{"question": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)\nQ: Is there a cycle in this graph?\nA: The edges (3,0), (1,0), (4,1), (3,4) form a cycle, so yes, there is a cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)\nQ: Is there a cycle in this graph?\nA: No, there is no cycle in this graph.\n\nIn an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)\nQ: Is there a cycle in this graph?\nA: The edges (0,1), (1,4), (6,4), (2,6), (2,0) form a cycle, so yes, there is a cycle in this graph.\n\nIn an 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: (19,23) (12,23) (16,2) (2,15) (10,8) (2,20) (3,0) (2,0) (22,2) (21,11) (12,14) (4,21) (17,21) (0,14) (18,6) (3,14) (7,1) (4,24) (6,9) (9,20) (7,21) (5,9) (15,8) (2,13) (23,9) (19,1) (0,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "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 15, and the edges are: (3,13) (2,0) (3,12) (5,12) (7,14) (8,1) (8,14) (10,11) (1,0) (5,9) (6,15) (3,2) (4,14) (14,2) (13,11) (6,1) (0,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "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 23, and the edges are: (10,8) (13,9) (18,16) (6,11) (0,22) (15,6) (17,14) (4,3) (1,19) (0,19) (14,3) (14,21) (12,3) (5,10) (22,23) (8,16) (9,5) (19,16) (5,14) (7,10) (11,3) (16,2) (8,20)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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 27, and the edges are: (3,17) (12,11) (0,27) (19,1) (2,13) (3,16) (4,14) (22,25) (12,3) (8,23) (11,2) (11,9) (5,4) (23,5) (21,19) (10,3) (20,3) (6,15) (11,26) (27,20) (5,18) (21,25) (19,26) (18,1) (15,12) (7,18) (24,17)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "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 28, and the edges are: (2,27) (15,1) (24,20) (19,24) (14,13) (20,17) (9,12) (10,17) (4,2) (3,20) (24,26) (22,8) (21,6) (23,28) (19,7) (14,6) (25,16) (11,21) (6,0) (1,0) (13,27) (18,25) (25,22) (4,20) (26,22) (0,2) (5,3) (12,0) (15,8) (6,23)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "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 7, and the edges are: (4,6) (6,3) (1,0) (2,7) (7,1) (0,2) (5,0) (5,4) (3,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "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 28, and the edges are: (22,15) (16,17) (3,27) (10,16) (28,8) (22,5) (15,13) (1,28) (23,18) (16,11) (27,5) (4,8) (14,6) (5,1) (14,19) (22,12) (0,3) (24,11) (27,0) (6,9) (0,4) (0,1) (23,1) (2,19) (21,1) (0,20) (25,4) (14,23) (23,11) (26,23) (0,2) (28,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "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 17, and the edges are: (0,12) (10,0) (12,1) (4,15) (2,6) (4,5) (13,17) (7,3) (14,13) (3,4) (9,0) (14,10) (6,10) (5,14) (7,16) (16,11) (8,5) (0,1)\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 9, and the edges are: (4,0) (2,0) (7,4) (1,2) (0,3) (0,5) (0,1) (7,2) (9,2) (5,8) (5,1) (7,6) (3,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "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 9, and the edges are: (0,4) (1,9) (0,3) (7,9) (6,7) (5,9) (5,0) (2,0) (2,5) (1,0) (8,3) (2,4) (9,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "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 27, and the edges are: (0,6) (3,22) (5,2) (27,20) (15,6) (0,2) (4,1) (21,1) (23,4) (19,11) (15,8) (14,24) (9,8) (18,26) (9,25) (11,2) (26,15) (20,16) (9,13) (8,11) (14,18) (7,21) (18,10) (20,21) (0,3) (18,12) (22,25) (2,17) (1,0) (23,17)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a 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 28, and the edges are: (15,11) (28,8) (4,9) (1,13) (18,28) (13,10) (6,26) (24,4) (11,18) (5,24) (16,4) (12,20) (12,2) (3,24) (27,9) (15,17) (7,28) (15,23) (14,16) (25,12) (8,1) (1,0) (27,0) (6,16) (25,19) (19,3) (22,9) (25,8) (0,2) (21,26) (0,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a 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 12, and the edges are: (12,8) (5,4) (5,1) (9,3) (8,1) (10,7) (11,3) (1,0) (7,0) (2,4) (10,6) (5,11) (12,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a 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 13, and the edges are: (2,0) (13,10) (9,11) (13,6) (12,2) (0,1) (0,4) (1,8) (9,10) (9,7) (3,12) (5,4) (6,0) (4,3) (8,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "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 34, and the edges are: (25,31) (28,19) (26,22) (8,17) (12,24) (5,6) (5,27) (21,27) (30,31) (9,20) (2,15) (0,4) (12,5) (26,20) (12,2) (7,6) (13,32) (18,30) (0,1) (10,1) (34,12) (28,21) (0,2) (33,6) (14,26) (3,0) (15,13) (11,10) (13,23) (4,16) (5,25) (0,9) (8,20) (3,16) (21,20) (29,33) (6,4) (26,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "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 17, and the edges are: (9,5) (13,4) (0,1) (9,2) (15,6) (13,1) (2,0) (10,12) (0,15) (1,12) (2,7) (6,5) (1,14) (1,2) (8,4) (11,4) (11,17) (14,3) (6,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "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 9, and the edges are: (1,3) (8,0) (9,7) (2,0) (2,7) (6,3) (6,8) (9,5) (4,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "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 17, and the edges are: (9,17) (0,11) (7,13) (6,12) (11,3) (1,8) (10,15) (3,0) (11,5) (16,0) (12,1) (14,2) (2,15) (4,1) (11,1) (6,15) (0,1) (0,4) (2,0) (9,13) (17,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "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 13, and the edges are: (2,1) (6,7) (10,11) (3,4) (0,4) (10,13) (0,2) (1,0) (2,13) (5,0) (3,0) (12,10) (5,1) (5,9) (2,7) (4,11) (8,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a 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 17, and the edges are: (1,0) (11,9) (13,9) (8,14) (0,13) (11,12) (17,8) (5,9) (13,16) (2,5) (0,15) (3,4) (13,6) (15,10) (0,7) (8,3) (17,1) (0,17)\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: (10,1) (5,2) (2,15) (0,9) (7,8) (16,7) (11,15) (3,9) (1,12) (9,8) (10,14) (12,4) (7,1) (4,6) (14,13) (5,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no 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 27, and the edges are: (14,26) (7,9) (21,15) (21,24) (0,4) (3,0) (27,22) (14,2) (6,20) (6,19) (11,8) (25,14) (8,23) (18,3) (1,4) (0,1) (13,20) (1,20) (0,2) (16,0) (10,1) (0,26) (9,21) (6,17) (4,18) (16,5) (23,16) (4,23) (22,19) (7,12) (24,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "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 9, and the edges are: (2,0) (3,1) (6,3) (7,9) (7,2) (4,3) (0,8) (6,8) (9,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "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 8, and the edges are: (8,5) (4,0) (3,1) (8,2) (0,2) (4,3) (3,0) (7,4) (7,2) (0,1) (6,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a 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 31, and the edges are: (7,14) (19,23) (3,26) (17,30) (1,14) (0,15) (20,25) (4,7) (31,22) (26,22) (20,17) (0,6) (29,10) (7,10) (27,4) (10,16) (24,19) (12,18) (2,22) (18,6) (21,18) (4,6) (8,11) (28,21) (25,24) (1,13) (5,7) (14,11) (18,2) (6,20) (9,24)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "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 22, and the edges are: (2,6) (16,18) (3,16) (2,0) (4,14) (14,11) (1,15) (13,14) (0,1) (0,21) (12,9) (7,21) (21,3) (14,20) (12,13) (17,11) (10,16) (19,5) (19,2) (21,19) (22,4) (19,9) (20,8) (20,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a 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 24, and the edges are: (17,4) (10,5) (2,11) (22,13) (20,0) (5,23) (15,18) (17,0) (11,15) (9,10) (7,6) (21,12) (14,10) (16,0) (2,24) (19,11) (5,3) (12,14) (6,10) (16,22) (2,22) (9,8) (20,10) (1,15)\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 34, and the edges are: (7,34) (29,7) (6,17) (27,5) (4,15) (14,3) (3,0) (4,0) (8,18) (23,6) (1,0) (12,4) (30,14) (21,13) (34,9) (27,3) (2,0) (26,24) (9,26) (13,2) (2,14) (20,0) (34,16) (25,10) (7,33) (3,11) (3,31) (18,26) (9,1) (32,20) (3,19) (8,2) (32,25) (27,23) (3,25) (4,28) (5,22) (15,5)\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 34, and the edges are: (2,1) (27,7) (24,5) (7,33) (3,1) (25,30) (26,23) (13,9) (8,18) (28,34) (0,1) (3,20) (34,15) (4,29) (29,30) (2,0) (1,8) (32,21) (2,10) (4,31) (9,23) (33,18) (4,17) (14,11) (19,20) (14,21) (25,5) (25,6) (12,33) (4,0) (2,16) (34,29) (22,21) (14,27) (28,32) (9,30)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a 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 9, and the edges are: (1,7) (7,4) (2,7) (1,6) (9,1) (8,6) (5,4) (7,0) (4,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "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 25, and the edges are: (17,25) (10,16) (3,1) (14,4) (7,5) (14,24) (17,23) (20,14) (18,13) (4,25) (17,10) (0,2) (1,6) (15,17) (3,25) (25,12) (21,0) (0,1) (2,5) (19,13) (0,3) (19,2) (11,8) (13,21) (14,18) (25,11) (16,22) (9,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "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 21, and the edges are: (0,6) (6,20) (6,19) (19,4) (16,6) (13,6) (4,7) (11,20) (14,13) (5,12) (9,5) (4,17) (3,1) (10,7) (5,4) (17,3) (15,14) (19,8) (21,0) (12,18) (2,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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 33, and the edges are: (9,12) (31,10) (12,8) (19,1) (29,10) (0,28) (32,31) (27,7) (27,24) (22,31) (29,24) (18,6) (15,22) (6,20) (19,3) (19,9) (29,1) (32,2) (30,14) (12,28) (5,16) (25,17) (11,29) (4,3) (26,1) (22,23) (33,4) (8,30) (2,13) (17,26) (5,20) (21,31) (16,17)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "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 33, and the edges are: (14,25) (18,25) (18,32) (11,15) (4,30) (22,26) (3,23) (12,28) (6,26) (8,19) (17,22) (11,2) (31,2) (16,28) (23,24) (29,13) (16,21) (3,6) (13,30) (7,12) (20,18) (24,28) (27,0) (12,1) (9,2) (5,13) (11,19) (8,6) (33,15) (28,4) (18,19) (31,0) (12,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "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 33, and the edges are: (23,0) (33,10) (18,30) (11,4) (13,9) (32,19) (23,25) (0,27) (33,2) (16,1) (24,30) (1,2) (20,6) (12,18) (12,29) (21,5) (15,31) (4,13) (19,9) (31,0) (6,17) (7,21) (3,33) (12,28) (8,33) (20,21) (31,2) (3,22) (32,7) (28,5) (8,26) (7,10) (15,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no 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 16, and the edges are: (3,8) (0,1) (6,7) (16,10) (1,16) (8,13) (16,5) (14,9) (9,4) (3,2) (12,11) (6,12) (4,8) (10,13) (3,15) (11,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no 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 12, and the edges are: (8,9) (4,11) (6,3) (2,12) (1,6) (6,12) (8,7) (7,4) (7,12) (0,4) (0,5) (6,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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) (2,0) (9,3) (12,2) (6,3) (4,1) (6,0) (10,3) (2,3) (0,3) (2,8) (5,6) (7,9) (4,0) (12,1) (13,11) (4,11)\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 34, and the edges are: (7,31) (18,1) (30,28) (11,29) (16,7) (19,14) (0,26) (4,20) (4,29) (34,30) (10,33) (17,21) (27,10) (3,18) (12,24) (13,33) (23,32) (18,27) (2,26) (25,14) (29,8) (14,23) (2,16) (25,28) (22,8) (28,15) (30,12) (21,16) (32,5) (28,9) (8,7) (33,14) (14,6) (22,23)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "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 33, and the edges are: (12,8) (26,20) (17,32) (28,14) (13,21) (33,0) (8,3) (10,23) (6,26) (2,7) (11,32) (19,26) (27,1) (14,7) (28,8) (4,15) (8,10) (12,25) (16,8) (22,13) (9,25) (26,1) (12,0) (18,29) (11,30) (14,17) (5,11) (24,12) (9,13) (15,29) (6,4) (31,33) (8,20)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "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 9, and the edges are: (5,6) (0,5) (0,4) (4,1) (2,0) (4,8) (8,7) (3,0) (1,0) (6,0) (7,5) (9,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "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 14, and the edges are: (6,12) (0,2) (10,11) (12,11) (8,2) (4,0) (10,5) (7,9) (3,0) (7,2) (7,1) (13,5) (12,1) (4,11) (14,9) (1,0) (0,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a 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 12, and the edges are: (1,0) (6,2) (6,0) (8,11) (1,5) (0,4) (5,3) (3,0) (2,0) (8,4) (6,12) (3,2) (11,9) (4,6) (7,9) (4,10)\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 30, and the edges are: (2,19) (27,21) (25,14) (22,29) (8,28) (3,12) (11,3) (26,16) (5,9) (1,27) (3,15) (14,3) (27,7) (19,16) (29,27) (25,24) (8,16) (6,11) (0,30) (20,28) (4,16) (9,18) (10,8) (5,14) (10,5) (23,6) (19,0) (29,14) (25,17) (10,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no 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 29, and the edges are: (16,15) (24,0) (24,29) (9,28) (5,20) (2,26) (5,22) (5,27) (7,12) (16,19) (0,23) (6,5) (11,5) (0,3) (7,28) (18,11) (21,17) (5,21) (1,29) (9,14) (2,10) (15,27) (8,20) (0,16) (4,18) (15,28) (26,3) (13,14) (8,25)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "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 16, and the edges are: (0,16) (1,5) (9,7) (3,5) (6,14) (4,2) (16,11) (11,9) (0,14) (5,12) (3,0) (5,13) (10,5) (15,8) (5,8) (7,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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 26, and the edges are: (3,18) (0,6) (14,15) (7,26) (3,13) (6,16) (11,9) (1,15) (5,26) (18,22) (9,18) (24,17) (8,1) (1,9) (24,3) (10,0) (24,4) (26,23) (12,2) (13,20) (21,23) (18,21) (25,6) (8,19) (12,20) (16,26)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "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 15, and the edges are: (14,8) (11,10) (12,7) (8,6) (0,12) (13,10) (1,7) (5,2) (12,11) (0,3) (4,7) (5,7) (15,3) (8,12) (14,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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 15, and the edges are: (9,13) (0,15) (0,2) (11,10) (13,5) (5,1) (4,9) (0,3) (8,0) (2,3) (14,13) (15,7) (9,11) (8,3) (6,0) (0,1) (13,0) (8,12) (0,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a 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 11, and the edges are: (3,10) (0,2) (2,6) (5,1) (7,4) (0,3) (2,11) (5,9) (10,4) (11,0) (10,8) (10,1) (0,1) (0,4) (2,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "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 12, and the edges are: (7,12) (1,5) (4,5) (2,4) (10,7) (1,8) (5,11) (12,8) (0,7) (11,3) (6,10) (3,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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 20, and the edges are: (13,1) (16,14) (19,12) (19,3) (2,13) (11,10) (1,18) (0,8) (8,10) (7,14) (8,15) (18,9) (5,2) (15,20) (17,6) (12,17) (11,4) (0,13) (3,0) (16,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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 21, and the edges are: (0,2) (6,3) (10,17) (19,9) (2,11) (18,8) (12,1) (4,14) (4,8) (9,21) (1,14) (16,7) (10,3) (16,17) (1,15) (17,20) (16,11) (7,19) (20,1) (13,5) (21,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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 33, and the edges are: (30,16) (3,20) (16,2) (20,21) (14,13) (33,12) (6,12) (18,22) (4,5) (29,24) (19,7) (13,30) (32,9) (16,31) (27,12) (10,12) (30,18) (11,24) (15,8) (9,15) (11,26) (0,25) (1,0) (15,23) (4,32) (1,31) (28,32) (7,20) (0,2) (5,7) (17,1) (12,14) (12,5) (0,17) (11,21)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "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 22, and the edges are: (21,8) (1,21) (16,10) (7,4) (4,10) (20,13) (2,21) (0,5) (1,0) (3,2) (20,11) (17,18) (22,6) (5,19) (6,13) (18,15) (10,15) (9,8) (14,18) (14,13) (13,0) (3,4) (12,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a 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 9, and the edges are: (0,2) (0,4) (8,1) (0,6) (4,3) (1,2) (9,8) (5,1) (7,3) (3,2) (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": "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 26, and the edges are: (10,25) (7,20) (22,9) (5,9) (13,15) (18,20) (23,4) (24,26) (11,7) (15,2) (17,8) (21,4) (0,7) (14,0) (13,21) (9,19) (12,14) (23,19) (9,26) (8,7) (10,21) (0,1) (15,3) (11,1) (6,13) (0,9) (22,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "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 10, and the edges are: (9,8) (7,4) (6,9) (5,1) (0,1) (4,10) (0,6) (4,8) (5,3) (3,2) (2,0) (6,2)\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 14, and the edges are: (1,4) (10,7) (7,11) (13,0) (4,2) (14,0) (3,4) (12,5) (9,2) (8,9) (14,5) (14,7) (3,12) (4,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no 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 9, and the edges are: (9,2) (2,1) (1,0) (6,7) (7,4) (5,8) (3,0) (3,4) (0,5) (7,2) (0,4) (2,0) (5,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "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 9, and the edges are: (8,5) (8,0) (6,5) (3,7) (8,1) (2,0) (9,8) (1,4) (3,6)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "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 16, and the edges are: (3,0) (5,7) (11,6) (14,12) (10,5) (12,1) (9,0) (2,5) (4,9) (2,4) (3,14) (0,16) (14,13) (6,8) (16,15) (6,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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 7, and the edges are: (1,7) (4,0) (6,0) (0,3) (0,2) (5,0) (7,0) (4,7) (2,6) (2,3) (0,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "doc_id": "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 19, and the edges are: (10,19) (7,1) (16,6) (2,9) (14,3) (4,7) (12,14) (17,2) (8,15) (18,1) (5,9) (9,19) (12,2) (9,6) (2,13) (15,2) (11,8) (0,14) (10,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no 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 28, and the edges are: (8,15) (12,3) (24,27) (7,18) (20,17) (1,14) (3,28) (21,23) (23,8) (3,25) (24,20) (19,16) (27,22) (13,15) (2,22) (13,7) (5,11) (9,16) (14,10) (6,26) (19,18) (23,4) (25,24) (0,23) (17,14) (10,21) (26,11) (17,5)\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 8, and the edges are: (8,7) (1,7) (4,3) (5,7) (7,6) (0,1) (2,1) (2,0) (1,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "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 21, and the edges are: (15,14) (12,1) (8,16) (0,20) (21,2) (10,1) (7,8) (9,3) (20,7) (7,1) (4,12) (13,21) (19,5) (11,4) (18,9) (5,4) (18,2) (6,9) (15,17) (10,14) (13,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no 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 16, and the edges are: (2,10) (3,6) (0,1) (1,8) (0,3) (13,0) (10,7) (11,6) (15,16) (9,15) (2,0) (0,8) (7,4) (4,16) (0,15) (9,3) (7,12) (5,6) (8,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "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 11, and the edges are: (5,4) (5,10) (1,5) (9,7) (8,0) (8,2) (6,1) (11,6) (3,0) (0,6) (9,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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 10, and the edges are: (9,4) (0,1) (4,2) (4,8) (3,6) (10,1) (7,4) (2,0) (8,1) (6,5) (3,7)\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 32, and the edges are: (22,21) (7,21) (30,5) (12,27) (28,1) (31,15) (26,8) (13,4) (9,19) (1,32) (1,16) (7,2) (25,23) (8,0) (0,31) (2,17) (19,6) (30,3) (23,0) (28,10) (5,21) (9,13) (18,12) (3,24) (29,18) (0,1) (20,6) (31,2) (4,11) (20,32) (28,12) (15,14) (7,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "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 16, and the edges are: (9,3) (16,15) (7,4) (0,3) (2,10) (1,8) (15,9) (15,0) (0,8) (14,8) (11,6) (0,2) (1,0) (7,12) (10,7) (16,4) (3,6) (0,13) (5,6)\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 9, and the edges are: (1,4) (8,9) (3,0) (6,4) (0,4) (8,4) (0,5) (7,4) (0,2) (5,3) (1,0) (6,2) (3,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "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 15, and the edges are: (0,5) (10,12) (6,7) (10,0) (6,14) (4,8) (13,11) (14,8) (11,4) (3,1) (2,9) (15,9) (14,12) (15,1) (15,10)\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 26, and the edges are: (3,10) (20,24) (9,3) (12,15) (26,2) (20,1) (6,5) (25,7) (21,9) (14,8) (26,0) (21,24) (16,13) (6,21) (12,19) (22,15) (8,23) (23,11) (18,4) (12,17) (6,22) (23,26) (0,17) (0,1) (1,13) (20,4) (7,23)\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 21, and the edges are: (2,17) (10,15) (4,2) (0,2) (4,11) (3,11) (8,7) (0,3) (15,9) (13,2) (3,20) (1,0) (21,18) (21,7) (17,14) (5,11) (8,1) (11,10) (0,15) (20,6) (7,10) (12,10) (19,17) (16,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a 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 10, and the edges are: (6,9) (6,3) (7,10) (1,7) (2,8) (4,7) (2,0) (4,5) (7,8) (7,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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 33, and the edges are: (28,32) (9,30) (11,14) (14,21) (7,29) (23,9) (12,33) (27,7) (20,19) (26,23) (20,3) (17,33) (10,2) (30,29) (28,17) (25,30) (6,25) (4,29) (16,4) (0,4) (5,24) (0,1) (1,8) (21,22) (9,13) (2,15) (18,33) (3,1) (32,21) (18,8) (31,4) (5,25) (1,2) (27,14) (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": "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 8, and the edges are: (7,1) (4,8) (4,3) (2,1) (0,3) (7,5) (6,5) (4,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "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 29, and the edges are: (18,3) (17,15) (29,20) (20,12) (15,23) (29,0) (5,17) (12,15) (11,19) (10,29) (22,15) (17,8) (18,16) (27,17) (19,2) (4,9) (22,6) (24,8) (18,2) (26,28) (4,11) (26,21) (7,25) (20,14) (6,7) (13,15) (7,1) (26,17) (19,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "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 17, and the edges are: (10,6) (16,13) (8,11) (15,4) (14,6) (3,5) (0,9) (3,0) (0,1) (0,4) (12,17) (17,7) (3,12) (12,2) (1,15) (8,6) (2,4) (2,0) (13,14) (6,0)\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 23, and the edges are: (2,1) (1,0) (11,5) (16,6) (18,6) (0,20) (16,7) (12,17) (9,4) (4,2) (0,2) (15,18) (15,12) (22,11) (14,22) (21,15) (10,6) (13,1) (4,7) (3,7) (6,23) (3,0) (14,12) (8,12) (14,0) (20,19)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a 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 8, and the edges are: (6,4) (2,4) (7,5) (5,2) (8,6) (2,3) (8,0) (1,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "doc_id": "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 13, and the edges are: (0,2) (4,6) (3,0) (8,3) (7,4) (10,6) (9,0) (11,9) (9,12) (10,13) (5,8) (7,5) (1,0) (2,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "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 29, and the edges are: (18,0) (1,27) (11,7) (14,22) (4,8) (5,4) (29,17) (2,25) (17,10) (2,10) (14,16) (13,29) (8,9) (10,0) (21,15) (19,22) (6,19) (28,12) (5,12) (24,19) (3,14) (16,20) (22,5) (1,23) (19,26) (14,23) (21,28) (27,11) (13,23)\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 18, and the edges are: (2,5) (11,10) (10,8) (17,3) (6,17) (1,12) (14,16) (7,14) (15,12) (13,1) (3,0) (0,13) (8,18) (8,0) (9,18) (11,4) (12,16) (2,13)\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 17, and the edges are: (2,15) (8,7) (10,0) (4,8) (0,3) (6,11) (14,13) (12,5) (2,0) (11,16) (1,0) (2,10) (12,1) (3,14) (17,14) (0,9) (17,10) (5,14) (16,1) (4,5)\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 20, and the edges are: (13,3) (16,3) (0,14) (15,9) (5,10) (10,20) (18,0) (6,18) (8,2) (16,2) (20,11) (9,12) (7,0) (14,13) (6,11) (1,0) (17,4) (19,6) (12,3) (16,17)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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 21, and the edges are: (3,17) (9,4) (6,8) (19,0) (17,16) (19,20) (15,10) (7,17) (2,13) (1,18) (19,16) (14,8) (12,4) (15,1) (2,20) (18,6) (5,16) (0,11) (20,6) (4,0) (20,21)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no 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 14, and the edges are: (0,7) (2,12) (13,4) (10,4) (13,12) (5,14) (7,10) (13,6) (1,6) (8,13) (0,14) (3,14) (9,0) (0,2) (1,0) (3,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "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 21, and the edges are: (14,18) (0,1) (17,19) (11,18) (17,21) (4,21) (13,17) (15,2) (1,9) (8,0) (5,2) (11,10) (18,3) (15,6) (0,2) (6,13) (15,16) (12,4) (10,0) (8,15) (0,3) (20,21) (8,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "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 16, and the edges are: (16,1) (1,3) (11,8) (15,7) (14,0) (1,0) (9,13) (2,8) (13,5) (11,5) (11,14) (13,15) (4,12) (4,5) (6,16) (10,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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 31, and the edges are: (21,18) (28,2) (22,13) (13,12) (11,24) (23,17) (19,21) (24,20) (3,12) (28,14) (2,24) (26,18) (5,27) (6,16) (31,3) (23,0) (29,9) (30,8) (6,9) (31,17) (28,4) (30,28) (0,24) (26,17) (7,19) (8,1) (10,31) (5,21) (15,14) (28,25) (16,17)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no 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 30, and the edges are: (18,8) (1,4) (24,12) (28,10) (11,0) (4,23) (26,15) (3,14) (2,26) (27,22) (8,12) (23,20) (19,24) (11,28) (16,15) (9,26) (22,17) (26,7) (28,3) (29,22) (3,29) (10,21) (2,24) (16,30) (17,13) (20,17) (8,0) (6,28) (6,5) (25,10)\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 14, and the edges are: (7,10) (6,12) (12,7) (1,11) (11,2) (6,14) (3,2) (1,0) (3,13) (4,2) (2,10) (11,9) (5,8) (8,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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 18, and the edges are: (14,16) (10,3) (7,8) (18,0) (10,17) (16,15) (6,4) (1,16) (15,11) (11,0) (5,2) (1,12) (13,3) (15,7) (9,0) (9,4) (10,1) (2,6)\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 11, and the edges are: (8,10) (7,8) (4,3) (5,11) (2,6) (10,4) (1,7) (5,9) (5,0) (2,10) (6,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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 27, and the edges are: (11,13) (25,24) (27,24) (14,3) (13,8) (16,7) (1,8) (18,9) (0,3) (20,5) (12,16) (16,22) (0,2) (3,4) (5,14) (15,12) (11,17) (0,13) (17,27) (1,0) (4,0) (26,0) (16,6) (9,21) (14,6) (23,8) (19,18) (15,2) (10,15) (18,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "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 7, and the edges are: (2,4) (3,2) (1,4) (6,5) (7,3) (1,5) (0,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "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 13, and the edges are: (6,12) (4,12) (0,1) (3,12) (10,8) (1,13) (13,4) (2,6) (7,8) (0,4) (9,0) (11,13) (6,7) (5,6)\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 14, and the edges are: (2,5) (6,14) (8,0) (1,5) (7,11) (8,13) (2,8) (3,11) (12,11) (10,4) (3,8) (12,4) (8,9) (6,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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: (25,14) (11,26) (16,15) (23,13) (22,13) (18,9) (5,2) (5,8) (26,3) (15,11) (9,6) (9,13) (21,12) (20,19) (0,24) (13,7) (1,17) (10,0) (17,8) (8,21) (14,11) (19,26) (11,13) (0,17) (0,23) (3,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no 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 23, and the edges are: (15,2) (15,16) (8,0) (12,2) (22,23) (1,4) (3,21) (10,13) (6,17) (16,19) (5,6) (8,9) (12,8) (7,3) (11,3) (17,18) (19,22) (11,0) (23,4) (0,1) (22,10) (20,10) (20,14) (22,17)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "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 8, and the edges are: (0,2) (1,0) (4,0) (6,7) (3,0) (8,6) (4,8) (1,6) (6,2) (5,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "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 9, and the edges are: (2,6) (4,5) (7,3) (0,5) (4,8) (3,5) (8,2) (7,1) (0,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "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 16, and the edges are: (12,16) (15,13) (0,2) (6,8) (11,4) (9,6) (0,6) (2,12) (1,0) (7,0) (8,10) (3,12) (14,6) (15,1) (4,2) (14,13) (3,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "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 30, and the edges are: (21,14) (4,19) (0,2) (21,9) (9,7) (0,1) (28,10) (17,16) (7,11) (2,30) (26,19) (23,11) (1,16) (14,6) (15,12) (18,0) (13,17) (0,28) (14,22) (17,12) (9,10) (0,27) (4,5) (21,4) (26,24) (20,5) (10,8) (26,15) (25,24) (3,0) (19,2) (29,23) (26,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "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) (10,11) (9,16) (7,15) (12,14) (11,15) (1,8) (6,16) (3,14) (0,1) (17,1) (2,6) (5,14) (8,4) (1,5) (4,11) (0,13)\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 34, and the edges are: (12,8) (23,10) (11,34) (30,34) (21,13) (7,33) (13,31) (9,12) (32,16) (2,26) (8,25) (0,33) (17,22) (30,32) (24,26) (9,34) (15,1) (4,7) (8,3) (6,19) (28,20) (29,3) (25,20) (7,17) (34,21) (27,16) (26,19) (14,18) (32,5) (1,23) (18,11) (24,15) (26,5) (19,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "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 13, and the edges are: (12,7) (6,10) (12,3) (11,2) (10,3) (13,9) (4,7) (2,0) (11,7) (4,8) (1,6) (12,13) (6,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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 26, and the edges are: (22,11) (13,7) (20,17) (26,6) (10,14) (24,25) (25,26) (16,9) (20,24) (3,19) (8,15) (14,1) (15,13) (22,2) (7,18) (11,5) (17,5) (17,14) (0,23) (8,23) (4,23) (21,10) (19,21) (12,3) (23,24) (16,18)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "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 30, and the edges are: (9,19) (7,11) (5,10) (4,24) (6,18) (22,17) (0,12) (2,17) (20,8) (2,30) (21,16) (22,21) (15,27) (1,12) (28,25) (6,15) (19,26) (8,23) (6,3) (7,4) (23,19) (6,25) (2,0) (18,19) (12,24) (2,14) (28,30) (1,0) (23,13) (7,5) (13,29) (12,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "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 18, and the edges are: (13,5) (13,2) (16,9) (14,15) (7,8) (0,4) (0,3) (9,11) (17,3) (9,3) (0,1) (15,0) (8,4) (12,10) (0,2) (2,1) (10,0) (18,2) (15,6) (8,2) (9,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "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 20, and the edges are: (9,2) (4,17) (10,12) (1,15) (8,16) (0,16) (16,14) (11,18) (0,5) (6,14) (15,13) (1,3) (7,10) (6,9) (17,8) (15,17) (12,14) (19,4) (20,10) (19,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "doc_id": "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 13, and the edges are: (6,2) (5,10) (8,2) (1,13) (12,8) (0,9) (11,3) (5,2) (1,9) (7,4) (10,4) (2,13) (3,7)\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: (4,5) (1,10) (11,9) (0,1) (0,17) (19,17) (10,17) (16,6) (6,7) (17,8) (6,12) (18,7) (3,4) (20,15) (5,13) (2,4) (16,17) (9,16) (15,3) (20,16) (13,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a 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 18, and the edges are: (14,3) (9,2) (14,0) (15,2) (17,2) (7,4) (4,10) (6,9) (1,0) (18,10) (2,12) (13,2) (16,6) (1,7) (12,14) (11,8) (9,5) (8,15) (9,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a 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 17, and the edges are: (16,7) (0,5) (10,16) (9,13) (4,15) (15,12) (8,3) (15,14) (11,10) (5,8) (14,9) (1,7) (16,5) (17,13) (17,6) (9,2) (16,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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 22, and the edges are: (5,18) (21,20) (1,2) (19,0) (14,19) (16,4) (8,12) (2,18) (10,21) (9,22) (7,22) (14,5) (11,15) (6,9) (4,13) (22,0) (8,4) (11,2) (13,10) (3,19) (6,17) (2,10) (0,1)\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 25, and the edges are: (18,15) (6,7) (5,15) (23,25) (7,12) (10,16) (22,8) (10,11) (20,17) (22,3) (6,20) (15,9) (21,2) (21,16) (14,8) (25,24) (14,4) (1,3) (5,0) (6,8) (14,9) (24,21) (13,15) (5,19) (3,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "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 17, and the edges are: (3,7) (13,3) (15,0) (12,11) (4,9) (11,6) (12,3) (17,1) (12,10) (1,5) (11,16) (5,14) (11,2) (8,2) (4,5) (3,17) (3,15)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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: (14,10) (5,4) (9,3) (1,10) (17,15) (18,2) (7,8) (6,9) (7,1) (15,14) (8,16) (13,0) (7,0) (1,12) (9,18) (19,13) (4,12) (4,11) (2,5)\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 19, and the edges are: (6,3) (4,6) (10,3) (5,17) (18,2) (19,16) (12,8) (11,3) (13,17) (17,15) (12,2) (11,0) (0,1) (14,10) (10,9) (4,1) (8,7) (0,8) (16,15) (2,0) (19,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "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 30, and the edges are: (30,13) (5,11) (21,28) (4,26) (24,30) (11,8) (17,7) (2,13) (23,30) (3,10) (12,22) (0,19) (12,11) (2,0) (16,18) (25,30) (4,3) (9,28) (11,19) (29,18) (9,10) (6,18) (8,3) (16,26) (1,0) (14,0) (0,20) (2,27) (1,16) (0,24) (28,7) (15,26)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "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 25, and the edges are: (1,18) (7,5) (5,21) (25,12) (23,24) (19,1) (1,0) (23,16) (11,25) (14,25) (21,15) (6,22) (0,2) (13,5) (3,2) (8,9) (23,10) (11,16) (17,9) (21,18) (2,4) (13,20) (3,0) (19,8) (11,2) (19,6) (20,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "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 9, and the edges are: (3,4) (4,8) (1,0) (6,3) (4,7) (9,1) (1,4) (9,2) (5,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "easy", "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 12, and the edges are: (7,10) (2,0) (5,3) (2,12) (6,7) (1,4) (5,8) (10,1) (0,1) (11,10) (7,3) (2,7) (3,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "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 23, and the edges are: (12,17) (18,0) (11,10) (12,14) (17,13) (9,11) (0,23) (18,16) (19,22) (7,5) (5,16) (7,12) (0,11) (15,11) (13,8) (1,19) (1,12) (3,12) (20,17) (21,7) (17,4) (6,22) (2,8)\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 14, and the edges are: (0,9) (10,7) (14,10) (0,1) (0,2) (2,1) (10,2) (4,7) (14,11) (4,0) (8,12) (3,13) (4,9) (3,5) (3,0) (13,14) (8,14) (6,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "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 34, and the edges are: (21,10) (13,20) (31,15) (18,33) (29,22) (27,1) (31,2) (10,26) (19,4) (11,23) (18,21) (20,28) (13,6) (11,3) (27,9) (8,25) (11,34) (0,32) (22,16) (12,18) (5,11) (22,17) (25,18) (9,8) (21,24) (31,21) (30,5) (7,20) (1,14) (23,20) (0,29) (28,21) (4,25) (1,32)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "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 28, and the edges are: (3,0) (0,1) (23,27) (9,23) (22,21) (2,0) (3,28) (7,12) (0,14) (25,4) (24,18) (26,14) (2,17) (25,24) (8,26) (5,21) (20,3) (22,2) (13,5) (24,0) (12,6) (19,4) (18,10) (5,6) (20,23) (22,9) (15,6) (5,11) (21,16) (27,14) (1,22)\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 32, and the edges are: (11,1) (1,2) (2,12) (1,0) (5,0) (3,0) (30,24) (11,10) (18,25) (6,10) (23,29) (9,13) (5,23) (10,27) (32,25) (31,15) (19,7) (26,17) (32,19) (0,4) (32,20) (23,28) (20,29) (5,4) (20,11) (2,17) (8,16) (13,10) (27,24) (22,28) (15,14) (1,14) (2,0) (5,3) (27,16) (23,21)\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 24, and the edges are: (6,2) (20,9) (4,22) (13,10) (10,0) (10,6) (12,16) (22,16) (11,0) (0,2) (4,21) (3,22) (19,5) (0,1) (15,24) (14,5) (19,4) (13,14) (21,18) (10,24) (20,14) (17,0) (12,1) (8,5) (3,7) (23,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a 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 19, and the edges are: (10,0) (11,15) (2,17) (5,0) (0,1) (5,7) (2,18) (10,3) (11,17) (9,2) (0,4) (16,8) (14,13) (13,18) (8,7) (13,19) (4,1) (0,3) (0,2) (9,6) (12,5) (8,17) (0,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "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 15, and the edges are: (5,8) (3,7) (8,6) (4,13) (14,5) (0,1) (10,2) (15,3) (10,1) (2,9) (5,13) (0,3) (11,1) (0,5) (13,15) (0,2) (5,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "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 32, and the edges are: (15,31) (7,2) (30,3) (6,20) (31,0) (2,31) (18,12) (23,25) (27,12) (21,22) (0,8) (30,5) (11,4) (26,8) (23,0) (5,21) (14,15) (21,7) (18,29) (32,20) (1,16) (13,9) (4,13) (7,10) (10,28) (32,1) (28,1) (2,17) (3,24) (9,19) (19,6) (12,28)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "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 24, and the edges are: (3,12) (0,8) (23,17) (21,12) (16,22) (20,9) (3,13) (1,24) (18,24) (15,16) (7,23) (14,0) (2,22) (24,10) (5,17) (13,14) (10,6) (16,3) (4,0) (23,9) (11,2) (19,20) (0,18) (23,24)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no 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 9, and the edges are: (7,0) (7,6) (7,2) (3,5) (8,5) (4,8) (8,6) (0,1) (8,1) (0,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "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 14, and the edges are: (0,4) (14,8) (13,3) (5,12) (0,1) (5,1) (0,3) (13,11) (6,5) (8,10) (11,4) (0,7) (9,2) (9,0) (10,13) (0,6) (7,4) (2,0)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a 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 26, and the edges are: (14,26) (3,12) (20,9) (10,8) (5,0) (14,13) (15,2) (10,23) (16,3) (23,12) (22,26) (26,7) (11,0) (1,25) (24,4) (22,2) (0,24) (23,21) (26,9) (23,18) (24,16) (1,0) (16,17) (3,26) (17,6) (19,20) (25,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "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 19, and the edges are: (10,11) (15,8) (2,12) (3,0) (9,10) (2,4) (7,10) (7,6) (0,15) (11,4) (10,14) (0,2) (13,17) (8,1) (7,19) (2,17) (5,11) (11,3) (15,7) (18,3) (0,1) (0,4) (16,17)\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 13, and the edges are: (3,4) (0,9) (13,6) (0,6) (6,5) (10,3) (1,5) (11,4) (0,2) (3,7) (4,8) (7,2) (0,1) (4,12) (0,4) (3,0) (13,12)\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 30, and the edges are: (14,9) (11,8) (5,7) (26,21) (12,5) (25,12) (8,4) (15,1) (29,23) (20,0) (26,2) (8,19) (2,6) (27,29) (7,15) (17,22) (2,23) (20,29) (26,15) (13,30) (18,30) (28,7) (26,24) (17,10) (26,11) (8,10) (20,18) (22,3) (9,6) (2,16) (0,1)\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 10, and the edges are: (8,2) (8,4) (8,7) (0,8) (8,3) (2,5) (3,6) (9,4) (6,10) (1,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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 30, and the edges are: (2,8) (9,25) (0,26) (16,22) (13,4) (6,16) (11,4) (19,7) (11,16) (25,0) (28,29) (5,16) (16,21) (12,8) (29,26) (15,26) (26,14) (4,24) (2,0) (8,20) (6,2) (6,19) (24,17) (3,10) (1,23) (1,19) (0,10) (0,1) (14,24) (11,30) (22,27) (18,6)\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 31, and the edges are: (15,12) (24,11) (0,13) (4,8) (26,28) (0,29) (14,3) (22,5) (3,10) (30,13) (24,20) (7,16) (13,31) (8,0) (23,7) (29,1) (15,6) (8,28) (27,8) (2,16) (17,11) (18,30) (19,15) (26,23) (25,17) (13,22) (21,6) (4,10) (24,10) (0,15) (9,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no 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 28, and the edges are: (19,23) (2,15) (11,1) (9,24) (28,0) (6,13) (0,7) (18,8) (9,19) (0,14) (7,20) (10,26) (15,13) (25,9) (21,16) (22,17) (21,10) (27,13) (4,21) (20,22) (9,5) (3,15) (26,27) (8,7) (14,12) (0,9) (4,23) (7,11)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no 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 11, and the edges are: (7,2) (7,6) (4,11) (11,10) (1,2) (3,4) (1,0) (1,5) (7,8) (10,2) (9,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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 9, and the edges are: (0,2) (6,1) (6,5) (9,4) (0,4) (0,8) (2,8) (4,3) (7,2) (0,3) (0,1) (4,5) (4,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "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 25, and the edges are: (0,3) (22,3) (12,18) (14,8) (24,17) (0,4) (5,22) (24,9) (15,5) (13,16) (1,21) (10,6) (20,6) (11,13) (3,17) (0,1) (2,23) (2,0) (14,23) (25,16) (1,8) (14,7) (21,20) (12,23) (11,19) (14,4) (3,2) (25,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "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 33, and the edges are: (32,22) (5,32) (21,17) (33,7) (29,28) (12,14) (32,25) (6,30) (25,3) (10,2) (23,27) (0,1) (12,28) (20,31) (2,0) (29,4) (13,0) (13,29) (16,3) (3,10) (11,23) (24,16) (1,2) (15,1) (30,8) (32,20) (14,23) (18,22) (8,19) (9,17) (26,10) (21,3) (8,22) (8,14) (33,9)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "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 8, and the edges are: (4,0) (2,8) (6,7) (2,0) (0,7) (3,0) (8,4) (8,1) (5,2) (0,1) (3,8)\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 20, and the edges are: (20,13) (10,15) (16,7) (18,0) (12,17) (4,19) (16,19) (12,11) (11,1) (0,6) (18,3) (13,9) (10,14) (12,20) (5,16) (1,2) (0,5) (8,7) (15,9) (11,19)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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 14, and the edges are: (8,5) (9,1) (5,9) (13,11) (0,4) (13,12) (12,14) (1,2) (2,7) (0,1) (14,10) (10,3) (14,5) (6,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no 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 29, and the edges are: (14,15) (12,13) (24,19) (24,28) (27,26) (4,1) (9,24) (3,6) (16,24) (6,23) (28,25) (18,20) (19,13) (15,3) (24,0) (21,25) (22,29) (26,12) (4,18) (0,1) (22,0) (8,2) (20,12) (17,14) (15,0) (27,5) (15,11) (0,2) (3,8) (2,10) (7,25)\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 7, and the edges are: (2,6) (3,7) (6,5) (7,0) (7,5) (4,0) (1,7) (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 26, and the edges are: (23,0) (15,19) (8,11) (10,22) (0,3) (21,3) (9,1) (0,16) (19,11) (4,14) (5,22) (12,13) (18,25) (11,18) (17,24) (25,20) (19,17) (12,26) (2,0) (15,22) (14,3) (9,21) (1,2) (0,4) (14,19) (1,0) (24,6) (13,24) (7,4) (16,13)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a 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 19, and the edges are: (8,3) (0,13) (15,10) (3,4) (13,16) (19,6) (5,0) (11,18) (14,18) (13,6) (5,12) (1,4) (4,10) (9,10) (2,3) (1,0) (2,17) (8,7) (0,2) (18,15) (13,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "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 31, and the edges are: (28,23) (14,10) (22,8) (26,11) (26,30) (1,2) (10,24) (17,14) (21,20) (26,21) (7,5) (30,31) (27,19) (12,22) (25,9) (15,14) (25,27) (28,6) (22,3) (18,4) (26,28) (5,18) (29,12) (14,26) (19,17) (5,31) (13,1) (6,2) (4,0) (27,12) (22,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "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 10, and the edges are: (0,5) (0,10) (10,9) (3,1) (8,5) (0,4) (3,0) (2,7) (0,6) (0,8) (2,0) (0,7) (0,1) (3,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a 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 11, and the edges are: (4,1) (7,4) (9,8) (10,3) (6,3) (5,3) (5,2) (7,8) (4,0) (9,11) (3,1)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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 29, and the edges are: (26,12) (17,21) (23,26) (13,23) (24,0) (6,9) (2,13) (3,29) (7,12) (24,5) (22,3) (8,27) (10,25) (20,27) (16,1) (19,17) (5,9) (25,16) (28,16) (8,21) (11,14) (10,20) (22,18) (0,7) (22,15) (9,11) (13,8) (25,4) (27,29)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "hard", "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 12, and the edges are: (4,0) (4,11) (2,1) (8,9) (8,7) (1,0) (0,3) (8,11) (5,6) (6,3) (2,0) (6,2) (10,1) (12,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "doc_id": "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 9, and the edges are: (0,2) (9,8) (3,0) (4,6) (7,4) (6,2) (0,5) (4,0) (0,1) (1,4) (8,4) (3,7) (5,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "easy", "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: (2,0) (0,3) (11,17) (4,12) (0,7) (1,4) (8,9) (8,13) (15,6) (0,1) (6,14) (13,1) (3,10) (6,2) (5,11) (0,16) (12,17) (9,3) (15,12) (7,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a 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 20, and the edges are: (2,17) (14,12) (19,12) (7,8) (10,7) (12,3) (6,7) (4,20) (20,11) (16,9) (13,8) (10,11) (14,2) (8,15) (5,16) (18,9) (19,1) (3,0) (3,8) (9,14)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no 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 24, and the edges are: (2,19) (7,10) (11,15) (19,18) (4,20) (24,0) (21,17) (12,7) (23,22) (11,5) (20,0) (13,17) (19,4) (22,10) (23,3) (9,11) (19,14) (22,8) (22,16) (9,23) (1,2) (6,5) (12,4) (22,21)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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 14, and the edges are: (3,11) (1,8) (0,10) (2,0) (4,0) (10,13) (12,9) (1,7) (2,6) (2,1) (14,11) (12,6) (5,7) (3,8)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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 21, and the edges are: (17,12) (20,7) (8,20) (0,2) (6,5) (1,16) (14,8) (0,4) (1,6) (18,3) (11,12) (18,2) (1,0) (4,6) (10,6) (15,21) (9,11) (15,0) (13,19) (19,14) (9,13) (18,9) (3,0) (14,6)\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 20, and the edges are: (15,17) (12,1) (12,4) (4,5) (10,14) (13,20) (6,9) (1,7) (13,0) (18,2) (0,19) (8,7) (16,8) (9,18) (4,11) (20,7) (10,1) (14,15) (5,2) (9,3)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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 30, and the edges are: (0,17) (30,29) (11,10) (23,17) (16,14) (12,18) (3,0) (25,28) (12,19) (12,16) (15,23) (21,0) (24,3) (11,4) (30,8) (30,27) (18,9) (7,14) (6,17) (10,8) (8,26) (2,13) (29,0) (13,20) (13,21) (25,1) (15,25) (19,1) (2,5) (22,30)\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 18, and the edges are: (17,18) (18,11) (2,17) (8,14) (9,14) (3,5) (10,16) (13,16) (4,2) (14,3) (17,1) (9,4) (14,0) (14,7) (16,15) (6,5) (15,5) (12,6)\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 34, and the edges are: (26,19) (28,16) (9,0) (34,22) (28,6) (25,12) (12,32) (0,1) (2,8) (29,16) (34,20) (0,2) (23,5) (5,30) (12,34) (6,18) (21,5) (10,0) (33,18) (0,3) (5,3) (23,26) (1,17) (27,31) (15,31) (2,6) (21,27) (13,20) (14,1) (2,12) (16,26) (4,31) (12,17) (11,23) (6,24) (9,30) (16,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a 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 24, and the edges are: (10,6) (0,4) (5,17) (9,23) (3,12) (13,14) (23,17) (3,16) (2,22) (24,18) (8,0) (20,9) (0,18) (21,12) (20,19) (24,23) (23,7) (15,16) (14,0) (11,2) (24,10) (22,16) (24,1) (13,3)\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 16, and the edges are: (9,0) (11,7) (4,12) (4,3) (10,8) (14,13) (0,2) (7,16) (1,13) (15,16) (3,5) (1,0) (8,7) (3,2) (6,2) (6,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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 24, and the edges are: (7,4) (24,9) (15,7) (17,11) (20,3) (17,19) (16,12) (9,14) (14,15) (13,5) (16,22) (20,5) (5,1) (6,8) (10,19) (16,18) (15,16) (9,2) (8,20) (21,20) (18,0) (10,21) (23,21) (20,2)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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 13, and the edges are: (5,12) (1,9) (11,6) (8,10) (13,0) (11,10) (0,8) (13,7) (3,11) (4,5) (11,9) (4,2) (13,12)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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 34, and the edges are: (3,4) (25,3) (7,27) (20,23) (31,29) (24,4) (5,9) (19,27) (22,25) (9,28) (32,10) (7,24) (6,9) (32,1) (23,13) (17,32) (29,15) (29,12) (23,11) (8,24) (2,0) (3,33) (30,8) (6,26) (10,6) (24,11) (3,34) (11,17) (21,27) (18,2) (31,32) (14,6) (18,1) (31,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no 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 16, and the edges are: (0,2) (7,12) (3,4) (9,14) (13,14) (7,14) (6,8) (0,3) (13,3) (11,10) (7,11) (15,12) (1,6) (7,6) (10,5) (1,0) (2,16)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "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 31, and the edges are: (21,25) (28,23) (9,2) (16,7) (15,11) (13,6) (12,6) (3,23) (11,26) (6,4) (24,22) (12,1) (21,26) (9,31) (14,25) (23,11) (27,11) (3,13) (27,22) (5,19) (18,9) (12,16) (30,17) (18,29) (19,24) (30,29) (1,0) (15,0) (20,0) (12,9) (27,8) (2,10)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "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 19, and the edges are: (18,9) (14,19) (3,10) (14,6) (3,2) (18,14) (11,8) (7,15) (10,7) (11,12) (6,0) (19,16) (19,1) (5,7) (13,17) (17,18) (4,6) (7,18) (12,17)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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 13, and the edges are: (1,12) (8,7) (5,6) (13,3) (10,3) (2,4) (11,3) (12,0) (4,1) (3,5) (8,9) (7,4) (9,13)\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 23, and the edges are: (14,17) (6,12) (22,8) (8,0) (9,15) (20,21) (5,15) (19,7) (19,18) (16,0) (17,4) (6,5) (1,8) (21,16) (4,7) (9,3) (15,0) (2,10) (10,6) (3,13) (23,6) (11,7) (17,20)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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 18, and the edges are: (0,3) (1,7) (2,17) (9,18) (5,2) (4,11) (9,6) (0,1) (9,3) (18,0) (15,14) (12,1) (0,2) (8,7) (5,4) (10,14) (13,8) (4,12) (16,15) (10,1) (0,7)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a 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 23, and the edges are: (12,1) (23,13) (2,0) (5,19) (14,15) (8,7) (4,21) (4,12) (5,22) (4,0) (3,9) (10,14) (0,13) (15,17) (7,20) (9,6) (23,5) (20,0) (10,1) (2,18) (1,7) (18,9) (21,2) (1,0) (3,0) (16,8) (11,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "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: (0,1) (7,14) (9,6) (14,2) (3,5) (12,11) (14,9) (2,0) (6,10) (13,8) (14,4) (5,1) (2,3) (0,4) (4,8) (0,3) (6,0) (4,11)\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 31, and the edges are: (29,22) (10,21) (31,2) (17,22) (25,18) (13,6) (18,21) (11,3) (8,9) (28,21) (0,5) (1,27) (19,4) (0,1) (27,9) (29,1) (23,21) (25,4) (12,18) (11,21) (30,18) (20,28) (5,11) (13,20) (0,26) (31,20) (16,22) (20,7) (1,14) (31,15) (8,25) (10,24)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "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 22, and the edges are: (17,2) (19,13) (2,0) (11,18) (7,21) (2,10) (16,6) (6,1) (16,18) (4,0) (17,22) (20,8) (1,15) (1,0) (3,0) (7,2) (5,4) (14,3) (20,13) (2,1) (12,17) (9,1) (13,2) (0,10) (11,3) (12,4)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "medium", "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 23, and the edges are: (12,19) (15,19) (2,4) (5,14) (23,7) (22,18) (11,10) (8,14) (3,23) (22,15) (5,13) (22,9) (3,6) (11,2) (21,15) (5,9) (7,17) (11,0) (13,23) (20,4) (16,7) (4,1) (0,6)\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 18, and the edges are: (6,12) (7,3) (17,15) (4,9) (14,15) (1,2) (16,0) (18,12) (6,13) (4,7) (7,16) (0,14) (4,2) (11,1) (14,12) (6,10) (12,8) (11,5)\nQ: Is there a cycle in this graph?\nA:", "answer": "No, there is no cycle in this graph.", "difficulty": "medium", "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 28, and the edges are: (12,27) (5,15) (21,19) (9,23) (8,1) (18,7) (20,16) (17,27) (7,20) (27,22) (4,21) (11,25) (2,17) (10,21) (28,4) (1,0) (14,28) (3,9) (23,20) (5,25) (0,13) (7,24) (4,13) (0,9) (6,27) (26,2) (4,5) (21,8) (6,23)\nQ: Is there a cycle in this graph?\nA:", "answer": "Yes, there is a cycle in this graph.", "difficulty": "hard", "doc_id": "190"}