (3,4) (5,6) (22,15) (30,4) (3,0) (4,7) (30,14) (13,30) (10,6) (2,20) (11,25) (7,8) (7,17)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "672"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (4,11) (5,1) (8,6) (8,10) (4,3) (7,9) (7,2) (6,9) (3,0) (10,0) (10,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "673"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (3,9) (0,3) (8,2) (6,8) (5,1) (1,0) (5,2) (8,0) (4,7) (8,4) (3,8) (0,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "674"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (3,14) (2,0) (15,7) (13,0) (12,14) (16,6) (16,5) (11,15) (1,17) (5,1) (6,2) (1,8) (0,3) (16,9) (0,1) (8,4) (14,5) (4,11) (11,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "675"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (8,0) (9,1) (4,5) (7,0) (5,10) (7,3) (8,6) (2,4) (9,10) (10,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "676"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (4,9) (0,4) (2,8) (8,1) (9,6) (2,7) (7,5) (9,10) (3,1) (4,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "677"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (2,3) (0,3) (11,10) (7,0) (10,0) (1,3) (0,4) (11,6) (8,5) (0,9) (2,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "678"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (2,22) (26,1) (25,18) (25,0) (4,17) (20,7) (5,12) (0,4) (9,26) (19,1) (8,18) (4,14) (6,1) (13,16) (2,25) (7,12) (21,0) (3,2) (15,18) (20,26) (17,9) (10,23) (1,24) (17,16) (11,18) (20,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "679"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (10,12) (4,8) (2,9) (11,4) (15,0) (6,16) (14,1) (1,12) (17,11) (13,1) (2,7) (2,1) (13,4) (9,5) (3,14) (6,15) (5,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "680"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (9,6) (9,7) (16,0) (3,16) (6,14) (2,14) (12,4) (17,14) (10,7) (4,1) (1,6) (1,5) (11,13) (8,11) (14,8) (16,4) (15,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "681"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,3) (0,9) (9,10) (5,7) (5,2) (8,3) (7,4) (6,0) (5,8) (6,9) (11,4) (1,0) (4,0) (5,0) (2,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "682"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (13,1) (21,20) (25,16) (7,15) (9,6) (24,2) (23,18) (24,6) (4,0) (25,12) (16,10) (17,9) (18,3) (15,3) (25,15) (14,5) (19,5) (17,4) (1,22) (3,4) (11,9) (15,13) (24,5) (21,8) (5,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "683"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (14,13) (12,8) (18,10) (17,14) (17,11) (6,17) (0,7) (11,12) (5,3) (17,2) (7,5) (16,15) (2,0) (1,0) (1,16) (10,16) (18,12) (8,7) (9,17) (7,4) (3,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "684"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (12,7) (0,1) (9,8) (3,1) (9,1) (7,6) (8,5) (0,2) (2,10) (7,2) (4,0) (4,9) (11,4) (7,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "685"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (22,13) (20,23) (25,2) (13,5) (16,9) (0,20) (4,5) (16,13) (15,10) (1,18) (12,14) (14,11) (4,19) (25,21) (14,0) (1,24) (12,17) (0,7) (1,17) (3,8) (23,8) (5,11) (15,11) (2,7) (1,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "686"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (8,4) (8,6) (1,0) (9,2) (3,4) (4,1) (4,9) (10,1) (10,5) (7,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "687"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (9,3) (9,18) (0,3) (19,1) (4,8) (0,10) (14,10) (0,2) (1,0) (1,20) (2,19) (5,8) (21,25) (20,23) (8,25) (3,22) (23,9) (8,11) (13,9) (6,13) (2,12) (15,0) (24,25) (2,4) (16,2) (15,17) (7,15)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "688"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (18,12) (11,2) (1,3) (7,14) (19,10) (12,13) (2,5) (9,2) (11,16) (15,9) (1,0) (11,6) (17,16) (14,3) (13,0) (2,19) (4,17) (19,8) (7,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "689"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (5,17) (16,17) (0,14) (17,1) (7,13) (5,11) (8,12) (14,11) (10,8) (13,17) (4,3) (15,9) (2,16) (1,3) (15,3) (7,6) (10,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "690"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (22,6) (13,17) (8,13) (18,16) (19,1) (4,17) (10,11) (14,12) (20,17) (12,17) (0,1) (15,11) (0,23) (9,11) (22,19) (12,7) (12,1) (8,2) (12,3) (16,5) (0,18) (21,7) (5,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "691"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (7,6) (18,11) (3,5) (1,18) (14,9) (8,14) (1,0) (5,4) (14,10) (15,6) (2,12) (12,5) (15,11) (19,17) (12,6) (13,14) (7,8) (20,2) (2,0) (14,16) (19,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "692"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (5,32) (21,16) (26,16) (19,1) (30,4) (7,29) (9,16) (17,23) (12,31) (7,12) (17,6) (18,6) (28,12) (7,3) (25,20) (19,20) (9,15) (13,33) (12,8) (2,33) (26,32) (0,2) (10,25) (33,27) (24,4) (26,1) (24,29) (4,6) (6,1) (11,22) (27,6) (20,22) (14,18)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "693"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (8,10) (18,26) (8,16) (15,4) (1,17) (17,31) (28,25) (7,2) (0,15) (6,30) (9,23) (0,27) (1,0) (11,19) (26,7) (31,26) (28,10) (2,0) (22,2) (14,17) (21,0) (3,32) (5,3) (4,10) (24,23) (26,12) (2,13) (30,31) (2,24) (28,20) (11,22) (30,10) (32,24) (0,3) (29,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "694"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (2,0) (2,4) (2,7) (9,2) (4,8) (6,2) (8,3) (1,7) (5,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "695"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (1,18) (17,14) (1,19) (20,16) (14,16) (13,4) (3,5) (4,1) (15,0) (4,15) (2,0) (17,3) (3,11) (7,12) (4,10) (3,0) (6,12) (1,9) (17,7) (0,4) (1,0) (7,4) (4,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "696"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (14,3) (12,5) (4,7) (2,7) (5,13) (4,6) (0,9) (7,8) (10,5) (1,16) (1,8) (1,13) (2,11) (10,15) (3,11) (0,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "697"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (1,4) (3,13) (10,3) (8,13) (9,14) (14,5) (2,10) (10,12) (11,2) (0,4) (10,6) (4,10) (12,7) (2,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "698"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (5,4) (2,8) (10,1) (3,11) (11,6) (9,3) (7,1) (2,15) (12,13) (2,13) (6,1) (10,0) (2,1) (14,13) (4,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "699"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (4,3) (5,6) (5,8) (3,12) (4,0) (2,13) (4,1) (1,13) (12,8) (7,9) (11,12) (9,0) (2,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "700"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (4,8) (8,3) (2,7) (9,7) (1,0) (3,0) (4,0) (5,9) (2,3) (2,6) (1,2) (2,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "701"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (7,5) (7,8) (9,6) (10,0) (11,17) (17,8) (18,2) (17,2) (2,0) (8,16) (13,18) (14,13) (12,5) (3,10) (1,0) (1,4) (19,13) (11,15) (16,0) (2,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "702"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,8) (16,14) (11,6) (5,6) (0,15) (6,3) (15,9) (16,8) (17,12) (17,0) (7,13) (4,17) (7,10) (3,9) (2,0) (7,4) (0,1) (2,10) (0,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "703"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (1,10) (5,10) (9,3) (11,0) (1,12) (14,11) (4,8) (13,14) (11,2) (0,7) (2,3) (6,1) (4,3) (11,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "704"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (2,14) (7,8) (6,20) (7,22) (22,9) (17,15) (10,13) (15,0) (11,3) (17,20) (1,8) (11,10) (21,19) (18,7) (17,2) (11,4) (15,12) (11,5) (10,16) (4,2) (21,3) (7,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "705"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (7,8) (21,5) (9,18) (22,2) (2,21) (7,20) (13,0) (9,6) (0,3) (18,15) (11,4) (0,2) (17,25) (0,1) (1,12) (7,1) (10,1) (3,9) (24,25) (25,19) (8,16) (12,4) (10,14) (15,14) (0,23) (25,20) (5,4) (13,25)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "706"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (23,20) (16,0) (17,2) (18,2) (0,1) (15,26) (0,4) (9,21) (17,8) (16,20) (29,8) (17,11) (26,13) (15,30) (10,25) (22,2) (3,0) (8,7) (12,29) (10,3) (28,11) (13,20) (4,1) (0,2) (5,25) (25,19) (0,24) (23,27) (28,9) (7,5) (29,14) (30,6) (18,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "707"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (26,16) (17,12) (21,5) (34,22) (4,31) (16,28) (12,34) (13,20) (12,25) (19,26) (5,3) (31,15) (23,5) (27,21) (9,0) (30,5) (6,2) (17,1) (23,11) (16,29) (23,26) (18,6) (2,8) (34,20) (27,31) (30,9) (6,28) (32,12) (2,12) (10,0) (16,7) (14,1) (24,6) (33,18)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "708"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (21,23) (4,6) (15,8) (6,8) (28,23) (4,1) (27,19) (12,0) (12,26) (25,7) (9,27) (1,2) (22,1) (11,19) (4,30) (11,6) (31,8) (3,13) (2,14) (3,1) (5,17) (5,32) (17,4) (15,20) (17,18) (10,23) (15,29) (16,26) (11,12) (28,16) (7,20) (24,30)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "709"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (1,0) (6,2) (13,6) (12,7) (0,3) (5,1) (6,3) (0,2) (4,0) (9,1) (13,14) (15,4) (13,8) (11,1) (4,10) (7,15) (5,13) (7,0) (0,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "710"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (2,4) (1,0) (6,2) (5,3) (0,2) (3,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "711"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (5,16) (19,6) (1,6) (3,18) (6,9) (12,7) (11,15) (8,11) (7,9) (14,19) (16,4) (8,14) (13,4) (4,1) (14,18) (0,2) (0,16) (0,1) (1,10) (2,14) (0,17)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "712"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (14,2) (9,5) (9,3) (13,11) (4,10) (1,8) (14,12) (4,2) (13,7) (8,6) (12,1) (1,5) (0,13) (13,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "713"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (1,25) (23,5) (20,24) (8,3) (7,2) (14,0) (0,7) (17,12) (13,16) (23,8) (25,21) (15,10) (19,4) (20,0) (11,5) (13,26) (9,16) (11,14) (15,11) (1,18) (17,1) (22,13) (12,14) (1,6) (26,2) (5,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "714"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (7,23) (13,1) (25,20) (2,7) (18,19) (1,11) (8,21) (18,3) (6,14) (0,18) (22,5) (4,25) (10,2) (0,6) (20,8) (15,10) (9,1) (5,1) (4,13) (12,13) (16,15) (24,16) (15,14) (23,11) (17,15)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "715"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,4) (9,7) (0,2) (11,2) (3,0) (10,5) (4,9) (10,4) (10,6) (1,3) (9,8) (7,1) (1,0) (5,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "716"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (8,12) (3,1) (4,13) (0,1) (12,11) (3,14) (2,10) (8,5) (3,0) (9,7) (9,0) (5,6) (0,5) (2,0) (4,0) (13,2) (4,1) (12,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "717"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (3,0) (3,13) (11,4) (6,0) (11,13) (12,10) (0,1) (0,4) (1,5) (6,5) (4,7) (8,0) (5,9) (2,0) (10,13) (7,0) (9,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "718"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (4,14) (0,3) (1,2) (4,6) (11,7) (3,10) (1,0) (19,15) (17,19) (8,21) (18,11) (14,3) (0,2) (1,9) (18,22) (22,5) (19,11) (0,16) (23,12) (19,14) (16,13) (13,17) (22,9) (21,0) (12,13) (15,20)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "719"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (4,3) (6,2) (1,8) (0,4) (8,7) (0,1) (9,8) (1,2) (6,5) (3,6) (10,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "720"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (18,24) (5,7) (19,28) (9,3) (23,10) (12,6) (4,26) (5,26) (23,0) (23,4) (27,23) (18,15) (27,17) (4,22) (2,8) (24,16) (0,29) (21,9) (14,1) (20,31) (18,23) (2,13) (0,30) (11,28) (20,1) (29,6) (3,5) (13,26) (28,2) (27,25) (4,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "721"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (13,1) (6,3) (4,5) (6,8) (12,11) (5,2) (1,3) (10,0) (0,13) (11,0) (5,9) (7,10) (5,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "722"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (17,24) (14,1) (25,28) (10,7) (11,21) (3,32) (19,30) (32,16) (11,9) (0,8) (20,23) (12,2) (6,7) (27,11) (17,5) (9,26) (12,6) (31,13) (19,32) (23,6) (22,17) (25,11) (1,8) (30,23) (18,2) (21,29) (12,15) (5,0) (31,10) (8,4) (23,24) (25,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "723"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (2,6) (8,7) (8,10) (10,5) (2,0) (9,3) (7,3) (4,7) (4,6) (1,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "724"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (4,12) (10,2) (9,1) (13,17) (16,22) (2,7) (17,2) (7,28) (6,16) (25,13) (11,18) (20,1) (6,1) (3,18) (26,18) (5,4) (3,15) (14,17) (27,2) (10,0) (1,13) (11,19) (26,1) (26,12) (20,8) (29,3) (29,21) (2,23) (13,24)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "725"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (5,11) (22,17) (10,7) (17,14) (1,2) (11,16) (22,23) (9,23) (8,5) (19,21) (0,25) (19,3) (4,12) (15,19) (20,4) (18,21) (20,0) (13,22) (22,24) (10,22) (4,19) (23,6) (9,11) (2,25) (7,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "726"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (2,8) (10,7) (3,7) (8,4) (0,2) (4,7) (9,12) (5,9) (6,3) (11,6) (7,1) (5,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "727"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,2) (1,0) (0,3) (6,3) (4,0) (6,7) (3,4) (6,0) (3,1) (0,5) (0,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "728"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (11,7) (2,9) (0,2) (11,3) (10,3) (14,5) (2,1) (5,6) (12,3) (1,5) (7,2) (4,7) (9,8) (11,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "729"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (17,0) (3,9) (24,19) (15,22) (0,7) (13,14) (22,6) (1,0) (20,1) (12,17) (23,10) (9,21) (7,23) (12,15) (20,21) (16,4) (8,11) (3,5) (8,23) (18,12) (6,2) (1,13) (4,20) (21,6) (24,23)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "730"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (5,2) (5,3) (0,7) (8,6) (3,4) (6,1) (0,8) (0,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "731"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (16,4) (9,5) (6,5) (1,2) (0,15) (2,9) (1,12) (1,13) (13,4) (14,3) (12,10) (15,6) (14,6) (4,8) (2,7) (11,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "732"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (5,3) (24,20) (26,6) (1,0) (6,21) (2,4) (21,11) (13,14) (10,17) (2,0) (8,22) (20,17) (22,23) (19,7) (24,19) (12,9) (13,2) (15,1) (25,24) (20,4) (6,0) (25,18) (3,20) (14,6) (26,22) (0,12) (15,8) (25,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "733"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (21,11) (16,22) (10,21) (25,8) (28,20) (29,22) (27,1) (21,18) (22,17) (21,28) (31,15) (27,9) (11,5) (1,29) (7,20) (19,4) (18,30) (21,23) (31,20) (20,13) (24,10) (25,4) (13,6) (0,5) (2,31) (26,0) (25,18) (11,3) (9,8) (18,12) (14,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "734"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (10,11) (3,6) (5,2) (9,10) (7,2) (9,4) (11,0) (10,2) (6,1) (3,2) (8,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "735"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (12,3) (0,3) (4,16) (4,5) (8,16) (4,15) (0,2) (16,6) (10,13) (4,1) (9,6) (0,1) (7,13) (16,14) (10,0) (5,11) (15,3) (6,7) (9,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "736"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,5) (5,7) (2,9) (0,12) (7,11) (13,12) (4,6) (3,4) (1,4) (7,10) (8,9) (2,4) (12,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "737"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (8,1) (3,5) (2,7) (7,6) (7,0) (8,6) (8,4) (0,9) (5,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "738"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (2,10) (9,13) (8,6) (15,1) (10,8) (5,15) (14,0) (12,9) (4,0) (7,13) (11,3) (6,1) (11,2) (7,3) (2,0) (0,1) (6,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "739"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,3) (0,1) (4,16) (11,12) (5,11) (2,20) (24,4) (8,11) (0,4) (13,9) (12,17) (10,9) (16,18) (6,18) (3,8) (22,3) (19,0) (3,10) (2,0) (7,15) (0,14) (19,11) (18,21) (13,2) (4,23) (7,0) (0,24) (1,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "740"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (2,0) (0,1) (0,4) (6,1) (3,4) (2,4) (1,2) (3,0) (5,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "741"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (17,21) (11,8) (26,15) (9,6) (22,26) (4,8) (16,8) (8,10) (26,11) (10,17) (14,2) (26,2) (20,0) (20,18) (13,9) (12,5) (20,23) (7,15) (7,5) (2,23) (1,15) (18,27) (6,2) (28,20) (7,25) (26,19) (22,3) (12,24)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "742"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (11,5) (7,15) (22,20) (6,19) (9,18) (21,25) (21,4) (12,24) (14,15) (21,17) (30,0) (3,23) (21,14) (14,20) (29,27) (26,27) (6,27) (30,8) (5,28) (5,16) (13,20) (4,5) (23,22) (12,4) (2,17) (27,17) (21,10) (22,9) (14,0) (1,31) (31,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "743"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (7,4) (10,3) (8,13) (2,1) (6,2) (7,1) (5,13) (10,0) (12,3) (0,6) (3,13) (7,9) (11,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "744"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (17,9) (9,14) (10,8) (8,6) (3,11) (4,0) (15,5) (13,15) (2,10) (17,6) (6,0) (0,16) (11,2) (17,1) (7,3) (16,12) (7,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "745"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,0) (5,4) (5,0) (1,0) (2,7) (7,3) (3,0) (6,3) (7,1) (6,4) (4,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "746"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (15,7) (14,2) (15,1) (12,2) (9,6) (14,0) (9,4) (1,9) (9,2) (1,0) (11,2) (8,2) (13,6) (5,8) (12,10) (14,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "747"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (15,14) (6,10) (0,12) (4,7) (8,12) (17,14) (1,2) (0,14) (7,3) (12,6) (4,2) (15,16) (11,5) (7,16) (1,11) (6,13) (9,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "748"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,2) (3,7) (5,3) (0,1) (3,0) (9,0) (8,4) (2,8) (1,7) (6,2) (5,0) (4,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "749"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,6) (2,3) (6,1) (3,5) (3,0) (6,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "750"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (18,4) (18,13) (17,2) (1,0) (2,11) (15,8) (8,9) (9,14) (1,2) (10,11) (18,6) (18,5) (11,8) (3,15) (4,17) (9,7) (0,6) (12,14) (15,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "751"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (12,24) (5,7) (5,4) (21,18) (22,23) (16,20) (26,1) (27,19) (2,16) (8,15) (0,7) (17,25) (9,7) (12,11) (22,17) (10,20) (3,17) (26,7) (26,6) (14,23) (18,10) (16,17) (27,8) (0,1) (11,21) (8,12) (17,13) (26,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "752"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (12,6) (3,11) (1,2) (3,8) (7,1) (12,9) (0,10) (4,0) (5,7) (8,1) (14,11) (6,2) (0,2) (13,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "753"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (2,6) (10,1) (8,10) (0,11) (7,4) (9,5) (10,4) (10,3) (2,9) (5,1) (11,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "754"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (6,2) (2,4) (3,1) (4,0) (5,2) (3,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "755"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (18,1) (11,12) (14,5) (18,8) (20,8) (15,20) (11,5) (13,16) (2,6) (9,21) (0,17) (10,9) (16,5) (0,15) (14,7) (15,21) (2,7) (3,5) (5,4) (19,5) (0,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "756"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (6,17) (22,20) (18,30) (13,14) (2,22) (21,23) (11,0) (19,16) (16,27) (10,23) (4,24) (26,9) (13,26) (1,25) (10,8) (25,12) (23,26) (7,26) (26,3) (24,23) (28,27) (16,3) (2,17) (28,29) (0,5) (0,18) (3,12) (20,9) (14,0) (24,15)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "757"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (1,6) (17,14) (16,12) (21,9) (17,13) (0,2) (18,12) (0,4) (15,12) (10,12) (1,0) (13,10) (20,17) (4,3) (11,2) (21,20) (7,5) (6,2) (0,3) (8,2) (9,5) (16,19) (9,4) (0,5) (15,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "758"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (15,16) (17,0) (10,0) (13,22) (0,1) (11,26) (26,19) (2,5) (14,11) (25,14) (4,3) (7,13) (20,19) (18,9) (2,0) (11,15) (17,1) (9,6) (8,21) (5,8) (23,0) (8,17) (9,13) (3,0) (11,13) (3,26) (21,12) (13,23) (24,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "759"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (8,17) (19,7) (11,4) (12,20) (19,2) (15,23) (4,9) (18,3) (15,11) (1,7) (17,15) (10,19) (7,6) (0,15) (6,22) (18,13) (22,17) (15,20) (0,16) (17,21) (5,17) (18,8) (14,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "760"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,4) (7,11) (3,0) (23,2) (19,22) (14,8) (1,15) (5,30) (19,5) (5,4) (0,31) (0,1) (31,16) (6,21) (0,5) (7,6) (27,20) (19,8) (12,2) (12,5) (11,25) (17,24) (13,1) (32,21) (5,6) (19,16) (24,10) (28,5) (31,18) (26,23) (20,19) (14,3) (29,2) (2,0) (29,9) (10,21)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "761"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (3,11) (0,1) (4,10) (2,0) (4,12) (7,0) (9,8) (8,12) (13,1) (5,0) (11,6) (10,7) (14,3) (8,2) (14,8) (6,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "762"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (24,16) (24,11) (0,3) (6,1) (25,0) (18,26) (9,16) (23,22) (0,20) (10,32) (29,7) (22,30) (2,0) (2,32) (15,14) (27,33) (6,0) (27,20) (26,14) (16,30) (3,22) (25,13) (12,21) (0,1) (2,23) (19,1) (4,27) (4,5) (15,12) (31,28) (33,15) (8,21) (22,21) (28,15) (32,29) (17,2) (0,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "763"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (4,8) (10,17) (13,19) (11,5) (2,9) (10,16) (6,15) (17,7) (1,5) (3,7) (0,18) (15,14) (12,16) (0,2) (19,5) (0,1) (2,18) (14,9) (16,8) (16,15) (9,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "764"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (4,14) (9,13) (2,0) (2,7) (13,3) (13,1) (3,2) (13,12) (14,13) (10,3) (3,0) (8,11) (8,5) (6,8) (1,0) (4,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "765"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,3) (8,7) (4,2) (6,5) (8,5) (1,5) (1,0) (2,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "766"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (5,7) (2,9) (7,3) (5,9) (6,3) (1,4) (0,2) (5,1) (0,1) (8,3) (3,0) (9,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "767"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (28,29) (19,10) (21,15) (22,30) (2,3) (10,17) (8,6) (17,5) (27,4) (18,1) (10,20) (10,1) (24,10) (31,11) (14,9) (9,32) (7,25) (13,4) (0,1) (26,21) (10,11) (23,26) (12,10) (23,27) (3,16) (30,6) (2,26) (14,11) (7,9) (26,0) (2,17) (14,30) (4,29)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "768"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (30,18) (28,24) (27,0) (3,5) (26,2) (9,1) (27,28) (32,7) (3,21) (10,7) (9,22) (3,0) (23,10) (27,15) (21,6) (11,5) (17,15) (25,23) (7,9) (2,0) (1,8) (30,12) (16,19) (14,7) (32,13) (4,29) (8,24) (28,20) (21,16) (29,6) (31,22) (11,12) (30,2) (1,0) (12,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "769"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (9,7) (1,8) (1,7) (2,7) (0,2) (5,10) (0,5) (4,2) (0,4) (10,9) (1,0) (5,6) (3,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "770"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (9,10) (4,6) (4,11) (16,12) (15,11) (1,9) (6,8) (2,3) (14,7) (5,18) (2,0) (0,16) (0,18) (8,14) (12,13) (0,14) (13,9) (17,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "771"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (2,30) (6,9) (24,5) (24,7) (24,29) (27,18) (19,5) (26,18) (2,15) (14,26) (25,20) (28,3) (8,5) (25,16) (12,9) (8,21) (1,13) (15,10) (25,1) (26,4) (29,6) (3,15) (22,5) (21,23) (17,26) (17,9) (13,15) (4,3) (4,0) (16,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "772"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (29,15) (16,11) (14,6) (11,23) (1,29) (1,24) (4,27) (7,28) (25,29) (2,19) (17,22) (0,21) (13,15) (16,10) (20,14) (8,28) (6,9) (28,23) (22,29) (23,1) (23,19) (18,16) (3,27) (0,27) (8,4) (26,5) (22,12) (14,23) (5,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "773"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (21,30) (10,17) (28,23) (20,29) (9,32) (4,0) (26,28) (8,25) (19,22) (32,5) (31,5) (16,10) (26,34) (22,15) (20,22) (14,11) (6,12) (30,31) (5,27) (31,4) (33,23) (12,19) (11,31) (18,13) (3,0) (7,30) (8,7) (0,15) (3,9) (1,34) (19,1) (18,16) (27,2) (0,11) (10,2) (0,1) (0,2) (24,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "774"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (15,18) (19,3) (23,13) (22,5) (25,6) (25,9) (7,21) (14,13) (21,8) (10,20) (11,24) (4,3) (13,0) (0,5) (1,23) (20,17) (13,6) (4,10) (14,18) (24,2) (26,6) (18,21) (2,3) (16,8) (12,4) (10,15)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "775"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (12,2) (6,16) (3,24) (18,28) (28,9) (15,23) (1,0) (13,10) (8,16) (22,9) (0,27) (17,12) (29,26) (25,20) (2,0) (1,8) (27,6) (11,18) (3,0) (25,29) (15,11) (16,4) (9,4) (13,1) (29,12) (24,4) (7,28) (15,14) (5,24) (21,26) (3,19) (25,19)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "776"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (1,0) (22,0) (25,13) (14,1) (7,2) (8,12) (20,23) (13,23) (15,18) (17,18) (4,16) (9,24) (0,2) (8,15) (19,24) (21,4) (10,11) (5,18) (25,3) (8,0) (21,11) (6,23) (25,15) (10,24) (24,6) (15,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "777"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (1,11) (0,1) (3,4) (2,1) (5,3) (10,7) (7,2) (9,6) (8,11) (12,6) (1,4) (6,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "778"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (19,23) (15,9) (24,12) (25,10) (22,2) (23,8) (2,10) (11,9) (27,28) (28,6) (6,1) (20,27) (16,14) (21,29) (1,22) (9,31) (9,30) (16,0) (12,3) (16,5) (24,26) (15,1) (4,20) (7,0) (1,18) (8,22) (17,3) (12,5) (12,9) (29,20) (13,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "779"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (10,2) (16,2) (32,33) (30,6) (9,28) (19,21) (33,27) (29,27) (31,26) (23,34) (20,17) (19,30) (1,32) (26,3) (24,23) (22,10) (25,14) (6,34) (15,0) (14,5) (15,31) (18,20) (17,21) (25,22) (29,12) (4,23) (5,33) (0,24) (23,13) (30,9) (27,7) (8,6) (4,11) (1,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "780"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (2,13) (12,3) (0,1) (12,15) (12,11) (0,2) (23,5) (8,23) (10,3) (4,5) (9,11) (24,17) (26,11) (18,5) (19,26) (16,3) (19,21) (18,1) (25,22) (27,0) (1,19) (3,20) (4,14) (17,3) (15,6) (2,11) (27,20) (21,25) (18,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "781"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (1,4) (9,21) (1,20) (7,13) (25,14) (23,27) (26,0) (11,8) (2,14) (11,22) (6,18) (6,28) (1,12) (20,6) (19,4) (17,21) (16,10) (28,8) (0,16) (4,23) (5,28) (15,20) (23,24) (14,26) (21,24) (18,3) (28,16) (7,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "782"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (11,14) (9,13) (8,12) (7,6) (11,0) (3,6) (9,3) (7,2) (5,11) (10,13) (14,7) (9,1) (0,1) (4,11) (1,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "783"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (9,7) (19,14) (4,14) (19,9) (11,7) (6,17) (5,16) (10,0) (10,3) (15,12) (14,2) (17,8) (10,9) (0,15) (5,4) (0,17) (11,18) (1,16) (13,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "784"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,4) (0,3) (1,2) (5,7) (1,5) (6,5) (1,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "785"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (15,12) (14,6) (7,0) (17,9) (11,22) (5,23) (5,22) (23,18) (8,4) (10,21) (16,19) (7,1) (0,15) (24,9) (19,0) (0,4) (17,15) (21,14) (2,3) (1,0) (9,4) (0,3) (24,21) (18,10) (12,20) (0,2) (0,13) (20,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "786"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (19,0) (0,4) (2,19) (25,23) (8,10) (22,6) (0,28) (10,13) (0,2) (17,25) (5,10) (14,5) (16,4) (27,7) (27,14) (20,28) (21,27) (3,12) (3,14) (1,0) (6,11) (8,26) (16,25) (16,8) (0,3) (1,27) (3,15) (16,19) (9,18) (9,5) (3,11) (14,24)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "787"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (20,2) (8,24) (7,16) (0,2) (17,12) (3,13) (8,11) (4,15) (9,24) (12,0) (23,14) (22,1) (3,0) (24,3) (9,21) (0,1) (17,16) (6,7) (9,10) (12,18) (7,1) (15,19) (3,5) (4,0) (5,0) (2,4) (11,17) (23,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "788"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (13,20) (2,29) (19,11) (4,24) (0,23) (1,15) (3,6) (17,12) (1,14) (10,13) (22,13) (23,7) (18,24) (21,26) (13,23) (16,19) (16,5) (6,27) (28,7) (19,21) (17,4) (6,25) (23,1) (9,6) (24,15) (25,29) (21,8) (5,20) (22,27)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "789"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (11,10) (3,0) (7,0) (9,5) (4,0) (0,6) (8,10) (7,4) (2,0) (5,1) (5,6) (8,12) (1,0) (9,2) (11,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "790"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,17) (22,13) (3,21) (0,1) (24,6) (21,4) (0,3) (23,16) (10,1) (24,17) (12,9) (5,13) (22,10) (7,20) (15,20) (5,4) (16,9) (3,15) (2,0) (18,22) (17,11) (6,7) (6,14) (8,17) (16,17) (2,4) (0,4) (24,19)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "791"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (14,20) (24,12) (7,27) (27,21) (9,14) (15,23) (10,16) (5,24) (2,21) (3,26) (29,28) (9,17) (7,8) (6,20) (12,25) (12,23) (0,3) (1,19) (8,3) (11,7) (18,23) (8,16) (4,22) (29,24) (8,13) (14,21) (28,27) (22,9) (2,19)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "792"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (17,0) (4,1) (19,6) (16,5) (1,10) (12,7) (8,11) (6,9) (16,4) (18,14) (14,2) (8,14) (19,14) (15,11) (3,18) (13,4) (7,9) (6,1) (16,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "793"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,1) (12,11) (7,10) (21,3) (24,8) (31,22) (22,9) (7,9) (27,0) (21,6) (21,16) (12,0) (29,4) (27,15) (32,7) (7,14) (23,25) (27,28) (6,29) (30,18) (9,1) (32,13) (17,15) (30,12) (28,24) (2,26) (19,16) (8,1) (11,5) (28,20) (30,2) (3,5) (23,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "794"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (4,7) (0,7) (5,7) (12,8) (16,10) (17,14) (16,1) (17,2) (16,17) (15,14) (10,18) (17,6) (18,11) (12,9) (5,3) (8,7) (17,13) (11,12) (8,19)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "795"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (13,12) (17,25) (4,17) (23,18) (12,28) (7,16) (0,2) (22,28) (17,2) (10,20) (25,15) (1,15) (23,26) (21,12) (7,14) (6,24) (23,6) (28,17) (15,8) (19,2) (4,0) (15,11) (19,14) (1,6) (5,9) (9,28) (0,1) (18,10) (14,27) (3,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "796"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (5,14) (25,22) (11,6) (26,14) (27,7) (8,16) (9,18) (10,5) (16,19) (0,27) (25,17) (24,16) (14,3) (8,25) (9,5) (20,27) (27,1) (10,13) (6,21) (12,3) (14,23) (3,11) (0,19) (8,10) (2,19) (0,1) (0,2) (15,3) (4,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "797"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (6,12) (5,8) (2,9) (6,0) (12,10) (4,12) (8,3) (9,7) (1,8) (12,13) (10,11) (9,12) (4,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "798"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (3,19) (22,5) (14,3) (27,23) (15,5) (25,32) (7,34) (6,17) (30,14) (6,23) (16,34) (7,33) (0,1) (32,20) (31,3) (8,2) (27,3) (25,3) (11,3) (24,26) (8,18) (4,15) (1,9) (34,9) (2,13) (5,27) (12,4) (25,10) (28,4) (7,29) (20,0) (18,26) (26,9) (2,0) (21,13) (2,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "799"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (32,14) (4,12) (26,23) (29,17) (28,13) (9,0) (24,0) (18,23) (10,21) (30,19) (15,24) (31,1) (25,5) (9,11) (6,17) (22,14) (0,16) (28,9) (23,10) (20,17) (32,3) (27,33) (4,32) (12,29) (30,2) (27,5) (7,33) (5,14) (25,21) (21,30) (3,13) (1,3) (8,22)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "800"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (15,29) (1,12) (0,3) (19,22) (25,14) (22,11) (2,30) (4,15) (32,5) (24,17) (28,23) (17,25) (24,26) (11,31) (29,16) (8,15) (1,28) (23,19) (16,13) (10,6) (32,12) (7,1) (33,18) (3,33) (27,7) (20,21) (23,21) (0,30) (10,30) (2,16) (14,9) (25,0) (28,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "801"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (28,19) (27,2) (18,23) (11,28) (29,0) (9,20) (26,5) (7,32) (4,21) (32,14) (18,22) (23,4) (14,4) (2,13) (32,13) (10,23) (16,24) (28,26) (27,17) (24,27) (3,9) (6,29) (6,12) (2,8) (31,23) (23,25) (5,3) (1,5) (0,32) (0,30) (18,15) (4,26)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "802"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (10,11) (16,0) (7,5) (15,8) (8,6) (11,12) (3,5) (1,0) (12,0) (12,7) (13,16) (7,4) (9,14) (10,14) (2,16) (8,12) (1,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "803"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (9,10) (1,0) (2,22) (16,22) (22,13) (20,10) (15,18) (5,10) (10,6) (9,8) (17,4) (1,15) (11,2) (19,11) (5,3) (0,17) (2,0) (0,16) (24,2) (10,14) (20,0) (12,14) (23,5) (6,7) (11,15) (21,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "804"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,1) (0,3) (12,9) (0,2) (18,6) (2,8) (0,7) (4,17) (14,13) (16,3) (11,6) (15,16) (10,9) (0,4) (6,17) (5,10) (14,0) (18,0) (2,16) (11,19) (3,13) (12,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "805"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (10,24) (12,6) (1,25) (4,18) (28,7) (3,26) (11,16) (9,16) (10,28) (30,0) (11,12) (6,20) (25,13) (24,3) (13,10) (21,18) (27,30) (15,3) (23,8) (9,0) (4,19) (14,16) (9,28) (1,5) (22,3) (26,8) (19,8) (8,29) (17,16) (2,21)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "806"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (10,17) (1,11) (0,9) (9,16) (15,7) (14,11) (13,14) (0,1) (8,7) (12,0) (15,3) (10,9) (9,4) (2,15) (13,5) (8,13) (7,0) (7,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "807"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (32,23) (15,23) (10,16) (17,30) (14,31) (29,10) (17,21) (19,9) (27,1) (7,17) (27,22) (11,3) (22,31) (13,22) (27,0) (17,4) (0,25) (26,29) (29,28) (2,13) (1,24) (6,7) (2,26) (4,23) (1,12) (18,19) (27,11) (8,5) (5,19) (20,27) (8,16) (19,30)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "808"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (12,13) (11,12) (10,8) (7,9) (0,3) (8,6) (4,11) (0,1) (6,9) (0,10) (2,7) (2,0) (5,0) (4,0) (3,4) (1,5) (1,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "809"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (17,7) (6,2) (0,1) (8,11) (15,5) (3,7) (16,9) (10,14) (14,11) (18,12) (12,8) (6,0) (0,16) (13,1) (4,11) (5,7) (1,4) (3,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "810"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (16,21) (23,25) (18,30) (24,28) (11,12) (2,30) (28,27) (9,7) (22,9) (30,12) (27,15) (16,19) (3,0) (20,28) (0,2) (32,7) (10,23) (4,29) (29,6) (0,12) (8,1) (21,3) (26,2) (4,0) (1,9) (0,1) (10,7) (17,15) (21,6) (5,3) (13,32) (27,0) (5,11) (22,31) (24,8) (7,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "811"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (13,15) (12,2) (1,12) (9,5) (6,3) (10,7) (0,12) (8,12) (7,4) (6,14) (8,11) (15,2) (7,5) (4,2) (13,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "812"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (10,11) (13,4) (21,10) (19,1) (8,20) (1,15) (3,2) (12,22) (18,11) (14,11) (19,9) (22,8) (9,22) (19,10) (16,21) (17,5) (18,5) (13,14) (0,20) (13,6) (3,7) (11,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "813"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (20,10) (11,14) (6,15) (0,3) (12,17) (2,17) (6,20) (19,6) (5,8) (13,14) (19,4) (6,18) (12,5) (1,4) (3,19) (5,4) (4,7) (9,7) (16,4) (6,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "814"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (4,16) (21,27) (1,10) (25,31) (6,5) (14,26) (27,5) (7,6) (23,13) (1,26) (31,30) (15,2) (8,20) (12,24) (33,5) (15,13) (20,21) (2,0) (30,18) (21,28) (12,2) (11,10) (3,0) (0,4) (29,33) (0,1) (16,3) (20,9) (32,13) (5,25) (26,22) (26,20) (9,0) (6,4) (12,6) (19,28) (8,17)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "815"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (25,0) (16,21) (2,8) (28,4) (11,16) (19,7) (3,10) (19,1) (6,2) (0,2) (0,1) (22,27) (4,13) (1,23) (6,19) (24,17) (22,16) (5,16) (26,0) (14,24) (26,11) (26,15) (24,4) (25,9) (6,16) (6,18) (8,20) (0,10) (14,26) (8,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "816"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,0) (0,9) (11,12) (2,7) (3,4) (7,3) (10,4) (5,1) (3,6) (4,8) (5,6) (4,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "817"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (8,2) (10,2) (7,4) (12,10) (10,5) (7,10) (3,4) (9,8) (1,2) (11,8) (6,3) (0,9) (0,3) (0,2) (0,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "818"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (5,6) (0,4) (3,0) (2,4) (7,1) (1,5) (7,2) (0,1) (7,8) (2,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "819"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (19,23) (27,8) (0,2) (18,16) (15,29) (13,10) (4,20) (17,12) (15,31) (26,18) (0,6) (28,22) (10,2) (7,29) (31,9) (31,14) (3,0) (1,2) (13,0) (24,22) (11,19) (27,3) (29,16) (26,2) (25,2) (24,26) (30,11) (30,5) (8,29) (8,23) (20,17) (4,15) (21,23) (1,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "820"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (3,10) (8,9) (4,11) (0,1) (2,3) (3,7) (12,2) (2,0) (5,6) (11,6) (0,6) (1,4) (14,6) (2,9) (1,12) (3,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "821"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,0) (6,0) (7,4) (3,5) (7,0) (6,1) (4,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "822"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (15,1) (8,21) (6,13) (16,14) (9,2) (17,15) (15,18) (0,5) (22,10) (16,0) (10,12) (22,17) (11,19) (3,1) (16,8) (7,21) (4,17) (19,4) (1,0) (10,9) (14,6) (14,12) (2,0) (20,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "823"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (11,15) (16,7) (5,1) (8,17) (13,12) (6,16) (13,2) (16,4) (21,22) (15,14) (19,8) (9,12) (22,17) (4,9) (1,8) (4,3) (6,18) (15,10) (3,19) (9,20) (18,11) (0,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "824"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (14,20) (14,5) (4,14) (11,19) (13,12) (0,3) (0,2) (19,9) (15,19) (8,16) (6,8) (5,1) (2,3) (7,13) (8,10) (1,17) (4,0) (1,0) (18,5) (9,1) (13,3) (13,15) (6,20)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "825"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (5,13) (0,2) (7,15) (0,13) (9,11) (9,4) (1,5) (13,9) (8,0) (1,0) (8,3) (3,2) (6,0) (15,0) (0,3) (14,13) (10,11) (12,8) (13,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "826"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (16,17) (6,12) (15,20) (2,4) (5,13) (1,0) (9,16) (21,4) (10,1) (17,20) (16,21) (3,18) (11,9) (6,7) (17,10) (7,19) (6,16) (14,13) (5,4) (8,17) (17,0) (15,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "827"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (22,15) (16,0) (16,13) (1,18) (20,8) (12,11) (2,6) (19,8) (7,14) (24,23) (10,9) (0,24) (18,0) (3,5) (11,5) (7,2) (5,20) (15,21) (17,5) (16,15) (5,4) (3,0) (5,14) (9,21)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "828"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (32,27) (9,4) (21,31) (26,6) (15,0) (23,1) (32,17) (0,22) (16,13) (18,10) (30,14) (31,7) (12,30) (33,5) (7,23) (4,25) (2,28) (26,27) (3,10) (19,33) (29,14) (13,30) (20,15) (24,27) (28,26) (2,14) (18,11) (8,26) (1,9) (2,21) (9,5) (0,23) (11,32)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "829"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (9,8) (8,13) (11,1) (12,4) (14,12) (5,15) (0,7) (3,10) (0,1) (0,3) (13,6) (4,1) (5,7) (2,0) (2,6) (3,9) (6,15) (12,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "830"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (3,7) (10,6) (9,13) (6,15) (0,1) (6,4) (14,12) (7,4) (1,4) (8,14) (5,2) (0,2) (11,6) (3,0) (4,0) (5,12) (4,13) (4,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "831"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (5,8) (1,5) (2,3) (8,2) (7,8) (8,0) (0,2) (0,1) (6,4) (4,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "832"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (8,11) (15,3) (14,15) (13,17) (2,14) (10,3) (12,0) (8,17) (10,18) (7,1) (11,0) (9,18) (1,16) (6,4) (13,5) (11,6) (0,1) (2,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "833"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (15,7) (1,12) (16,1) (0,18) (15,16) (14,16) (10,17) (2,6) (4,9) (8,7) (1,10) (5,2) (13,3) (19,0) (9,0) (11,19) (10,3) (15,11) (4,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "834"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (8,21) (17,20) (12,6) (17,13) (9,15) (18,7) (1,8) (6,10) (19,21) (6,3) (15,5) (15,0) (16,20) (4,17) (5,22) (4,7) (19,14) (3,9) (7,11) (0,16) (8,0) (2,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "835"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (24,4) (20,15) (19,8) (13,5) (0,1) (8,1) (1,7) (6,18) (4,9) (11,18) (17,8) (15,13) (10,16) (24,2) (19,3) (17,22) (0,12) (4,16) (9,21) (11,15) (3,23) (16,6) (24,22) (9,12) (12,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "836"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (10,0) (1,5) (7,2) (3,4) (6,8) (7,9) (4,11) (1,0) (1,10) (0,3) (9,6) (8,10) (11,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "837"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,6) (7,3) (6,4) (7,2) (0,3) (2,0) (5,7) (10,6) (8,4) (0,1) (0,4) (1,5) (7,0) (9,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "838"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (17,9) (11,6) (1,11) (0,8) (16,19) (9,12) (4,0) (6,18) (18,0) (15,20) (2,16) (17,5) (0,14) (10,2) (13,3) (13,14) (6,20) (3,16) (1,21) (12,3) (7,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "839"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (17,18) (21,33) (9,11) (8,21) (34,23) (26,0) (30,4) (6,19) (8,7) (23,17) (23,30) (1,3) (13,16) (21,2) (21,10) (28,1) (27,12) (31,32) (31,6) (9,18) (3,31) (27,23) (4,10) (33,16) (21,29) (5,20) (6,0) (10,5) (25,32) (0,24) (22,23) (14,3) (15,20) (15,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "840"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (2,6) (5,13) (5,4) (12,8) (0,9) (8,0) (12,7) (3,12) (0,10) (11,9) (13,6) (12,13) (1,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "841"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (11,9) (7,2) (5,11) (1,8) (11,0) (11,4) (6,7) (12,7) (10,8) (9,1) (9,3) (3,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "842"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (26,0) (22,15) (0,7) (4,8) (14,0) (13,22) (1,0) (19,0) (12,15) (20,2) (21,28) (5,23) (18,23) (27,4) (24,5) (17,27) (11,9) (25,28) (19,20) (9,24) (10,18) (26,12) (2,3) (7,1) (21,16) (6,14) (17,9) (10,21) (25,15)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "843"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (4,13) (5,0) (17,16) (0,1) (1,18) (9,17) (12,0) (1,15) (5,17) (2,8) (19,0) (3,6) (4,10) (2,0) (0,4) (11,15) (3,0) (14,2) (8,6) (19,3) (6,18) (16,7) (19,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "844"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (18,6) (14,0) (2,17) (16,15) (9,14) (27,1) (4,2) (21,16) (22,30) (20,15) (12,14) (1,0) (19,25) (4,9) (29,5) (18,24) (17,25) (5,3) (22,28) (3,14) (27,8) (24,11) (27,23) (25,26) (19,20) (6,5) (27,16) (13,14) (17,7) (25,28) (2,0) (10,29)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "845"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (2,5) (2,8) (5,1) (14,6) (8,9) (11,3) (13,8) (12,6) (3,8) (8,0) (10,4) (12,4) (11,12) (11,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "846"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (22,11) (32,18) (6,16) (4,25) (14,2) (7,17) (25,31) (29,4) (21,32) (24,6) (11,20) (22,26) (2,9) (22,12) (6,22) (27,6) (10,12) (2,19) (12,7) (19,20) (30,23) (3,0) (29,10) (24,1) (30,8) (13,16) (0,13) (19,5) (4,32) (30,4) (26,28) (27,15)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "847"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (5,12) (9,4) (1,15) (0,2) (13,2) (8,14) (15,7) (0,20) (8,10) (1,0) (20,2) (0,3) (2,6) (17,10) (11,12) (18,21) (20,18) (6,9) (4,0) (5,7) (16,17) (15,2) (3,8) (11,8) (19,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "848"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (20,25) (18,12) (19,13) (23,24) (13,12) (11,24) (20,17) (0,15) (19,24) (10,15) (12,22) (8,2) (15,3) (7,24) (9,2) (18,4) (6,21) (0,24) (25,5) (8,3) (4,1) (15,14) (0,25) (14,16) (3,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "849"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (3,23) (0,20) (15,11) (17,13) (9,11) (2,19) (17,21) (12,7) (19,14) (12,4) (11,5) (10,7) (4,20) (22,21) (4,19) (1,2) (8,22) (16,22) (24,0) (23,22) (6,5) (23,9) (18,19) (22,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "850"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,5) (13,0) (25,9) (21,7) (1,0) (25,6) (13,23) (15,10) (10,4) (18,15) (20,10) (3,0) (24,2) (20,17) (18,21) (1,23) (18,14) (14,13) (13,6) (3,4) (8,16) (3,2) (24,11) (8,21) (2,0) (5,22) (12,4) (3,19)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "851"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (17,8) (12,15) (9,10) (5,4) (2,14) (16,1) (15,0) (4,14) (7,17) (12,13) (14,0) (5,16) (10,0) (11,9) (6,17) (7,11) (3,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "852"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,7) (3,0) (0,12) (13,5) (11,8) (0,4) (17,8) (14,2) (16,1) (0,1) (9,18) (6,4) (10,18) (3,10) (17,13) (3,15) (11,0) (6,11) (14,15) (0,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "853"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (3,5) (6,2) (0,5) (7,0) (8,9) (10,5) (6,1) (0,8) (10,2) (4,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "854"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (8,3) (4,3) (5,7) (5,2) (0,8) (7,1) (0,1) (2,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "855"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,9) (0,7) (7,2) (4,7) (3,4) (7,1) (6,8) (6,1) (5,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "856"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (6,1) (0,2) (8,7) (2,11) (10,6) (3,10) (11,8) (7,4) (7,3) (6,5) (4,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "857"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (2,22) (0,19) (2,16) (1,0) (7,12) (6,13) (20,3) (15,21) (5,12) (14,0) (0,2) (1,22) (18,8) (9,23) (4,22) (18,9) (21,14) (17,4) (20,22) (23,3) (5,10) (3,0) (11,6) (5,6) (5,21) (14,23)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "858"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (2,9) (2,5) (3,9) (8,2) (5,4) (6,1) (5,1) (1,7) (0,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "859"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (5,10) (11,6) (8,20) (8,10) (3,12) (11,3) (14,3) (4,3) (13,9) (18,16) (17,14) (7,10) (9,5) (0,22) (1,19) (1,0) (16,8) (0,2) (16,19) (0,19) (22,23) (15,6) (5,14) (2,16) (21,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "860"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (5,1) (2,5) (6,4) (0,2) (0,8) (4,2) (9,4) (7,11) (0,1) (3,0) (5,8) (2,3) (10,6) (11,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "861"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (13,19) (26,16) (31,12) (29,18) (7,27) (15,10) (14,11) (10,28) (15,12) (21,31) (19,16) (12,6) (12,23) (31,8) (4,21) (29,23) (13,30) (25,12) (24,16) (28,3) (22,18) (30,17) (15,11) (7,2) (31,9) (20,11) (11,1) (7,20) (0,16) (5,15) (0,21)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "862"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (32,27) (30,20) (8,23) (23,1) (2,0) (15,16) (22,4) (14,18) (3,19) (5,27) (24,7) (13,0) (12,28) (11,17) (7,32) (6,31) (21,8) (29,13) (13,20) (4,2) (34,19) (15,9) (8,24) (16,6) (11,29) (19,30) (0,1) (1,28) (33,18) (33,29) (4,23) (25,10) (26,29) (26,10) (31,33)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "863"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (4,6) (3,5) (1,2) (0,1) (3,4) (2,0) (0,4) (0,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "864"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (16,22) (21,13) (13,6) (10,9) (8,17) (7,0) (15,2) (23,4) (20,18) (15,3) (5,9) (21,10) (7,11) (14,0) (20,9) (11,1) (0,1) (12,14) (8,7) (4,21) (9,0) (22,23) (2,0) (15,13) (7,19)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "865"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (8,17) (12,1) (11,4) (7,16) (9,16) (8,11) (3,7) (0,4) (1,0) (1,4) (14,11) (10,14) (0,15) (5,7) (0,3) (0,6) (3,10) (5,13) (0,2) (2,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "866"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (7,17) (11,8) (6,13) (5,16) (0,2) (12,1) (12,15) (14,11) (9,11) (3,12) (12,13) (5,7) (7,12) (20,16) (4,17) (10,17) (1,0) (0,17) (2,8) (1,19) (18,19) (11,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "867"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (32,19) (1,4) (23,27) (17,14) (27,1) (22,13) (16,11) (28,19) (11,12) (16,21) (1,16) (30,7) (7,10) (3,24) (29,26) (20,18) (20,21) (3,17) (25,19) (0,8) (20,3) (11,25) (3,7) (32,9) (11,22) (9,31) (12,26) (28,6) (8,11) (15,2) (15,5) (14,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "868"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (11,1) (12,8) (20,16) (20,15) (12,14) (7,16) (7,3) (0,1) (6,12) (15,18) (6,10) (4,2) (0,2) (14,0) (0,17) (7,4) (14,19) (13,6) (2,1) (15,12) (4,9) (5,11) (3,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "869"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (23,28) (19,27) (25,23) (15,10) (0,24) (13,9) (20,28) (26,18) (20,3) (29,16) (12,22) (6,19) (2,0) (27,0) (26,5) (9,15) (13,20) (8,0) (12,3) (17,10) (29,12) (11,12) (3,0) (14,7) (5,16) (11,19) (28,21) (0,1) (1,11) (0,4) (1,2) (4,18) (16,7) (30,23)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "870"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (17,6) (29,28) (14,13) (1,0) (21,23) (2,0) (17,2) (25,1) (22,2) (7,26) (4,24) (30,18) (0,5) (8,10) (27,16) (26,13) (10,23) (3,26) (9,20) (20,22) (9,26) (0,18) (24,23) (28,27) (3,16) (19,16) (24,15) (26,23) (11,0) (25,12) (12,3) (14,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "871"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (14,8) (7,6) (9,11) (7,2) (4,13) (8,6) (2,12) (3,1) (9,1) (0,4) (1,7) (7,10) (5,8) (4,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "872"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (1,2) (0,8) (6,5) (7,9) (13,10) (4,9) (9,11) (4,1) (12,6) (8,5) (6,13) (5,3) (8,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "873"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (3,9) (8,23) (23,0) (20,24) (17,5) (24,22) (15,13) (23,4) (20,17) (19,10) (3,19) (23,24) (16,6) (14,10) (14,1) (8,15) (18,12) (7,16) (11,21) (7,13) (22,2) (14,17) (11,5) (18,21)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "874"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (7,5) (3,1) (7,4) (6,9) (0,4) (8,2) (9,4) (8,1) (7,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "875"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (15,14) (25,16) (17,3) (13,16) (8,1) (6,20) (24,18) (8,14) (23,2) (22,5) (9,26) (10,7) (23,12) (14,4) (14,23) (27,17) (2,3) (1,21) (7,9) (19,5) (21,20) (13,11) (0,4) (28,26) (10,6) (12,22) (3,25) (11,24)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "876"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (6,0) (0,5) (4,0) (3,2) (1,6) (6,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "877"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,6) (8,3) (0,2) (7,4) (0,1) (4,1) (5,7) (0,8) (5,6) (0,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "878"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,2) (6,4) (0,8) (3,0) (1,3) (7,4) (4,1) (9,6) (0,2) (4,0) (3,5) (1,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "879"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (7,2) (2,11) (3,11) (10,16) (5,14) (5,17) (0,9) (10,19) (12,14) (4,7) (1,8) (13,1) (0,19) (15,3) (18,5) (19,1) (17,13) (8,7) (6,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "880"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (7,30) (1,4) (5,14) (2,15) (27,23) (22,11) (14,17) (29,26) (22,13) (12,26) (20,3) (31,9) (27,1) (21,20) (3,0) (0,8) (16,11) (3,7) (32,9) (25,19) (8,11) (17,3) (28,19) (11,25) (15,5) (10,7) (16,1) (0,2) (12,11) (1,0) (21,16) (18,20) (32,19) (3,24) (28,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "881"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (14,12) (6,9) (4,2) (1,8) (8,6) (0,5) (14,7) (1,12) (13,0) (2,15) (11,4) (0,1) (3,0) (0,7) (12,10) (0,2) (9,3) (4,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "882"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (1,0) (13,20) (0,2) (26,27) (1,22) (13,5) (20,10) (12,6) (26,3) (14,21) (27,0) (6,3) (2,8) (24,18) (23,2) (11,8) (8,4) (25,0) (10,17) (10,9) (24,10) (11,10) (21,0) (4,16) (12,15) (16,25) (7,11) (19,1) (22,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "883"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,3) (1,0) (1,3) (0,13) (7,14) (0,2) (6,11) (12,4) (4,11) (11,9) (4,1) (6,14) (3,5) (0,14) (13,2) (10,13) (8,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "884"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (14,24) (6,11) (25,15) (28,14) (13,3) (2,16) (4,27) (16,25) (9,5) (18,28) (14,5) (29,21) (27,20) (14,3) (26,29) (22,6) (12,10) (5,10) (3,7) (27,8) (11,3) (17,9) (16,8) (10,8) (19,16) (19,1) (23,25) (27,0) (19,29)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "885"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (18,4) (33,26) (24,28) (12,31) (15,1) (4,0) (2,1) (5,7) (12,23) (26,29) (28,27) (14,16) (9,22) (2,6) (22,21) (13,26) (22,18) (31,5) (14,26) (19,27) (17,32) (25,11) (26,21) (6,28) (19,17) (30,33) (14,32) (14,10) (25,10) (5,20) (12,27) (32,8) (3,22)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "886"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (13,10) (2,3) (12,6) (16,1) (5,16) (3,8) (7,6) (11,12) (0,2) (14,9) (8,4) (9,4) (0,1) (3,15) (10,16) (11,16) (13,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "887"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (19,1) (18,5) (1,14) (2,0) (6,13) (1,0) (11,17) (12,14) (3,7) (2,11) (19,10) (13,11) (3,0) (4,0) (19,9) (10,11) (2,3) (20,15) (0,20) (4,13) (8,18) (5,16) (15,9) (10,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "888"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (9,5) (18,22) (16,7) (4,1) (9,22) (14,8) (2,4) (0,1) (0,2) (19,12) (11,2) (5,14) (17,7) (15,19) (22,23) (7,23) (24,15) (11,10) (13,15) (0,6) (11,0) (5,13) (6,3) (23,3) (4,20) (21,15)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "889"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (2,12) (1,9) (2,17) (2,15) (2,0) (10,4) (8,11) (4,0) (2,13) (15,8) (16,6) (2,9) (9,5) (12,14) (18,10) (1,0) (7,1) (3,0) (6,9) (14,0) (7,4) (3,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "890"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (15,13) (6,13) (2,15) (18,4) (7,11) (0,14) (15,3) (9,10) (0,9) (0,7) (16,7) (9,17) (1,11) (7,8) (9,5) (12,14) (4,10) (8,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "891"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,2) (7,5) (3,0) (5,10) (1,0) (0,2) (10,8) (1,7) (0,6) (4,3) (0,5) (11,2) (10,4) (9,8) (4,0) (7,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "892"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (1,6) (12,11) (5,9) (4,0) (12,14) (4,9) (13,12) (0,1) (2,6) (10,15) (2,8) (3,0) (4,3) (9,15) (10,12) (5,7) (2,0) (11,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "893"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (14,19) (16,3) (20,7) (24,10) (12,9) (29,17) (29,1) (9,11) (17,24) (4,11) (19,13) (3,13) (32,18) (27,7) (14,21) (10,7) (25,6) (13,25) (27,15) (22,8) (31,21) (28,5) (29,25) (26,23) (0,9) (2,29) (7,33) (5,29) (26,13) (30,16) (32,11) (12,22) (23,22)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "894"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (24,17) (25,19) (21,20) (25,2) (15,16) (0,1) (10,26) (8,25) (20,10) (13,25) (4,18) (3,22) (18,11) (26,24) (5,15) (16,1) (25,9) (5,26) (3,18) (13,0) (21,14) (21,18) (8,12) (2,18) (17,7) (17,6) (23,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "895"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (6,2) (11,4) (5,13) (4,15) (7,17) (3,6) (14,5) (17,9) (6,13) (1,10) (7,15) (13,8) (16,1) (0,6) (1,12) (7,0) (13,16) (1,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "896"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (8,15) (13,27) (6,25) (0,8) (11,26) (14,8) (3,25) (26,7) (10,24) (17,29) (1,16) (25,15) (23,6) (0,1) (2,9) (17,28) (0,2) (3,0) (24,0) (15,18) (5,18) (13,29) (21,4) (19,4) (2,15) (11,10) (12,24) (0,4) (23,22) (23,27) (24,21) (20,18)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "897"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (15,14) (1,11) (7,9) (20,2) (12,13) (15,7) (6,8) (17,1) (13,7) (3,0) (21,23) (10,17) (14,19) (12,5) (14,4) (7,10) (9,6) (2,10) (1,0) (3,11) (16,9) (0,2) (21,0) (22,9) (18,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "898"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (8,1) (4,7) (0,1) (1,4) (5,3) (3,4) (8,2) (4,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "899"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (22,29) (2,18) (4,32) (9,7) (32,7) (34,2) (33,17) (14,13) (12,11) (20,25) (3,26) (21,18) (30,21) (25,24) (23,0) (6,4) (27,32) (34,8) (24,19) (0,6) (20,17) (18,15) (10,7) (28,19) (20,6) (22,4) (10,31) (6,18) (10,26) (16,1) (14,1) (7,14) (11,24) (5,33)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "900"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (15,32) (1,4) (32,23) (27,4) (8,4) (31,20) (6,19) (32,24) (9,30) (16,10) (21,31) (14,22) (20,0) (12,27) (28,27) (21,6) (7,32) (30,10) (10,8) (29,31) (26,13) (9,17) (12,11) (18,21) (2,8) (1,13) (19,5) (8,3) (13,14) (15,6) (25,9) (18,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "901"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (19,15) (14,0) (11,5) (0,16) (3,7) (15,17) (6,13) (2,4) (4,9) (7,16) (4,7) (6,12) (15,12) (8,12) (1,2) (10,6) (12,14) (14,18) (1,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "902"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (13,30) (7,29) (14,24) (12,30) (27,26) (1,0) (21,2) (23,0) (20,4) (31,7) (2,28) (0,15) (22,14) (21,31) (27,19) (27,25) (23,30) (1,23) (18,0) (10,3) (11,17) (5,7) (9,4) (5,9) (16,13) (15,11) (18,10) (26,8) (9,1) (6,26) (14,2) (26,28)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "903"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (11,8) (15,8) (1,16) (10,5) (4,10) (0,18) (9,13) (2,17) (12,8) (11,3) (3,17) (10,7) (18,13) (6,4) (11,0) (1,14) (16,18) (9,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "904"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (2,0) (4,8) (1,8) (4,7) (6,5) (1,0) (3,8) (5,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "905"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (5,3) (20,21) (0,15) (1,10) (14,22) (12,6) (15,4) (1,4) (21,9) (8,4) (1,21) (3,17) (7,17) (3,12) (2,0) (19,1) (23,22) (17,23) (11,4) (23,18) (13,7) (16,4) (7,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "906"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,33) (17,27) (11,28) (27,23) (32,13) (22,34) (24,16) (26,5) (2,33) (9,3) (4,34) (15,18) (4,26) (19,28) (2,8) (31,0) (14,6) (1,5) (23,10) (32,23) (32,0) (24,18) (21,4) (30,26) (23,18) (23,4) (29,6) (27,25) (2,28) (32,7) (13,29) (33,12) (5,3) (20,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "907"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (4,6) (8,0) (3,10) (14,17) (0,11) (1,4) (2,21) (16,15) (12,8) (16,19) (2,19) (10,17) (5,17) (7,8) (2,12) (15,18) (20,13) (3,11) (10,9) (21,20) (6,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "908"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (3,9) (9,7) (4,1) (0,6) (8,2) (8,5) (9,1) (4,8) (6,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "909"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (24,9) (27,15) (5,1) (6,8) (16,19) (3,5) (25,14) (4,24) (10,14) (13,11) (13,17) (13,7) (3,15) (9,1) (2,3) (6,20) (13,15) (5,14) (21,3) (8,12) (21,26) (22,21) (2,0) (18,19) (19,8) (23,5) (20,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "910"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (4,24) (28,2) (12,25) (4,19) (4,17) (1,3) (1,0) (4,26) (3,23) (13,21) (24,14) (4,8) (5,26) (9,17) (20,18) (14,20) (6,22) (13,7) (6,19) (13,0) (6,0) (10,19) (5,15) (22,11) (23,6) (16,7) (2,7) (27,6) (5,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "911"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (15,2) (15,1) (8,6) (14,13) (3,12) (14,6) (3,5) (6,0) (8,10) (2,4) (9,6) (13,12) (0,7) (2,0) (4,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "912"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (3,10) (2,13) (8,11) (13,9) (7,15) (1,16) (11,12) (19,11) (4,0) (0,19) (21,18) (3,22) (18,16) (17,12) (7,0) (16,4) (0,14) (3,8) (10,9) (20,2) (23,4) (6,18) (5,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "913"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (9,1) (0,16) (8,21) (14,15) (22,13) (17,19) (19,15) (4,6) (14,4) (2,1) (18,21) (0,20) (1,0) (22,5) (3,10) (19,11) (13,17) (9,22) (19,12) (13,16) (7,11) (11,18) (3,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "914"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,4) (3,7) (4,1) (4,2) (5,2) (7,8) (7,6) (3,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "915"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (2,5) (11,15) (10,17) (18,0) (13,3) (8,7) (3,10) (15,7) (9,0) (10,1) (15,16) (14,16) (1,12) (0,19) (1,16) (9,4) (6,2) (6,4) (19,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "916"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (15,13) (2,15) (12,22) (16,17) (11,3) (0,12) (1,18) (11,7) (4,18) (14,9) (6,15) (10,1) (1,20) (6,12) (1,5) (0,11) (22,19) (11,20) (8,13) (9,21) (2,17) (0,21)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "917"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,5) (0,9) (7,0) (2,7) (4,8) (3,7) (0,1) (4,6) (5,7) (6,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "918"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (7,27) (23,16) (21,2) (5,24) (30,11) (12,26) (15,8) (6,20) (23,19) (21,14) (23,9) (25,12) (14,9) (3,8) (17,8) (27,28) (22,4) (1,19) (29,3) (21,27) (7,8) (7,13) (12,24) (10,16) (2,20) (30,28) (14,22) (18,9) (3,0) (24,29)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "919"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (15,16) (8,23) (6,2) (16,3) (19,9) (19,5) (11,18) (4,14) (4,24) (20,16) (1,17) (13,23) (14,13) (10,20) (14,21) (19,22) (0,21) (11,14) (2,19) (3,21) (9,12) (12,23) (20,1) (21,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "920"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (10,0) (1,0) (10,9) (6,2) (0,2) (4,7) (1,5) (7,6) (8,11) (8,1) (3,0) (1,2) (4,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "921"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (27,15) (6,9) (26,27) (12,25) (18,19) (10,14) (7,22) (4,26) (13,24) (3,5) (6,7) (21,23) (11,20) (17,7) (27,17) (18,21) (12,17) (1,22) (3,10) (24,21) (14,24) (0,6) (29,19) (24,7) (29,16) (19,2) (28,27) (8,28) (18,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "922"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (15,9) (10,14) (17,0) (5,16) (12,11) (1,11) (13,12) (18,11) (0,5) (13,9) (7,16) (2,1) (12,19) (19,4) (15,10) (3,18) (16,19) (7,8) (6,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "923"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (7,0) (5,4) (1,10) (11,1) (1,12) (10,13) (1,8) (10,7) (4,3) (1,0) (7,2) (4,7) (9,6) (6,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "924"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,18) (1,5) (15,14) (16,15) (15,12) (21,16) (13,22) (18,17) (6,0) (2,10) (2,0) (9,13) (11,7) (5,20) (15,10) (14,6) (2,7) (1,11) (8,19) (3,18) (4,1) (20,8) (1,0) (1,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "925"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (5,10) (2,0) (7,9) (0,3) (1,4) (9,6) (2,8) (5,7) (0,1) (0,4) (3,4) (4,2) (7,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "926"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (1,0) (10,23) (5,9) (15,17) (0,3) (16,21) (0,2) (8,23) (23,11) (6,9) (2,9) (7,2) (10,12) (23,13) (12,17) (23,4) (19,15) (22,13) (11,2) (1,6) (14,5) (12,20) (16,12) (18,21) (3,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "927"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (3,0) (7,17) (9,2) (16,15) (13,9) (18,0) (8,4) (10,12) (5,11) (15,6) (5,1) (16,10) (15,14) (3,7) (18,13) (16,5) (8,16) (2,17) (0,2) (0,1) (14,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "928"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (20,10) (2,12) (5,10) (0,13) (20,0) (17,4) (10,14) (19,5) (11,15) (5,3) (10,6) (2,11) (7,6) (17,15) (18,11) (9,8) (12,14) (16,21) (15,1) (0,16) (9,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "929"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (20,15) (18,24) (1,0) (19,2) (1,27) (10,20) (0,12) (0,4) (14,15) (18,6) (3,7) (26,0) (5,17) (23,17) (9,16) (11,19) (6,25) (20,8) (3,0) (24,0) (0,2) (1,6) (8,18) (9,24) (10,2) (13,17) (4,27) (7,22) (22,13) (11,3) (16,21)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "930"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (28,7) (4,15) (4,23) (27,2) (3,21) (19,16) (7,16) (3,20) (26,18) (22,6) (23,21) (9,3) (7,14) (0,17) (5,20) (6,2) (10,0) (29,22) (13,1) (13,18) (8,12) (23,28) (8,7) (17,6) (0,19) (24,17) (11,23) (25,2) (1,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "931"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,2) (10,18) (14,12) (0,6) (1,7) (5,9) (15,12) (14,2) (16,9) (19,5) (8,0) (4,7) (15,17) (2,3) (0,1) (0,13) (5,10) (4,0) (19,11) (9,4) (0,15) (3,0) (17,18)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "932"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (22,17) (4,7) (14,9) (28,13) (26,10) (7,26) (20,3) (15,16) (28,24) (19,16) (20,21) (14,15) (1,5) (11,8) (28,2) (16,27) (18,28) (0,18) (9,21) (25,19) (5,20) (23,5) (16,17) (6,26) (8,15) (10,21) (20,12) (2,20)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "933"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (14,11) (21,14) (29,7) (32,28) (18,8) (30,25) (4,16) (21,22) (4,31) (20,3) (25,6) (33,12) (13,9) (33,18) (30,9) (28,17) (30,29) (0,4) (24,5) (2,1) (4,29) (1,3) (8,1) (26,23) (25,5) (2,15) (17,33) (14,27) (2,10) (20,19) (21,32) (7,27) (23,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "934"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (6,0) (0,2) (2,3) (6,1) (11,7) (18,8) (4,20) (10,20) (0,5) (1,19) (0,17) (17,15) (9,18) (12,16) (20,7) (0,3) (16,1) (4,13) (4,0) (2,18) (1,0) (10,2) (12,5) (14,18)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "935"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (16,9) (10,21) (6,13) (18,19) (0,2) (0,17) (20,13) (23,14) (9,5) (4,3) (1,0) (15,11) (21,0) (0,7) (13,22) (3,8) (17,8) (17,1) (8,19) (13,9) (2,5) (15,12) (23,0) (13,11) (11,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "936"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,3) (4,5) (6,3) (5,1) (5,0) (0,2) (1,3) (2,1) (1,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "937"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (12,0) (0,7) (9,4) (5,6) (8,5) (1,11) (8,1) (6,3) (13,9) (12,3) (8,10) (2,10) (8,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "938"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (13,1) (11,0) (0,1) (1,20) (9,23) (11,8) (14,15) (25,20) (19,21) (11,24) (15,6) (24,22) (18,26) (10,13) (4,18) (16,9) (2,17) (12,1) (6,12) (15,23) (0,26) (7,1) (21,17) (5,26) (25,2) (25,22) (3,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "939"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (24,17) (21,24) (0,4) (16,5) (24,4) (1,23) (6,2) (9,13) (23,13) (17,11) (7,23) (2,0) (8,6) (16,19) (25,28) (27,6) (22,27) (22,13) (0,3) (4,14) (19,10) (18,15) (19,21) (25,6) (3,21) (20,13) (1,0) (12,1) (15,1) (0,23) (7,26) (20,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "940"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (2,17) (1,8) (20,6) (7,21) (12,10) (15,10) (4,11) (5,11) (7,10) (9,15) (17,14) (4,2) (8,7) (0,15) (3,11) (10,11) (18,21) (13,2) (7,16) (19,17) (20,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "941"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (2,0) (0,1) (3,7) (0,8) (5,10) (4,0) (11,12) (6,3) (0,3) (9,8) (4,3) (12,10) (2,12) (1,11) (6,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "942"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (26,4) (8,4) (16,7) (21,13) (22,11) (19,6) (1,0) (4,19) (17,4) (13,7) (22,6) (4,24) (17,9) (5,12) (6,27) (1,3) (2,7) (20,18) (15,5) (0,6) (3,23) (2,0) (13,0) (28,2) (12,25) (24,14) (5,26) (19,10) (0,4) (14,20) (0,3) (6,23)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "943"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (4,0) (5,0) (1,6) (3,2) (0,6) (0,1) (2,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "944"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (10,25) (19,23) (24,26) (11,7) (18,20) (9,5) (0,7) (23,4) (13,21) (1,11) (2,15) (7,8) (0,14) (15,3) (21,10) (13,15) (9,22) (0,1) (7,20) (26,9) (6,13) (17,8) (16,22) (2,0) (12,14) (4,21) (19,9) (0,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "945"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (19,16) (18,29) (13,19) (32,12) (23,30) (33,21) (11,1) (28,11) (30,17) (15,10) (7,27) (21,4) (15,12) (31,13) (0,21) (7,20) (31,8) (25,12) (15,5) (9,31) (32,23) (24,16) (12,6) (7,2) (18,22) (3,28) (11,14) (11,15) (20,33) (31,12) (16,26) (16,0) (29,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "946"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (8,9) (4,12) (4,0) (0,3) (1,13) (4,10) (8,12) (0,1) (11,3) (3,14) (11,6) (13,6) (2,0) (5,0) (8,14) (8,2) (7,10) (0,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "947"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (4,8) (22,5) (3,10) (16,3) (1,12) (15,14) (30,19) (26,27) (10,13) (7,18) (6,23) (29,1) (4,29) (34,10) (13,25) (28,30) (0,13) (33,9) (15,6) (32,0) (24,21) (20,15) (22,34) (10,24) (33,13) (23,7) (0,15) (11,17) (26,17) (11,24) (31,8) (28,8) (2,16) (8,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "948"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,6) (4,8) (1,5) (2,7) (0,7) (3,7) (5,7) (4,6) (9,3) (10,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "949"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (19,23) (29,16) (31,11) (9,14) (32,12) (24,17) (10,28) (25,17) (10,6) (0,2) (16,2) (22,11) (7,27) (30,0) (0,25) (33,3) (33,18) (19,22) (21,23) (26,24) (13,16) (20,21) (23,28) (12,1) (32,5) (15,8) (1,28) (1,7) (10,30) (4,15) (14,25) (29,15) (30,2) (3,0) (1,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "950"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,4) (1,3) (1,0) (5,6) (2,0) (5,4) (1,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "951"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (14,16) (31,25) (1,28) (10,7) (25,13) (12,26) (12,33) (25,29) (1,5) (34,15) (18,8) (11,4) (34,14) (4,0) (19,1) (7,25) (17,12) (23,26) (1,29) (16,2) (3,30) (11,6) (9,5) (6,2) (12,5) (34,27) (13,20) (27,8) (24,28) (17,21) (13,18) (0,32) (5,30) (9,22)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "doc_id": "952"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (11,17) (13,5) (23,14) (8,4) (17,16) (22,24) (21,1) (3,6) (25,13) (23,24) (7,16) (3,0) (23,1) (4,0) (25,8) (19,7) (1,20) (24,10) (14,4) (0,1) (12,16) (26,9) (21,18) (1,15) (17,20) (2,0) (2,11) (19,9) (3,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "953"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,18) (2,0) (3,12) (13,14) (20,21) (24,11) (4,24) (16,17) (9,20) (25,24) (7,10) (8,23) (13,3) (24,18) (2,22) (23,9) (14,0) (16,23) (22,12) (0,1) (0,10) (0,5) (2,15) (16,3) (1,25) (19,23) (17,6) (3,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "954"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (5,2) (6,3) (1,0) (4,5) (1,3) (8,0) (6,7) (5,1) (0,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "955"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (11,20) (7,4) (7,10) (5,4) (17,3) (0,6) (1,3) (6,19) (4,2) (13,14) (5,9) (16,6) (0,21) (8,19) (5,12) (17,4) (20,6) (6,13) (4,19) (15,14) (12,18)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "956"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (5,12) (4,2) (7,12) (11,6) (11,3) (1,9) (0,7) (11,10) (8,10) (0,8) (4,5) (9,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "957"}
{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (20,11) (21,0) (8,13) (22,12) (6,15) (2,0) (15,13) (14,9) (1,5) (12,6) (18,1) (0,11) (11,7) (2,17) (1,10) (12,0) (3,0) (15,2) (16,17) (0,1) (21,9) (3,11) (20,1) (19,22) (18,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "958"}