{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 31 nodes numbered from 0 to 30:\nnode 0 should be visited before node 27\nnode 0 should be visited before node 30\nnode 0 should be visited before node 23\nnode 0 should be visited before node 3\nnode 0 should be visited before node 1\nnode 0 should be visited before node 2\nnode 0 should be visited before node 29\nnode 0 should be visited before node 21\nnode 0 should be visited before node 4\nnode 0 should be visited before node 22\nnode 0 should be visited before node 12\nnode 0 should be visited before node 24\nnode 0 should be visited before node 13\nnode 0 should be visited before node 6\nnode 0 should be visited before node 16\nnode 1 should be visited before node 15\nnode 1 should be visited before node 2\nnode 1 should be visited before node 29\nnode 1 should be visited before node 21\nnode 1 should be visited before node 22\nnode 1 should be visited before node 17\nnode 1 should be visited before node 8\nnode 1 should be visited before node 14\nnode 1 should be visited before node 24\nnode 1 should be visited before node 25\nnode 1 should be visited before node 16\nnode 2 should be visited before node 29\nnode 2 should be visited before node 4\nnode 2 should be visited before node 28\nnode 2 should be visited before node 17\nnode 2 should be visited before node 12\nnode 2 should be visited before node 16\nnode 3 should be visited before node 1\nnode 3 should be visited before node 15\nnode 3 should be visited before node 21\nnode 3 should be visited before node 28\nnode 3 should be visited before node 12\nnode 3 should be visited before node 8\nnode 3 should be visited before node 24\nnode 3 should be visited before node 13\nnode 3 should be visited before node 6\nnode 3 should be visited before node 16\nnode 4 should be visited before node 22\nnode 4 should be visited before node 28\nnode 4 should be visited before node 17\nnode 4 should be visited before node 8\nnode 4 should be visited before node 13\nnode 4 should be visited before node 6\nnode 5 should be visited before node 11\nnode 5 should be visited before node 26\nnode 5 should be visited before node 9\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nnode 5 should be visited before node 29\nnode 5 should be visited before node 22\nnode 5 should be visited before node 28\nnode 5 should be visited before node 17\nnode 5 should be visited before node 14\nnode 5 should be visited before node 24\nnode 5 should be visited before node 25\nnode 5 should be visited before node 6\nnode 6 should be visited before node 16\nnode 7 should be visited before node 23\nnode 7 should be visited before node 9\nnode 7 should be visited before node 3\nnode 7 should be visited before node 1\nnode 7 should be visited before node 15\nnode 7 should be visited before node 2\nnode 7 should be visited before node 28\nnode 7 should be visited before node 17\nnode 7 should be visited before node 12\nnode 7 should be visited before node 24\nnode 7 should be visited before node 25\nnode 8 should be visited before node 14\nnode 8 should be visited before node 24\nnode 9 should be visited before node 15\nnode 9 should be visited before node 2\nnode 9 should be visited before node 29\nnode 9 should be visited before node 8\nnode 10 should be visited before node 9\nnode 10 should be visited before node 3\nnode 10 should be visited before node 29\nnode 10 should be visited before node 17\nnode 10 should be visited before node 12\nnode 10 should be visited before node 8\nnode 10 should be visited before node 14\nnode 10 should be visited before node 25\nnode 11 should be visited before node 26\nnode 11 should be visited before node 3\nnode 11 should be visited before node 15\nnode 11 should be visited before node 29\nnode 11 should be visited before node 21\nnode 11 should be visited before node 4\nnode 11 should be visited before node 22\nnode 11 should be visited before node 28\nnode 11 should be visited before node 12\nnode 11 should be visited before node 8\nnode 11 should be visited before node 13\nnode 11 should be visited before node 25\nnode 12 should be visited before node 14\nnode 12 should be visited before node 24\nnode 13 should be visited before node 25\nnode 13 should be visited before node 16\nnode 15 should be visited before node 2\nnode 15 should be visited before node 29\nnode 15 should be visited before node 4\nnode 15 should be visited before node 22\nnode 15 should be visited before node 28\nnode 15 should be visited before node 17\nnode 15 should be visited before node 8\nnode 15 should be visited before node 14\nnode 15 should be visited before node 13\nnode 15 should be visited before node 25\nnode 15 should be visited before node 6\nnode 17 should be visited before node 13\nnode 17 should be visited before node 6\nnode 17 should be visited before node 16\nnode 18 should be visited before node 7\nnode 18 should be visited before node 23\nnode 18 should be visited before node 26\nnode 18 should be visited before node 1\nnode 18 should be visited before node 29\nnode 18 should be visited before node 12\nnode 18 should be visited before node 13\nnode 18 should be visited before node 25\nnode 18 should be visited before node 16\nnode 19 should be visited before node 5\nnode 19 should be visited before node 11\nnode 19 should be visited before node 23\nnode 19 should be visited before node 2\nnode 19 should be visited before node 29\nnode 19 should be visited before node 21\nnode 19 should be visited before node 4\nnode 19 should be visited before node 17\nnode 19 should be visited before node 12\nnode 19 should be visited before node 8\nnode 19 should be visited before node 14\nnode 19 should be visited before node 25\nnode 19 should be visited before node 6\nnode 20 should be visited before node 10\nnode 20 should be visited before node 27\nnode 20 should be visited before node 18\nnode 20 should be visited before node 11\nnode 20 should be visited before node 7\nnode 20 should be visited before node 23\nnode 20 should be visited before node 26\nnode 20 should be visited before node 9\nnode 20 should be visited before node 3\nnode 20 should be visited before node 21\nnode 20 should be visited before node 22\nnode 20 should be visited before node 17\nnode 20 should be visited before node 12\nnode 20 should be visited before node 14\nnode 20 should be visited before node 6\nnode 20 should be visited before node 16\nnode 21 should be visited before node 4\nnode 21 should be visited before node 24\nnode 21 should be visited before node 16\nnode 22 should be visited before node 8\nnode 22 should be visited before node 16\nnode 23 should be visited before node 3\nnode 23 should be visited before node 2\nnode 23 should be visited before node 29\nnode 23 should be visited before node 17\nnode 23 should be visited before node 12\nnode 23 should be visited before node 25\nnode 23 should be visited before node 6\nnode 24 should be visited before node 16\nnode 25 should be visited before node 16\nnode 26 should be visited before node 9\nnode 26 should be visited before node 29\nnode 26 should be visited before node 21\nnode 26 should be visited before node 4\nnode 26 should be visited before node 28\nnode 26 should be visited before node 17\nnode 26 should be visited before node 12\nnode 26 should be visited before node 14\nnode 26 should be visited before node 13\nnode 26 should be visited before node 6\nnode 27 should be visited before node 5\nnode 27 should be visited before node 7\nnode 27 should be visited before node 23\nnode 27 should be visited before node 26\nnode 27 should be visited before node 1\nnode 27 should be visited before node 29\nnode 27 should be visited before node 28\nnode 27 should be visited before node 17\nnode 27 should be visited before node 8\nnode 27 should be visited before node 14\nnode 27 should be visited before node 25\nnode 27 should be visited before node 6\nnode 27 should be visited before node 16\nnode 28 should be visited before node 17\nnode 28 should be visited before node 8\nnode 28 should be visited before node 14\nnode 28 should be visited before node 13\nnode 28 should be visited before node 25\nnode 28 should be visited before node 16\nnode 29 should be visited before node 4\nnode 29 should be visited before node 22\nnode 29 should be visited before node 14\nnode 29 should be visited before node 24\nnode 29 should be visited before node 13\nnode 30 should be visited before node 11\nnode 30 should be visited before node 23\nnode 30 should be visited before node 9\nnode 30 should be visited before node 15\nnode 30 should be visited before node 29\nnode 30 should be visited before node 21\nnode 30 should be visited before node 4\nnode 30 should be visited before node 22\nnode 30 should be visited before node 12\nnode 30 should be visited before node 14\nnode 30 should be visited before node 16\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 0,19,20,30,10,27,18,5,7,11,23,26,3,9,1,15,21,2,29,12,4,22,28,17,8,13,6,14,24,25,16.", "difficulty": "hard", "doc_id": "0"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 10 nodes numbered from 0 to 9:\nnode 0 should be visited before node 7\nnode 0 should be visited before node 9\nnode 2 should be visited before node 9\nnode 3 should be visited before node 4\nnode 3 should be visited before node 0\nnode 3 should be visited before node 1\nnode 3 should be visited before node 5\nnode 3 should be visited before node 9\nnode 4 should be visited before node 6\nnode 4 should be visited before node 0\nnode 4 should be visited before node 7\nnode 4 should be visited before node 8\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 2\nnode 6 should be visited before node 0\nnode 6 should be visited before node 7\nnode 6 should be visited before node 8\nnode 6 should be visited before node 2\nnode 6 should be visited before node 9\nnode 7 should be visited before node 8\nnode 7 should be visited before node 9\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 3,4,5,6,1,0,2,7,8,9.", "difficulty": "easy", "doc_id": "1"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 21 nodes numbered from 0 to 20:\nnode 0 should be visited before node 19\nnode 0 should be visited before node 13\nnode 0 should be visited before node 4\nnode 0 should be visited before node 12\nnode 0 should be visited before node 20\nnode 1 should be visited before node 18\nnode 2 should be visited before node 16\nnode 2 should be visited before node 13\nnode 2 should be visited before node 12\nnode 2 should be visited before node 10\nnode 2 should be visited before node 18\nnode 3 should be visited before node 9\nnode 3 should be visited before node 16\nnode 3 should be visited before node 4\nnode 3 should be visited before node 12\nnode 3 should be visited before node 20\nnode 3 should be visited before node 10\nnode 3 should be visited before node 1\nnode 3 should be visited before node 18\nnode 4 should be visited before node 12\nnode 4 should be visited before node 10\nnode 4 should be visited before node 1\nnode 5 should be visited before node 7\nnode 5 should be visited before node 11\nnode 5 should be visited before node 9\nnode 5 should be visited before node 19\nnode 5 should be visited before node 16\nnode 5 should be visited before node 13\nnode 5 should be visited before node 4\nnode 5 should be visited before node 20\nnode 5 should be visited before node 10\nnode 6 should be visited before node 14\nnode 6 should be visited before node 5\nnode 6 should be visited before node 7\nnode 6 should be visited before node 15\nnode 6 should be visited before node 11\nnode 6 should be visited before node 8\nnode 6 should be visited before node 0\nnode 6 should be visited before node 2\nnode 6 should be visited before node 3\nnode 6 should be visited before node 9\nnode 6 should be visited before node 16\nnode 6 should be visited before node 13\nnode 6 should be visited before node 12\nnode 6 should be visited before node 1\nnode 7 should be visited before node 11\nnode 7 should be visited before node 8\nnode 7 should be visited before node 0\nnode 7 should be visited before node 2\nnode 7 should be visited before node 3\nnode 7 should be visited before node 9\nnode 7 should be visited before node 19\nnode 7 should be visited before node 16\nnode 7 should be visited before node 13\nnode 7 should be visited before node 12\nnode 7 should be visited before node 10\nnode 7 should be visited before node 18\nnode 8 should be visited before node 0\nnode 8 should be visited before node 2\nnode 8 should be visited before node 3\nnode 8 should be visited before node 9\nnode 8 should be visited before node 16\nnode 8 should be visited before node 13\nnode 8 should be visited before node 4\nnode 8 should be visited before node 1\nnode 9 should be visited before node 19\nnode 9 should be visited before node 16\nnode 9 should be visited before node 12\nnode 9 should be visited before node 10\nnode 9 should be visited before node 1\nnode 10 should be visited before node 1\nnode 10 should be visited before node 18\nnode 11 should be visited before node 0\nnode 11 should be visited before node 2\nnode 11 should be visited before node 3\nnode 11 should be visited before node 9\nnode 11 should be visited before node 19\nnode 11 should be visited before node 16\nnode 11 should be visited before node 13\nnode 11 should be visited before node 4\nnode 11 should be visited before node 12\nnode 11 should be visited before node 20\nnode 11 should be visited before node 10\nnode 11 should be visited before node 1\nnode 11 should be visited before node 18\nnode 12 should be visited before node 20\nnode 12 should be visited before node 10\nnode 12 should be visited before node 18\nnode 13 should be visited before node 12\nnode 13 should be visited before node 10\nnode 13 should be visited before node 1\nnode 13 should be visited before node 18\nnode 14 should be visited before node 5\nnode 14 should be visited before node 15\nnode 14 should be visited before node 11\nnode 14 should be visited before node 0\nnode 14 should be visited before node 3\nnode 14 should be visited before node 9\nnode 14 should be visited before node 19\nnode 14 should be visited before node 12\nnode 14 should be visited before node 1\nnode 15 should be visited before node 11\nnode 15 should be visited before node 0\nnode 15 should be visited before node 9\nnode 15 should be visited before node 19\nnode 15 should be visited before node 16\nnode 15 should be visited before node 13\nnode 15 should be visited before node 4\nnode 15 should be visited before node 12\nnode 15 should be visited before node 20\nnode 15 should be visited before node 10\nnode 15 should be visited before node 1\nnode 15 should be visited before node 18\nnode 16 should be visited before node 12\nnode 16 should be visited before node 20\nnode 16 should be visited before node 10\nnode 16 should be visited before node 1\nnode 17 should be visited before node 6\nnode 17 should be visited before node 14\nnode 17 should be visited before node 5\nnode 17 should be visited before node 7\nnode 17 should be visited before node 15\nnode 17 should be visited before node 11\nnode 17 should be visited before node 8\nnode 17 should be visited before node 0\nnode 17 should be visited before node 2\nnode 17 should be visited before node 3\nnode 17 should be visited before node 19\nnode 17 should be visited before node 16\nnode 17 should be visited before node 13\nnode 17 should be visited before node 4\nnode 17 should be visited before node 12\nnode 17 should be visited before node 20\nnode 17 should be visited before node 1\nnode 17 should be visited before node 18\nnode 19 should be visited before node 16\nnode 19 should be visited before node 20\nnode 19 should be visited before node 10\nnode 19 should be visited before node 1\nnode 19 should be visited before node 18\nnode 20 should be visited before node 10\nnode 20 should be visited before node 1\nnode 20 should be visited before node 18\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 17,6,14,5,15,7,11,8,0,2,3,13,9,4,19,16,12,20,10,1,18.", "difficulty": "medium", "doc_id": "2"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 21 nodes numbered from 0 to 20:\nnode 0 should be visited before node 15\nnode 0 should be visited before node 1\nnode 0 should be visited before node 19\nnode 0 should be visited before node 18\nnode 0 should be visited before node 9\nnode 0 should be visited before node 12\nnode 1 should be visited before node 7\nnode 1 should be visited before node 17\nnode 1 should be visited before node 18\nnode 2 should be visited before node 6\nnode 2 should be visited before node 3\nnode 2 should be visited before node 10\nnode 2 should be visited before node 15\nnode 2 should be visited before node 13\nnode 2 should be visited before node 14\nnode 2 should be visited before node 7\nnode 2 should be visited before node 18\nnode 2 should be visited before node 4\nnode 2 should be visited before node 9\nnode 2 should be visited before node 16\nnode 3 should be visited before node 0\nnode 3 should be visited before node 15\nnode 3 should be visited before node 14\nnode 3 should be visited before node 7\nnode 3 should be visited before node 19\nnode 3 should be visited before node 9\nnode 3 should be visited before node 12\nnode 4 should be visited before node 9\nnode 4 should be visited before node 12\nnode 5 should be visited before node 11\nnode 5 should be visited before node 3\nnode 5 should be visited before node 8\nnode 5 should be visited before node 0\nnode 5 should be visited before node 13\nnode 5 should be visited before node 14\nnode 5 should be visited before node 1\nnode 5 should be visited before node 7\nnode 5 should be visited before node 17\nnode 5 should be visited before node 18\nnode 5 should be visited before node 20\nnode 5 should be visited before node 4\nnode 5 should be visited before node 9\nnode 5 should be visited before node 12\nnode 6 should be visited before node 11\nnode 6 should be visited before node 8\nnode 6 should be visited before node 0\nnode 6 should be visited before node 1\nnode 6 should be visited before node 7\nnode 6 should be visited before node 19\nnode 6 should be visited before node 18\nnode 6 should be visited before node 20\nnode 7 should be visited before node 20\nnode 7 should be visited before node 12\nnode 8 should be visited before node 15\nnode 8 should be visited before node 13\nnode 8 should be visited before node 1\nnode 8 should be visited before node 7\nnode 8 should be visited before node 19\nnode 8 should be visited before node 18\nnode 8 should be visited before node 20\nnode 8 should be visited before node 16\nnode 8 should be visited before node 12\nnode 9 should be visited before node 16\nnode 9 should be visited before node 12\nnode 10 should be visited before node 0\nnode 10 should be visited before node 15\nnode 10 should be visited before node 1\nnode 10 should be visited before node 19\nnode 10 should be visited before node 20\nnode 10 should be visited before node 4\nnode 10 should be visited before node 16\nnode 10 should be visited before node 12\nnode 11 should be visited before node 8\nnode 11 should be visited before node 0\nnode 11 should be visited before node 14\nnode 11 should be visited before node 1\nnode 11 should be visited before node 7\nnode 11 should be visited before node 17\nnode 11 should be visited before node 20\nnode 11 should be visited before node 9\nnode 11 should be visited before node 12\nnode 13 should be visited before node 18\nnode 14 should be visited before node 1\nnode 14 should be visited before node 18\nnode 14 should be visited before node 20\nnode 14 should be visited before node 4\nnode 14 should be visited before node 9\nnode 14 should be visited before node 16\nnode 14 should be visited before node 12\nnode 15 should be visited before node 13\nnode 15 should be visited before node 14\nnode 15 should be visited before node 18\nnode 15 should be visited before node 20\nnode 15 should be visited before node 4\nnode 17 should be visited before node 16\nnode 18 should be visited before node 4\nnode 18 should be visited before node 16\nnode 18 should be visited before node 12\nnode 19 should be visited before node 20\nnode 19 should be visited before node 4\nnode 19 should be visited before node 16\nnode 19 should be visited before node 12\nnode 20 should be visited before node 4\nnode 20 should be visited before node 16\nnode 20 should be visited before node 12\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 2,5,6,10,3,11,8,0,15,19,13,14,1,7,17,18,20,4,9,16,12.", "difficulty": "medium", "doc_id": "3"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 34 nodes numbered from 0 to 33:\nnode 0 should be visited before node 24\nnode 0 should be visited before node 15\nnode 1 should be visited before node 27\nnode 1 should be visited before node 2\nnode 1 should be visited before node 18\nnode 1 should be visited before node 10\nnode 1 should be visited before node 7\nnode 1 should be visited before node 21\nnode 1 should be visited before node 31\nnode 1 should be visited before node 3\nnode 1 should be visited before node 24\nnode 1 should be visited before node 5\nnode 1 should be visited before node 29\nnode 1 should be visited before node 28\nnode 1 should be visited before node 15\nnode 2 should be visited before node 25\nnode 2 should be visited before node 18\nnode 2 should be visited before node 4\nnode 2 should be visited before node 21\nnode 2 should be visited before node 17\nnode 2 should be visited before node 31\nnode 2 should be visited before node 8\nnode 2 should be visited before node 20\nnode 2 should be visited before node 13\nnode 2 should be visited before node 6\nnode 2 should be visited before node 28\nnode 2 should be visited before node 15\nnode 3 should be visited before node 6\nnode 3 should be visited before node 22\nnode 4 should be visited before node 10\nnode 4 should be visited before node 7\nnode 4 should be visited before node 21\nnode 4 should be visited before node 17\nnode 4 should be visited before node 8\nnode 4 should be visited before node 20\nnode 4 should be visited before node 6\nnode 4 should be visited before node 5\nnode 4 should be visited before node 22\nnode 4 should be visited before node 15\nnode 5 should be visited before node 22\nnode 6 should be visited before node 5\nnode 6 should be visited before node 28\nnode 6 should be visited before node 22\nnode 7 should be visited before node 17\nnode 7 should be visited before node 31\nnode 7 should be visited before node 8\nnode 7 should be visited before node 20\nnode 7 should be visited before node 0\nnode 7 should be visited before node 24\nnode 7 should be visited before node 5\nnode 7 should be visited before node 28\nnode 7 should be visited before node 22\nnode 8 should be visited before node 13\nnode 8 should be visited before node 28\nnode 9 should be visited before node 26\nnode 9 should be visited before node 14\nnode 9 should be visited before node 32\nnode 9 should be visited before node 16\nnode 9 should be visited before node 33\nnode 9 should be visited before node 25\nnode 9 should be visited before node 18\nnode 9 should be visited before node 10\nnode 9 should be visited before node 7\nnode 9 should be visited before node 21\nnode 9 should be visited before node 17\nnode 9 should be visited before node 31\nnode 9 should be visited before node 20\nnode 9 should be visited before node 0\nnode 9 should be visited before node 23\nnode 9 should be visited before node 6\nnode 9 should be visited before node 29\nnode 9 should be visited before node 15\nnode 10 should be visited before node 7\nnode 10 should be visited before node 21\nnode 10 should be visited before node 17\nnode 10 should be visited before node 31\nnode 10 should be visited before node 8\nnode 10 should be visited before node 0\nnode 10 should be visited before node 3\nnode 10 should be visited before node 24\nnode 10 should be visited before node 29\nnode 11 should be visited before node 32\nnode 11 should be visited before node 1\nnode 11 should be visited before node 27\nnode 11 should be visited before node 4\nnode 11 should be visited before node 10\nnode 11 should be visited before node 7\nnode 11 should be visited before node 17\nnode 11 should be visited before node 20\nnode 11 should be visited before node 23\nnode 11 should be visited before node 3\nnode 11 should be visited before node 6\nnode 11 should be visited before node 29\nnode 11 should be visited before node 28\nnode 12 should be visited before node 9\nnode 12 should be visited before node 30\nnode 12 should be visited before node 19\nnode 12 should be visited before node 14\nnode 12 should be visited before node 1\nnode 12 should be visited before node 27\nnode 12 should be visited before node 4\nnode 12 should be visited before node 10\nnode 12 should be visited before node 7\nnode 12 should be visited before node 21\nnode 12 should be visited before node 17\nnode 12 should be visited before node 8\nnode 12 should be visited before node 20\nnode 12 should be visited before node 6\nnode 12 should be visited before node 29\nnode 12 should be visited before node 28\nnode 12 should be visited before node 15\nnode 13 should be visited before node 22\nnode 13 should be visited before node 15\nnode 14 should be visited before node 11\nnode 14 should be visited before node 32\nnode 14 should be visited before node 2\nnode 14 should be visited before node 25\nnode 14 should be visited before node 18\nnode 14 should be visited before node 21\nnode 14 should be visited before node 8\nnode 14 should be visited before node 20\nnode 14 should be visited before node 23\nnode 14 should be visited before node 24\nnode 14 should be visited before node 5\nnode 14 should be visited before node 22\nnode 14 should be visited before node 15\nnode 16 should be visited before node 1\nnode 16 should be visited before node 33\nnode 16 should be visited before node 25\nnode 16 should be visited before node 18\nnode 16 should be visited before node 10\nnode 16 should be visited before node 7\nnode 16 should be visited before node 31\nnode 16 should be visited before node 29\nnode 16 should be visited before node 15\nnode 17 should be visited before node 31\nnode 17 should be visited before node 8\nnode 17 should be visited before node 20\nnode 17 should be visited before node 24\nnode 17 should be visited before node 5\nnode 17 should be visited before node 28\nnode 17 should be visited before node 22\nnode 18 should be visited before node 4\nnode 18 should be visited before node 10\nnode 18 should be visited before node 17\nnode 18 should be visited before node 20\nnode 18 should be visited before node 13\nnode 18 should be visited before node 3\nnode 18 should be visited before node 6\nnode 18 should be visited before node 5\nnode 18 should be visited before node 29\nnode 18 should be visited before node 15\nnode 19 should be visited before node 14\nnode 19 should be visited before node 27\nnode 19 should be visited before node 2\nnode 19 should be visited before node 0\nnode 19 should be visited before node 23\nnode 19 should be visited before node 13\nnode 19 should be visited before node 6\nnode 19 should be visited before node 28\nnode 19 should be visited before node 22\nnode 20 should be visited before node 0\nnode 20 should be visited before node 23\nnode 20 should be visited before node 13\nnode 20 should be visited before node 3\nnode 20 should be visited before node 6\nnode 20 should be visited before node 5\nnode 20 should be visited before node 22\nnode 21 should be visited before node 31\nnode 21 should be visited before node 20\nnode 21 should be visited before node 3\nnode 21 should be visited before node 6\nnode 21 should be visited before node 24\nnode 21 should be visited before node 29\nnode 21 should be visited before node 28\nnode 21 should be visited before node 22\nnode 23 should be visited before node 13\nnode 23 should be visited before node 24\nnode 23 should be visited before node 5\nnode 23 should be visited before node 29\nnode 23 should be visited before node 15\nnode 24 should be visited before node 5\nnode 24 should be visited before node 29\nnode 24 should be visited before node 15\nnode 25 should be visited before node 18\nnode 25 should be visited before node 4\nnode 25 should be visited before node 10\nnode 25 should be visited before node 21\nnode 25 should be visited before node 17\nnode 25 should be visited before node 8\nnode 25 should be visited before node 20\nnode 25 should be visited before node 0\nnode 25 should be visited before node 23\nnode 25 should be visited before node 13\nnode 25 should be visited before node 3\nnode 25 should be visited before node 6\nnode 25 should be visited before node 29\nnode 25 should be visited before node 22\nnode 25 should be visited before node 15\nnode 26 should be visited before node 19\nnode 26 should be visited before node 11\nnode 26 should be visited before node 32\nnode 26 should be visited before node 27\nnode 26 should be visited before node 18\nnode 26 should be visited before node 10\nnode 26 should be visited before node 7\nnode 26 should be visited before node 21\nnode 26 should be visited before node 17\nnode 26 should be visited before node 31\nnode 26 should be visited before node 8\nnode 26 should be visited before node 20\nnode 26 should be visited before node 23\nnode 26 should be visited before node 3\nnode 26 should be visited before node 5\nnode 26 should be visited before node 29\nnode 26 should be visited before node 28\nnode 26 should be visited before node 22\nnode 26 should be visited before node 15\nnode 27 should be visited before node 2\nnode 27 should be visited before node 10\nnode 27 should be visited before node 8\nnode 27 should be visited before node 0\nnode 27 should be visited before node 13\nnode 27 should be visited before node 6\nnode 27 should be visited before node 24\nnode 27 should be visited before node 5\nnode 27 should be visited before node 29\nnode 27 should be visited before node 28\nnode 27 should be visited before node 22\nnode 28 should be visited before node 22\nnode 28 should be visited before node 15\nnode 29 should be visited before node 28\nnode 30 should be visited before node 32\nnode 30 should be visited before node 25\nnode 30 should be visited before node 18\nnode 30 should be visited before node 4\nnode 30 should be visited before node 7\nnode 30 should be visited before node 20\nnode 30 should be visited before node 0\nnode 30 should be visited before node 23\nnode 30 should be visited before node 3\nnode 30 should be visited before node 6\nnode 30 should be visited before node 24\nnode 30 should be visited before node 5\nnode 30 should be visited before node 28\nnode 30 should be visited before node 15\nnode 31 should be visited before node 8\nnode 31 should be visited before node 20\nnode 31 should be visited before node 0\nnode 31 should be visited before node 3\nnode 31 should be visited before node 5\nnode 31 should be visited before node 29\nnode 31 should be visited before node 28\nnode 32 should be visited before node 16\nnode 32 should be visited before node 33\nnode 32 should be visited before node 2\nnode 32 should be visited before node 10\nnode 32 should be visited before node 7\nnode 32 should be visited before node 31\nnode 32 should be visited before node 0\nnode 32 should be visited before node 13\nnode 32 should be visited before node 3\nnode 32 should be visited before node 6\nnode 32 should be visited before node 5\nnode 32 should be visited before node 28\nnode 32 should be visited before node 22\nnode 32 should be visited before node 15\nnode 33 should be visited before node 27\nnode 33 should be visited before node 2\nnode 33 should be visited before node 18\nnode 33 should be visited before node 4\nnode 33 should be visited before node 10\nnode 33 should be visited before node 7\nnode 33 should be visited before node 21\nnode 33 should be visited before node 17\nnode 33 should be visited before node 8\nnode 33 should be visited before node 20\nnode 33 should be visited before node 13\nnode 33 should be visited before node 5\nnode 33 should be visited before node 29\nnode 33 should be visited before node 28\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 12,9,30,26,19,14,11,32,16,1,33,27,2,25,18,4,10,7,21,17,31,8,20,0,23,3,13,24,6,29,5,28,22,15.", "difficulty": "hard", "doc_id": "4"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 10 nodes numbered from 0 to 9:\nnode 0 should be visited before node 9\nnode 2 should be visited before node 9\nnode 3 should be visited before node 2\nnode 3 should be visited before node 6\nnode 3 should be visited before node 1\nnode 4 should be visited before node 3\nnode 4 should be visited before node 6\nnode 4 should be visited before node 9\nnode 4 should be visited before node 1\nnode 5 should be visited before node 4\nnode 5 should be visited before node 3\nnode 5 should be visited before node 2\nnode 5 should be visited before node 6\nnode 5 should be visited before node 7\nnode 5 should be visited before node 1\nnode 6 should be visited before node 1\nnode 7 should be visited before node 9\nnode 8 should be visited before node 2\nnode 8 should be visited before node 9\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 0,5,8,4,7,3,2,6,9,1.", "difficulty": "easy", "doc_id": "5"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 15 nodes numbered from 0 to 14:\nnode 1 should be visited before node 5\nnode 1 should be visited before node 13\nnode 2 should be visited before node 11\nnode 3 should be visited before node 14\nnode 3 should be visited before node 5\nnode 3 should be visited before node 9\nnode 3 should be visited before node 12\nnode 3 should be visited before node 13\nnode 4 should be visited before node 3\nnode 4 should be visited before node 11\nnode 4 should be visited before node 1\nnode 5 should be visited before node 13\nnode 5 should be visited before node 0\nnode 6 should be visited before node 14\nnode 6 should be visited before node 9\nnode 7 should be visited before node 4\nnode 7 should be visited before node 1\nnode 7 should be visited before node 12\nnode 8 should be visited before node 13\nnode 8 should be visited before node 0\nnode 9 should be visited before node 8\nnode 10 should be visited before node 3\nnode 10 should be visited before node 6\nnode 10 should be visited before node 11\nnode 10 should be visited before node 1\nnode 10 should be visited before node 5\nnode 10 should be visited before node 0\nnode 11 should be visited before node 1\nnode 11 should be visited before node 14\nnode 11 should be visited before node 9\nnode 11 should be visited before node 8\nnode 11 should be visited before node 13\nnode 12 should be visited before node 13\nnode 12 should be visited before node 0\nnode 14 should be visited before node 8\nnode 14 should be visited before node 13\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 2,7,10,4,6,3,11,12,1,14,9,5,8,13,0.", "difficulty": "medium", "doc_id": "6"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 22 nodes numbered from 0 to 21:\nnode 0 should be visited before node 5\nnode 0 should be visited before node 11\nnode 0 should be visited before node 3\nnode 0 should be visited before node 16\nnode 0 should be visited before node 18\nnode 0 should be visited before node 10\nnode 0 should be visited before node 14\nnode 0 should be visited before node 2\nnode 0 should be visited before node 8\nnode 0 should be visited before node 21\nnode 0 should be visited before node 17\nnode 0 should be visited before node 7\nnode 1 should be visited before node 20\nnode 1 should be visited before node 12\nnode 1 should be visited before node 0\nnode 1 should be visited before node 4\nnode 1 should be visited before node 5\nnode 1 should be visited before node 11\nnode 1 should be visited before node 6\nnode 1 should be visited before node 18\nnode 1 should be visited before node 2\nnode 1 should be visited before node 8\nnode 1 should be visited before node 21\nnode 1 should be visited before node 7\nnode 2 should be visited before node 21\nnode 2 should be visited before node 13\nnode 2 should be visited before node 7\nnode 3 should be visited before node 16\nnode 3 should be visited before node 18\nnode 3 should be visited before node 10\nnode 3 should be visited before node 14\nnode 3 should be visited before node 2\nnode 3 should be visited before node 21\nnode 3 should be visited before node 17\nnode 3 should be visited before node 7\nnode 4 should be visited before node 5\nnode 4 should be visited before node 6\nnode 4 should be visited before node 3\nnode 4 should be visited before node 18\nnode 4 should be visited before node 14\nnode 4 should be visited before node 2\nnode 4 should be visited before node 7\nnode 5 should be visited before node 11\nnode 5 should be visited before node 6\nnode 5 should be visited before node 3\nnode 5 should be visited before node 16\nnode 5 should be visited before node 18\nnode 5 should be visited before node 14\nnode 5 should be visited before node 2\nnode 5 should be visited before node 21\nnode 5 should be visited before node 17\nnode 5 should be visited before node 13\nnode 6 should be visited before node 18\nnode 6 should be visited before node 10\nnode 6 should be visited before node 2\nnode 6 should be visited before node 8\nnode 6 should be visited before node 21\nnode 6 should be visited before node 13\nnode 6 should be visited before node 7\nnode 8 should be visited before node 21\nnode 8 should be visited before node 13\nnode 9 should be visited before node 15\nnode 9 should be visited before node 19\nnode 9 should be visited before node 1\nnode 9 should be visited before node 20\nnode 9 should be visited before node 12\nnode 9 should be visited before node 0\nnode 9 should be visited before node 4\nnode 9 should be visited before node 5\nnode 9 should be visited before node 11\nnode 9 should be visited before node 6\nnode 9 should be visited before node 16\nnode 9 should be visited before node 18\nnode 9 should be visited before node 10\nnode 9 should be visited before node 14\nnode 9 should be visited before node 2\nnode 9 should be visited before node 8\nnode 9 should be visited before node 17\nnode 9 should be visited before node 13\nnode 10 should be visited before node 2\nnode 10 should be visited before node 21\nnode 10 should be visited before node 17\nnode 10 should be visited before node 13\nnode 11 should be visited before node 6\nnode 11 should be visited before node 3\nnode 11 should be visited before node 18\nnode 11 should be visited before node 10\nnode 11 should be visited before node 14\nnode 11 should be visited before node 2\nnode 11 should be visited before node 21\nnode 11 should be visited before node 17\nnode 11 should be visited before node 7\nnode 12 should be visited before node 0\nnode 12 should be visited before node 5\nnode 12 should be visited before node 6\nnode 12 should be visited before node 3\nnode 12 should be visited before node 18\nnode 12 should be visited before node 10\nnode 12 should be visited before node 2\nnode 12 should be visited before node 21\nnode 12 should be visited before node 17\nnode 12 should be visited before node 7\nnode 13 should be visited before node 7\nnode 14 should be visited before node 2\nnode 14 should be visited before node 8\nnode 14 should be visited before node 13\nnode 14 should be visited before node 7\nnode 15 should be visited before node 19\nnode 15 should be visited before node 1\nnode 15 should be visited before node 20\nnode 15 should be visited before node 12\nnode 15 should be visited before node 0\nnode 15 should be visited before node 5\nnode 15 should be visited before node 11\nnode 15 should be visited before node 6\nnode 15 should be visited before node 3\nnode 15 should be visited before node 16\nnode 15 should be visited before node 10\nnode 15 should be visited before node 2\nnode 15 should be visited before node 21\nnode 15 should be visited before node 13\nnode 15 should be visited before node 7\nnode 16 should be visited before node 10\nnode 16 should be visited before node 14\nnode 16 should be visited before node 2\nnode 16 should be visited before node 8\nnode 16 should be visited before node 17\nnode 17 should be visited before node 13\nnode 17 should be visited before node 7\nnode 18 should be visited before node 10\nnode 18 should be visited before node 14\nnode 18 should be visited before node 2\nnode 18 should be visited before node 21\nnode 18 should be visited before node 7\nnode 19 should be visited before node 1\nnode 19 should be visited before node 20\nnode 19 should be visited before node 12\nnode 19 should be visited before node 0\nnode 19 should be visited before node 4\nnode 19 should be visited before node 6\nnode 19 should be visited before node 3\nnode 19 should be visited before node 16\nnode 19 should be visited before node 18\nnode 19 should be visited before node 14\nnode 19 should be visited before node 2\nnode 19 should be visited before node 21\nnode 19 should be visited before node 17\nnode 19 should be visited before node 13\nnode 20 should be visited before node 12\nnode 20 should be visited before node 0\nnode 20 should be visited before node 4\nnode 20 should be visited before node 5\nnode 20 should be visited before node 6\nnode 20 should be visited before node 3\nnode 20 should be visited before node 16\nnode 20 should be visited before node 18\nnode 20 should be visited before node 10\nnode 20 should be visited before node 2\nnode 20 should be visited before node 8\nnode 20 should be visited before node 17\nnode 20 should be visited before node 13\nnode 21 should be visited before node 7\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 9,15,19,1,20,12,4,0,5,11,6,3,16,18,10,14,17,2,8,21,13,7.", "difficulty": "medium", "doc_id": "7"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 13 nodes numbered from 0 to 12:\nnode 1 should be visited before node 8\nnode 1 should be visited before node 12\nnode 1 should be visited before node 5\nnode 2 should be visited before node 8\nnode 2 should be visited before node 3\nnode 2 should be visited before node 6\nnode 2 should be visited before node 12\nnode 2 should be visited before node 5\nnode 3 should be visited before node 7\nnode 4 should be visited before node 11\nnode 4 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 4 should be visited before node 7\nnode 4 should be visited before node 12\nnode 6 should be visited before node 10\nnode 8 should be visited before node 5\nnode 9 should be visited before node 12\nnode 11 should be visited before node 2\nnode 11 should be visited before node 3\nnode 11 should be visited before node 12\nnode 11 should be visited before node 5\nnode 11 should be visited before node 10\nnode 12 should be visited before node 5\nnode 12 should be visited before node 10\nnode 12 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 4,9,11,1,2,8,3,6,12,7,5,10,0.", "difficulty": "medium", "doc_id": "8"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 27 nodes numbered from 0 to 26:\nnode 0 should be visited before node 18\nnode 0 should be visited before node 21\nnode 0 should be visited before node 8\nnode 1 should be visited before node 7\nnode 1 should be visited before node 11\nnode 1 should be visited before node 18\nnode 2 should be visited before node 17\nnode 2 should be visited before node 25\nnode 2 should be visited before node 6\nnode 2 should be visited before node 23\nnode 2 should be visited before node 19\nnode 2 should be visited before node 8\nnode 3 should be visited before node 23\nnode 3 should be visited before node 7\nnode 3 should be visited before node 11\nnode 3 should be visited before node 18\nnode 3 should be visited before node 21\nnode 3 should be visited before node 12\nnode 4 should be visited before node 22\nnode 4 should be visited before node 16\nnode 4 should be visited before node 13\nnode 4 should be visited before node 5\nnode 4 should be visited before node 8\nnode 6 should be visited before node 0\nnode 6 should be visited before node 19\nnode 6 should be visited before node 5\nnode 6 should be visited before node 18\nnode 7 should be visited before node 19\nnode 9 should be visited before node 17\nnode 9 should be visited before node 0\nnode 9 should be visited before node 19\nnode 9 should be visited before node 21\nnode 9 should be visited before node 12\nnode 12 should be visited before node 8\nnode 13 should be visited before node 0\nnode 13 should be visited before node 7\nnode 13 should be visited before node 21\nnode 13 should be visited before node 12\nnode 13 should be visited before node 8\nnode 14 should be visited before node 2\nnode 14 should be visited before node 15\nnode 14 should be visited before node 24\nnode 14 should be visited before node 6\nnode 14 should be visited before node 10\nnode 14 should be visited before node 19\nnode 14 should be visited before node 18\nnode 14 should be visited before node 21\nnode 14 should be visited before node 8\nnode 15 should be visited before node 6\nnode 15 should be visited before node 26\nnode 15 should be visited before node 3\nnode 15 should be visited before node 11\nnode 15 should be visited before node 12\nnode 16 should be visited before node 15\nnode 16 should be visited before node 26\nnode 16 should be visited before node 1\nnode 16 should be visited before node 0\nnode 16 should be visited before node 21\nnode 16 should be visited before node 12\nnode 17 should be visited before node 3\nnode 17 should be visited before node 23\nnode 17 should be visited before node 1\nnode 17 should be visited before node 5\nnode 17 should be visited before node 8\nnode 18 should be visited before node 21\nnode 19 should be visited before node 5\nnode 19 should be visited before node 18\nnode 20 should be visited before node 22\nnode 20 should be visited before node 16\nnode 20 should be visited before node 15\nnode 20 should be visited before node 25\nnode 20 should be visited before node 26\nnode 20 should be visited before node 3\nnode 20 should be visited before node 23\nnode 20 should be visited before node 1\nnode 20 should be visited before node 0\nnode 20 should be visited before node 7\nnode 20 should be visited before node 5\nnode 20 should be visited before node 18\nnode 22 should be visited before node 9\nnode 22 should be visited before node 16\nnode 22 should be visited before node 14\nnode 22 should be visited before node 6\nnode 22 should be visited before node 26\nnode 22 should be visited before node 23\nnode 22 should be visited before node 1\nnode 22 should be visited before node 7\nnode 22 should be visited before node 18\nnode 23 should be visited before node 0\nnode 23 should be visited before node 10\nnode 23 should be visited before node 19\nnode 23 should be visited before node 5\nnode 24 should be visited before node 26\nnode 24 should be visited before node 23\nnode 24 should be visited before node 7\nnode 24 should be visited before node 5\nnode 24 should be visited before node 18\nnode 24 should be visited before node 8\nnode 25 should be visited before node 3\nnode 25 should be visited before node 18\nnode 25 should be visited before node 21\nnode 26 should be visited before node 3\nnode 26 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 4,20,13,22,9,16,14,2,15,24,17,25,6,26,1,3,23,7,11,12,0,10,19,8,5,18,21.", "difficulty": "hard", "doc_id": "9"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 15 nodes numbered from 0 to 14:\nnode 0 should be visited before node 9\nnode 1 should be visited before node 13\nnode 1 should be visited before node 0\nnode 1 should be visited before node 2\nnode 4 should be visited before node 14\nnode 4 should be visited before node 3\nnode 5 should be visited before node 9\nnode 6 should be visited before node 5\nnode 6 should be visited before node 13\nnode 7 should be visited before node 6\nnode 7 should be visited before node 1\nnode 7 should be visited before node 3\nnode 7 should be visited before node 2\nnode 8 should be visited before node 6\nnode 8 should be visited before node 10\nnode 8 should be visited before node 14\nnode 8 should be visited before node 1\nnode 8 should be visited before node 5\nnode 10 should be visited before node 5\nnode 10 should be visited before node 13\nnode 10 should be visited before node 9\nnode 10 should be visited before node 2\nnode 11 should be visited before node 6\nnode 11 should be visited before node 10\nnode 11 should be visited before node 12\nnode 11 should be visited before node 3\nnode 11 should be visited before node 13\nnode 11 should be visited before node 0\nnode 12 should be visited before node 5\nnode 12 should be visited before node 0\nnode 12 should be visited before node 2\nnode 13 should be visited before node 9\nnode 14 should be visited before node 12\nnode 14 should be visited before node 5\nnode 14 should be visited before node 3\nnode 14 should be visited before node 13\nnode 14 should be visited before node 9\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 4,7,8,11,14,1,6,10,12,3,13,5,0,2,9.", "difficulty": "medium", "doc_id": "10"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 20 nodes numbered from 0 to 19:\nnode 1 should be visited before node 9\nnode 1 should be visited before node 5\nnode 1 should be visited before node 4\nnode 1 should be visited before node 0\nnode 2 should be visited before node 3\nnode 2 should be visited before node 17\nnode 2 should be visited before node 7\nnode 2 should be visited before node 6\nnode 2 should be visited before node 1\nnode 2 should be visited before node 9\nnode 2 should be visited before node 4\nnode 2 should be visited before node 0\nnode 3 should be visited before node 17\nnode 3 should be visited before node 7\nnode 3 should be visited before node 8\nnode 3 should be visited before node 6\nnode 3 should be visited before node 1\nnode 3 should be visited before node 9\nnode 3 should be visited before node 5\nnode 3 should be visited before node 4\nnode 4 should be visited before node 0\nnode 5 should be visited before node 4\nnode 5 should be visited before node 0\nnode 6 should be visited before node 1\nnode 6 should be visited before node 9\nnode 6 should be visited before node 4\nnode 6 should be visited before node 0\nnode 7 should be visited before node 8\nnode 7 should be visited before node 6\nnode 7 should be visited before node 9\nnode 7 should be visited before node 5\nnode 7 should be visited before node 4\nnode 7 should be visited before node 0\nnode 8 should be visited before node 6\nnode 8 should be visited before node 1\nnode 8 should be visited before node 4\nnode 8 should be visited before node 0\nnode 9 should be visited before node 5\nnode 9 should be visited before node 4\nnode 10 should be visited before node 18\nnode 10 should be visited before node 12\nnode 10 should be visited before node 16\nnode 10 should be visited before node 15\nnode 10 should be visited before node 13\nnode 10 should be visited before node 3\nnode 10 should be visited before node 17\nnode 10 should be visited before node 8\nnode 10 should be visited before node 1\nnode 10 should be visited before node 9\nnode 10 should be visited before node 5\nnode 10 should be visited before node 4\nnode 11 should be visited before node 10\nnode 11 should be visited before node 18\nnode 11 should be visited before node 12\nnode 11 should be visited before node 16\nnode 11 should be visited before node 15\nnode 11 should be visited before node 2\nnode 11 should be visited before node 3\nnode 11 should be visited before node 17\nnode 11 should be visited before node 7\nnode 11 should be visited before node 8\nnode 11 should be visited before node 9\nnode 11 should be visited before node 5\nnode 11 should be visited before node 4\nnode 12 should be visited before node 16\nnode 12 should be visited before node 15\nnode 12 should be visited before node 13\nnode 12 should be visited before node 3\nnode 12 should be visited before node 17\nnode 12 should be visited before node 7\nnode 12 should be visited before node 6\nnode 12 should be visited before node 1\nnode 12 should be visited before node 5\nnode 12 should be visited before node 4\nnode 12 should be visited before node 0\nnode 13 should be visited before node 2\nnode 13 should be visited before node 3\nnode 13 should be visited before node 17\nnode 13 should be visited before node 7\nnode 13 should be visited before node 8\nnode 13 should be visited before node 6\nnode 13 should be visited before node 1\nnode 13 should be visited before node 5\nnode 13 should be visited before node 0\nnode 14 should be visited before node 12\nnode 14 should be visited before node 16\nnode 14 should be visited before node 15\nnode 14 should be visited before node 17\nnode 14 should be visited before node 6\nnode 14 should be visited before node 1\nnode 14 should be visited before node 9\nnode 14 should be visited before node 5\nnode 14 should be visited before node 4\nnode 15 should be visited before node 13\nnode 15 should be visited before node 2\nnode 15 should be visited before node 3\nnode 15 should be visited before node 7\nnode 15 should be visited before node 8\nnode 15 should be visited before node 6\nnode 15 should be visited before node 9\nnode 15 should be visited before node 0\nnode 16 should be visited before node 2\nnode 16 should be visited before node 3\nnode 16 should be visited before node 8\nnode 16 should be visited before node 6\nnode 16 should be visited before node 9\nnode 17 should be visited before node 7\nnode 17 should be visited before node 8\nnode 17 should be visited before node 6\nnode 17 should be visited before node 9\nnode 17 should be visited before node 5\nnode 17 should be visited before node 4\nnode 17 should be visited before node 0\nnode 18 should be visited before node 12\nnode 18 should be visited before node 16\nnode 18 should be visited before node 15\nnode 18 should be visited before node 13\nnode 18 should be visited before node 2\nnode 18 should be visited before node 17\nnode 18 should be visited before node 7\nnode 18 should be visited before node 8\nnode 18 should be visited before node 6\nnode 18 should be visited before node 1\nnode 18 should be visited before node 9\nnode 18 should be visited before node 4\nnode 19 should be visited before node 11\nnode 19 should be visited before node 10\nnode 19 should be visited before node 14\nnode 19 should be visited before node 12\nnode 19 should be visited before node 15\nnode 19 should be visited before node 13\nnode 19 should be visited before node 2\nnode 19 should be visited before node 3\nnode 19 should be visited before node 17\nnode 19 should be visited before node 7\nnode 19 should be visited before node 8\nnode 19 should be visited before node 1\nnode 19 should be visited before node 4\nnode 19 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 19,11,14,10,18,12,16,15,13,2,3,17,7,8,6,1,9,5,4,0.", "difficulty": "medium", "doc_id": "11"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 34 nodes numbered from 0 to 33:\nnode 0 should be visited before node 8\nnode 0 should be visited before node 19\nnode 0 should be visited before node 9\nnode 0 should be visited before node 28\nnode 1 should be visited before node 18\nnode 1 should be visited before node 14\nnode 1 should be visited before node 17\nnode 1 should be visited before node 5\nnode 1 should be visited before node 10\nnode 2 should be visited before node 14\nnode 2 should be visited before node 17\nnode 3 should be visited before node 30\nnode 3 should be visited before node 8\nnode 3 should be visited before node 12\nnode 3 should be visited before node 2\nnode 3 should be visited before node 31\nnode 3 should be visited before node 21\nnode 3 should be visited before node 9\nnode 3 should be visited before node 28\nnode 3 should be visited before node 15\nnode 3 should be visited before node 11\nnode 4 should be visited before node 14\nnode 4 should be visited before node 31\nnode 4 should be visited before node 5\nnode 4 should be visited before node 15\nnode 4 should be visited before node 11\nnode 4 should be visited before node 22\nnode 5 should be visited before node 11\nnode 6 should be visited before node 32\nnode 6 should be visited before node 19\nnode 6 should be visited before node 14\nnode 6 should be visited before node 11\nnode 7 should be visited before node 8\nnode 7 should be visited before node 12\nnode 7 should be visited before node 19\nnode 7 should be visited before node 1\nnode 7 should be visited before node 28\nnode 7 should be visited before node 15\nnode 7 should be visited before node 10\nnode 7 should be visited before node 11\nnode 8 should be visited before node 4\nnode 8 should be visited before node 1\nnode 8 should be visited before node 31\nnode 8 should be visited before node 25\nnode 8 should be visited before node 21\nnode 8 should be visited before node 5\nnode 8 should be visited before node 15\nnode 8 should be visited before node 10\nnode 9 should be visited before node 28\nnode 10 should be visited before node 11\nnode 10 should be visited before node 22\nnode 12 should be visited before node 4\nnode 12 should be visited before node 5\nnode 12 should be visited before node 9\nnode 12 should be visited before node 28\nnode 12 should be visited before node 11\nnode 13 should be visited before node 8\nnode 13 should be visited before node 32\nnode 13 should be visited before node 4\nnode 13 should be visited before node 1\nnode 13 should be visited before node 21\nnode 14 should be visited before node 17\nnode 14 should be visited before node 15\nnode 15 should be visited before node 22\nnode 16 should be visited before node 8\nnode 16 should be visited before node 32\nnode 16 should be visited before node 12\nnode 16 should be visited before node 19\nnode 16 should be visited before node 2\nnode 16 should be visited before node 14\nnode 16 should be visited before node 17\nnode 16 should be visited before node 22\nnode 17 should be visited before node 5\nnode 17 should be visited before node 28\nnode 17 should be visited before node 15\nnode 17 should be visited before node 10\nnode 17 should be visited before node 11\nnode 17 should be visited before node 22\nnode 18 should be visited before node 14\nnode 18 should be visited before node 25\nnode 18 should be visited before node 22\nnode 19 should be visited before node 4\nnode 19 should be visited before node 14\nnode 19 should be visited before node 31\nnode 19 should be visited before node 25\nnode 19 should be visited before node 10\nnode 20 should be visited before node 16\nnode 20 should be visited before node 8\nnode 20 should be visited before node 1\nnode 20 should be visited before node 14\nnode 20 should be visited before node 17\nnode 20 should be visited before node 25\nnode 20 should be visited before node 9\nnode 20 should be visited before node 15\nnode 20 should be visited before node 10\nnode 20 should be visited before node 22\nnode 21 should be visited before node 9\nnode 23 should be visited before node 16\nnode 23 should be visited before node 19\nnode 23 should be visited before node 14\nnode 23 should be visited before node 25\nnode 23 should be visited before node 22\nnode 24 should be visited before node 27\nnode 24 should be visited before node 6\nnode 24 should be visited before node 7\nnode 24 should be visited before node 20\nnode 24 should be visited before node 0\nnode 24 should be visited before node 32\nnode 24 should be visited before node 12\nnode 24 should be visited before node 1\nnode 24 should be visited before node 15\nnode 25 should be visited before node 5\nnode 25 should be visited before node 28\nnode 25 should be visited before node 22\nnode 26 should be visited before node 29\nnode 26 should be visited before node 33\nnode 26 should be visited before node 12\nnode 26 should be visited before node 4\nnode 26 should be visited before node 18\nnode 26 should be visited before node 14\nnode 26 should be visited before node 31\nnode 26 should be visited before node 15\nnode 26 should be visited before node 10\nnode 26 should be visited before node 22\nnode 27 should be visited before node 8\nnode 27 should be visited before node 12\nnode 27 should be visited before node 21\nnode 27 should be visited before node 28\nnode 27 should be visited before node 15\nnode 27 should be visited before node 11\nnode 27 should be visited before node 22\nnode 28 should be visited before node 22\nnode 29 should be visited before node 33\nnode 29 should be visited before node 20\nnode 29 should be visited before node 8\nnode 29 should be visited before node 12\nnode 29 should be visited before node 18\nnode 29 should be visited before node 25\nnode 29 should be visited before node 28\nnode 30 should be visited before node 0\nnode 30 should be visited before node 12\nnode 30 should be visited before node 19\nnode 30 should be visited before node 2\nnode 30 should be visited before node 1\nnode 30 should be visited before node 14\nnode 30 should be visited before node 17\nnode 30 should be visited before node 25\nnode 30 should be visited before node 21\nnode 31 should be visited before node 17\nnode 31 should be visited before node 9\nnode 31 should be visited before node 10\nnode 31 should be visited before node 11\nnode 31 should be visited before node 22\nnode 32 should be visited before node 4\nnode 32 should be visited before node 1\nnode 32 should be visited before node 11\nnode 33 should be visited before node 6\nnode 33 should be visited before node 30\nnode 33 should be visited before node 7\nnode 33 should be visited before node 20\nnode 33 should be visited before node 8\nnode 33 should be visited before node 18\nnode 33 should be visited before node 14\nnode 33 should be visited before node 31\nnode 33 should be visited before node 5\nnode 33 should be visited before node 28\nnode 33 should be visited before node 11\nnode 33 should be visited before node 22\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 3,13,23,24,26,27,29,33,6,30,7,20,0,16,8,32,12,19,2,21,1,4,18,31,14,25,9,17,5,28,15,10,11,22.", "difficulty": "hard", "doc_id": "12"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 14 nodes numbered from 0 to 13:\nnode 0 should be visited before node 12\nnode 1 should be visited before node 10\nnode 1 should be visited before node 7\nnode 1 should be visited before node 5\nnode 1 should be visited before node 0\nnode 2 should be visited before node 13\nnode 2 should be visited before node 0\nnode 3 should be visited before node 2\nnode 3 should be visited before node 6\nnode 3 should be visited before node 12\nnode 4 should be visited before node 1\nnode 4 should be visited before node 11\nnode 4 should be visited before node 2\nnode 4 should be visited before node 6\nnode 4 should be visited before node 8\nnode 4 should be visited before node 0\nnode 5 should be visited before node 2\nnode 5 should be visited before node 8\nnode 5 should be visited before node 12\nnode 6 should be visited before node 0\nnode 7 should be visited before node 3\nnode 7 should be visited before node 5\nnode 8 should be visited before node 12\nnode 11 should be visited before node 3\nnode 13 should be visited before node 8\nnode 13 should be visited before node 12\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 4,9,1,11,10,7,3,5,6,2,13,0,8,12.", "difficulty": "medium", "doc_id": "13"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 28 nodes numbered from 0 to 27:\nnode 0 should be visited before node 26\nnode 0 should be visited before node 19\nnode 0 should be visited before node 23\nnode 0 should be visited before node 24\nnode 1 should be visited before node 0\nnode 1 should be visited before node 10\nnode 1 should be visited before node 8\nnode 1 should be visited before node 25\nnode 1 should be visited before node 23\nnode 2 should be visited before node 8\nnode 2 should be visited before node 7\nnode 2 should be visited before node 4\nnode 2 should be visited before node 18\nnode 2 should be visited before node 22\nnode 2 should be visited before node 15\nnode 3 should be visited before node 19\nnode 3 should be visited before node 13\nnode 5 should be visited before node 16\nnode 5 should be visited before node 1\nnode 5 should be visited before node 17\nnode 5 should be visited before node 26\nnode 5 should be visited before node 11\nnode 5 should be visited before node 8\nnode 5 should be visited before node 9\nnode 5 should be visited before node 3\nnode 5 should be visited before node 25\nnode 5 should be visited before node 23\nnode 5 should be visited before node 18\nnode 5 should be visited before node 14\nnode 6 should be visited before node 22\nnode 6 should be visited before node 13\nnode 6 should be visited before node 14\nnode 6 should be visited before node 15\nnode 7 should be visited before node 19\nnode 7 should be visited before node 4\nnode 7 should be visited before node 24\nnode 8 should be visited before node 9\nnode 8 should be visited before node 25\nnode 8 should be visited before node 4\nnode 8 should be visited before node 23\nnode 8 should be visited before node 18\nnode 8 should be visited before node 22\nnode 8 should be visited before node 20\nnode 9 should be visited before node 19\nnode 9 should be visited before node 22\nnode 9 should be visited before node 14\nnode 9 should be visited before node 15\nnode 10 should be visited before node 21\nnode 10 should be visited before node 7\nnode 10 should be visited before node 4\nnode 10 should be visited before node 18\nnode 10 should be visited before node 22\nnode 10 should be visited before node 24\nnode 11 should be visited before node 21\nnode 11 should be visited before node 25\nnode 11 should be visited before node 18\nnode 11 should be visited before node 13\nnode 11 should be visited before node 20\nnode 11 should be visited before node 14\nnode 12 should be visited before node 3\nnode 12 should be visited before node 19\nnode 12 should be visited before node 23\nnode 12 should be visited before node 6\nnode 12 should be visited before node 22\nnode 12 should be visited before node 20\nnode 12 should be visited before node 15\nnode 16 should be visited before node 26\nnode 16 should be visited before node 10\nnode 16 should be visited before node 4\nnode 16 should be visited before node 6\nnode 16 should be visited before node 22\nnode 16 should be visited before node 20\nnode 16 should be visited before node 14\nnode 17 should be visited before node 12\nnode 17 should be visited before node 9\nnode 17 should be visited before node 7\nnode 17 should be visited before node 4\nnode 17 should be visited before node 23\nnode 17 should be visited before node 15\nnode 18 should be visited before node 6\nnode 18 should be visited before node 13\nnode 19 should be visited before node 18\nnode 19 should be visited before node 6\nnode 19 should be visited before node 22\nnode 19 should be visited before node 20\nnode 19 should be visited before node 15\nnode 20 should be visited before node 24\nnode 20 should be visited before node 15\nnode 21 should be visited before node 3\nnode 21 should be visited before node 6\nnode 21 should be visited before node 22\nnode 21 should be visited before node 14\nnode 22 should be visited before node 24\nnode 23 should be visited before node 22\nnode 23 should be visited before node 20\nnode 23 should be visited before node 15\nnode 24 should be visited before node 15\nnode 25 should be visited before node 4\nnode 26 should be visited before node 8\nnode 26 should be visited before node 25\nnode 26 should be visited before node 19\nnode 26 should be visited before node 6\nnode 26 should be visited before node 13\nnode 26 should be visited before node 20\nnode 26 should be visited before node 24\nnode 27 should be visited before node 10\nnode 27 should be visited before node 11\nnode 27 should be visited before node 18\nnode 27 should be visited before node 22\nnode 27 should be visited before node 24\nnode 27 should be visited before node 15\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 2,5,27,16,1,17,11,0,10,12,26,21,7,8,3,9,25,23,19,4,18,20,6,22,13,14,24,15.", "difficulty": "hard", "doc_id": "14"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 32 nodes numbered from 0 to 31:\nnode 0 should be visited before node 5\nnode 0 should be visited before node 14\nnode 0 should be visited before node 9\nnode 1 should be visited before node 12\nnode 1 should be visited before node 4\nnode 1 should be visited before node 29\nnode 1 should be visited before node 7\nnode 1 should be visited before node 3\nnode 1 should be visited before node 6\nnode 1 should be visited before node 11\nnode 1 should be visited before node 20\nnode 1 should be visited before node 19\nnode 1 should be visited before node 21\nnode 1 should be visited before node 10\nnode 1 should be visited before node 18\nnode 1 should be visited before node 31\nnode 1 should be visited before node 5\nnode 1 should be visited before node 14\nnode 2 should be visited before node 8\nnode 2 should be visited before node 31\nnode 2 should be visited before node 15\nnode 2 should be visited before node 26\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 2 should be visited before node 9\nnode 3 should be visited before node 6\nnode 3 should be visited before node 16\nnode 3 should be visited before node 20\nnode 3 should be visited before node 19\nnode 3 should be visited before node 2\nnode 3 should be visited before node 13\nnode 3 should be visited before node 10\nnode 3 should be visited before node 17\nnode 3 should be visited before node 15\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 3 should be visited before node 9\nnode 4 should be visited before node 28\nnode 4 should be visited before node 7\nnode 4 should be visited before node 3\nnode 4 should be visited before node 30\nnode 4 should be visited before node 24\nnode 4 should be visited before node 6\nnode 4 should be visited before node 11\nnode 4 should be visited before node 19\nnode 4 should be visited before node 21\nnode 4 should be visited before node 13\nnode 4 should be visited before node 17\nnode 4 should be visited before node 8\nnode 4 should be visited before node 31\nnode 4 should be visited before node 26\nnode 4 should be visited before node 0\nnode 4 should be visited before node 5\nnode 5 should be visited before node 14\nnode 5 should be visited before node 9\nnode 6 should be visited before node 16\nnode 6 should be visited before node 2\nnode 6 should be visited before node 21\nnode 6 should be visited before node 13\nnode 6 should be visited before node 22\nnode 6 should be visited before node 8\nnode 6 should be visited before node 18\nnode 6 should be visited before node 0\nnode 6 should be visited before node 14\nnode 7 should be visited before node 3\nnode 7 should be visited before node 24\nnode 7 should be visited before node 6\nnode 7 should be visited before node 20\nnode 7 should be visited before node 2\nnode 7 should be visited before node 21\nnode 7 should be visited before node 13\nnode 7 should be visited before node 10\nnode 7 should be visited before node 22\nnode 7 should be visited before node 8\nnode 7 should be visited before node 15\nnode 7 should be visited before node 26\nnode 8 should be visited before node 18\nnode 8 should be visited before node 31\nnode 8 should be visited before node 26\nnode 8 should be visited before node 5\nnode 10 should be visited before node 22\nnode 10 should be visited before node 17\nnode 10 should be visited before node 26\nnode 11 should be visited before node 21\nnode 11 should be visited before node 13\nnode 11 should be visited before node 17\nnode 11 should be visited before node 8\nnode 11 should be visited before node 31\nnode 11 should be visited before node 15\nnode 11 should be visited before node 26\nnode 11 should be visited before node 5\nnode 11 should be visited before node 9\nnode 12 should be visited before node 23\nnode 12 should be visited before node 7\nnode 12 should be visited before node 3\nnode 12 should be visited before node 24\nnode 12 should be visited before node 6\nnode 12 should be visited before node 11\nnode 12 should be visited before node 19\nnode 12 should be visited before node 10\nnode 12 should be visited before node 17\nnode 12 should be visited before node 8\nnode 12 should be visited before node 18\nnode 12 should be visited before node 31\nnode 12 should be visited before node 15\nnode 12 should be visited before node 0\nnode 12 should be visited before node 5\nnode 12 should be visited before node 9\nnode 13 should be visited before node 10\nnode 13 should be visited before node 17\nnode 13 should be visited before node 18\nnode 13 should be visited before node 15\nnode 13 should be visited before node 26\nnode 13 should be visited before node 5\nnode 14 should be visited before node 9\nnode 15 should be visited before node 26\nnode 15 should be visited before node 14\nnode 16 should be visited before node 20\nnode 16 should be visited before node 2\nnode 16 should be visited before node 8\nnode 16 should be visited before node 18\nnode 16 should be visited before node 14\nnode 16 should be visited before node 9\nnode 17 should be visited before node 8\nnode 17 should be visited before node 14\nnode 17 should be visited before node 9\nnode 18 should be visited before node 31\nnode 18 should be visited before node 15\nnode 18 should be visited before node 0\nnode 18 should be visited before node 5\nnode 18 should be visited before node 9\nnode 19 should be visited before node 2\nnode 19 should be visited before node 10\nnode 19 should be visited before node 22\nnode 19 should be visited before node 17\nnode 19 should be visited before node 18\nnode 19 should be visited before node 31\nnode 19 should be visited before node 15\nnode 19 should be visited before node 5\nnode 19 should be visited before node 9\nnode 20 should be visited before node 21\nnode 20 should be visited before node 10\nnode 20 should be visited before node 22\nnode 20 should be visited before node 8\nnode 20 should be visited before node 15\nnode 20 should be visited before node 5\nnode 20 should be visited before node 14\nnode 20 should be visited before node 9\nnode 21 should be visited before node 10\nnode 21 should be visited before node 22\nnode 21 should be visited before node 17\nnode 21 should be visited before node 31\nnode 21 should be visited before node 5\nnode 21 should be visited before node 9\nnode 22 should be visited before node 8\nnode 22 should be visited before node 26\nnode 22 should be visited before node 9\nnode 23 should be visited before node 6\nnode 23 should be visited before node 21\nnode 23 should be visited before node 13\nnode 23 should be visited before node 10\nnode 23 should be visited before node 17\nnode 23 should be visited before node 31\nnode 23 should be visited before node 26\nnode 23 should be visited before node 5\nnode 23 should be visited before node 9\nnode 24 should be visited before node 6\nnode 24 should be visited before node 20\nnode 24 should be visited before node 19\nnode 24 should be visited before node 13\nnode 24 should be visited before node 22\nnode 24 should be visited before node 31\nnode 24 should be visited before node 15\nnode 24 should be visited before node 26\nnode 24 should be visited before node 0\nnode 24 should be visited before node 9\nnode 25 should be visited before node 29\nnode 25 should be visited before node 28\nnode 25 should be visited before node 7\nnode 25 should be visited before node 24\nnode 25 should be visited before node 6\nnode 25 should be visited before node 11\nnode 25 should be visited before node 16\nnode 25 should be visited before node 20\nnode 25 should be visited before node 2\nnode 25 should be visited before node 21\nnode 25 should be visited before node 10\nnode 25 should be visited before node 22\nnode 25 should be visited before node 31\nnode 25 should be visited before node 14\nnode 25 should be visited before node 9\nnode 26 should be visited before node 0\nnode 26 should be visited before node 9\nnode 27 should be visited before node 25\nnode 27 should be visited before node 23\nnode 27 should be visited before node 28\nnode 27 should be visited before node 7\nnode 27 should be visited before node 30\nnode 27 should be visited before node 11\nnode 27 should be visited before node 20\nnode 27 should be visited before node 22\nnode 27 should be visited before node 18\nnode 27 should be visited before node 15\nnode 27 should be visited before node 26\nnode 27 should be visited before node 0\nnode 27 should be visited before node 14\nnode 28 should be visited before node 7\nnode 28 should be visited before node 24\nnode 28 should be visited before node 6\nnode 28 should be visited before node 11\nnode 28 should be visited before node 16\nnode 28 should be visited before node 19\nnode 28 should be visited before node 2\nnode 28 should be visited before node 17\nnode 28 should be visited before node 8\nnode 28 should be visited before node 18\nnode 28 should be visited before node 26\nnode 28 should be visited before node 14\nnode 29 should be visited before node 23\nnode 29 should be visited before node 28\nnode 29 should be visited before node 7\nnode 29 should be visited before node 30\nnode 29 should be visited before node 24\nnode 29 should be visited before node 16\nnode 29 should be visited before node 19\nnode 29 should be visited before node 2\nnode 29 should be visited before node 21\nnode 29 should be visited before node 15\nnode 29 should be visited before node 0\nnode 29 should be visited before node 5\nnode 29 should be visited before node 14\nnode 30 should be visited before node 24\nnode 30 should be visited before node 6\nnode 30 should be visited before node 20\nnode 30 should be visited before node 19\nnode 30 should be visited before node 21\nnode 30 should be visited before node 8\nnode 30 should be visited before node 26\nnode 30 should be visited before node 0\nnode 30 should be visited before node 9\nnode 31 should be visited before node 0\nnode 31 should be visited before node 5\nnode 31 should be visited before node 14\nnode 31 should be visited before node 9\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 1,27,12,4,25,29,23,28,30,7,11,3,24,6,19,16,13,20,2,21,10,22,17,8,18,31,15,26,0,5,14,9.", "difficulty": "hard", "doc_id": "15"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 22 nodes numbered from 0 to 21:\nnode 0 should be visited before node 13\nnode 0 should be visited before node 16\nnode 0 should be visited before node 18\nnode 0 should be visited before node 12\nnode 0 should be visited before node 19\nnode 0 should be visited before node 8\nnode 1 should be visited before node 0\nnode 1 should be visited before node 15\nnode 1 should be visited before node 13\nnode 1 should be visited before node 18\nnode 1 should be visited before node 10\nnode 1 should be visited before node 3\nnode 1 should be visited before node 20\nnode 2 should be visited before node 18\nnode 2 should be visited before node 12\nnode 2 should be visited before node 5\nnode 2 should be visited before node 19\nnode 2 should be visited before node 8\nnode 3 should be visited before node 4\nnode 3 should be visited before node 20\nnode 4 should be visited before node 20\nnode 5 should be visited before node 19\nnode 5 should be visited before node 8\nnode 5 should be visited before node 3\nnode 5 should be visited before node 20\nnode 6 should be visited before node 9\nnode 6 should be visited before node 2\nnode 6 should be visited before node 21\nnode 6 should be visited before node 18\nnode 6 should be visited before node 10\nnode 6 should be visited before node 5\nnode 6 should be visited before node 19\nnode 6 should be visited before node 8\nnode 6 should be visited before node 3\nnode 6 should be visited before node 20\nnode 7 should be visited before node 1\nnode 7 should be visited before node 14\nnode 7 should be visited before node 2\nnode 7 should be visited before node 16\nnode 7 should be visited before node 18\nnode 7 should be visited before node 10\nnode 7 should be visited before node 12\nnode 7 should be visited before node 5\nnode 7 should be visited before node 3\nnode 7 should be visited before node 20\nnode 9 should be visited before node 7\nnode 9 should be visited before node 2\nnode 9 should be visited before node 0\nnode 9 should be visited before node 13\nnode 9 should be visited before node 16\nnode 9 should be visited before node 10\nnode 11 should be visited before node 14\nnode 11 should be visited before node 2\nnode 11 should be visited before node 0\nnode 11 should be visited before node 13\nnode 11 should be visited before node 18\nnode 11 should be visited before node 10\nnode 11 should be visited before node 12\nnode 11 should be visited before node 19\nnode 11 should be visited before node 8\nnode 11 should be visited before node 3\nnode 11 should be visited before node 20\nnode 12 should be visited before node 3\nnode 12 should be visited before node 4\nnode 13 should be visited before node 16\nnode 13 should be visited before node 18\nnode 13 should be visited before node 12\nnode 13 should be visited before node 3\nnode 13 should be visited before node 4\nnode 14 should be visited before node 0\nnode 14 should be visited before node 21\nnode 14 should be visited before node 15\nnode 14 should be visited before node 13\nnode 14 should be visited before node 16\nnode 14 should be visited before node 18\nnode 14 should be visited before node 10\nnode 14 should be visited before node 12\nnode 14 should be visited before node 5\nnode 14 should be visited before node 19\nnode 14 should be visited before node 8\nnode 14 should be visited before node 20\nnode 15 should be visited before node 13\nnode 15 should be visited before node 10\nnode 15 should be visited before node 5\nnode 15 should be visited before node 8\nnode 15 should be visited before node 3\nnode 15 should be visited before node 4\nnode 16 should be visited before node 18\nnode 16 should be visited before node 5\nnode 16 should be visited before node 3\nnode 16 should be visited before node 20\nnode 17 should be visited before node 6\nnode 17 should be visited before node 9\nnode 17 should be visited before node 7\nnode 17 should be visited before node 1\nnode 17 should be visited before node 2\nnode 17 should be visited before node 15\nnode 17 should be visited before node 13\nnode 17 should be visited before node 16\nnode 17 should be visited before node 12\nnode 17 should be visited before node 19\nnode 17 should be visited before node 8\nnode 17 should be visited before node 4\nnode 18 should be visited before node 8\nnode 18 should be visited before node 3\nnode 19 should be visited before node 20\nnode 21 should be visited before node 16\nnode 21 should be visited before node 12\nnode 21 should be visited before node 5\nnode 21 should be visited before node 19\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 11,17,6,9,7,1,14,2,0,21,15,13,10,16,12,18,5,19,8,3,4,20.", "difficulty": "medium", "doc_id": "16"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 23 nodes numbered from 0 to 22:\nnode 1 should be visited before node 16\nnode 1 should be visited before node 15\nnode 1 should be visited before node 8\nnode 1 should be visited before node 6\nnode 1 should be visited before node 0\nnode 2 should be visited before node 22\nnode 2 should be visited before node 1\nnode 2 should be visited before node 16\nnode 2 should be visited before node 12\nnode 2 should be visited before node 6\nnode 2 should be visited before node 18\nnode 3 should be visited before node 19\nnode 3 should be visited before node 7\nnode 3 should be visited before node 4\nnode 4 should be visited before node 11\nnode 4 should be visited before node 6\nnode 4 should be visited before node 20\nnode 5 should be visited before node 8\nnode 5 should be visited before node 19\nnode 5 should be visited before node 18\nnode 6 should be visited before node 18\nnode 8 should be visited before node 19\nnode 8 should be visited before node 20\nnode 9 should be visited before node 1\nnode 9 should be visited before node 16\nnode 9 should be visited before node 8\nnode 9 should be visited before node 19\nnode 9 should be visited before node 4\nnode 10 should be visited before node 11\nnode 10 should be visited before node 18\nnode 10 should be visited before node 20\nnode 11 should be visited before node 20\nnode 12 should be visited before node 19\nnode 12 should be visited before node 11\nnode 12 should be visited before node 6\nnode 13 should be visited before node 2\nnode 13 should be visited before node 9\nnode 13 should be visited before node 5\nnode 13 should be visited before node 15\nnode 13 should be visited before node 10\nnode 14 should be visited before node 1\nnode 14 should be visited before node 3\nnode 14 should be visited before node 7\nnode 14 should be visited before node 4\nnode 14 should be visited before node 11\nnode 14 should be visited before node 0\nnode 15 should be visited before node 8\nnode 15 should be visited before node 0\nnode 16 should be visited before node 8\nnode 16 should be visited before node 3\nnode 16 should be visited before node 12\nnode 16 should be visited before node 7\nnode 16 should be visited before node 11\nnode 16 should be visited before node 0\nnode 16 should be visited before node 20\nnode 17 should be visited before node 2\nnode 17 should be visited before node 4\nnode 17 should be visited before node 6\nnode 19 should be visited before node 7\nnode 19 should be visited before node 4\nnode 19 should be visited before node 18\nnode 21 should be visited before node 1\nnode 21 should be visited before node 12\nnode 21 should be visited before node 19\nnode 21 should be visited before node 4\nnode 21 should be visited before node 11\nnode 21 should be visited before node 0\nnode 22 should be visited before node 5\nnode 22 should be visited before node 1\nnode 22 should be visited before node 12\nnode 22 should be visited before node 7\nnode 22 should be visited before node 6\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 13,14,17,21,9,10,2,22,5,1,16,15,3,12,8,0,19,7,4,11,6,20,18.", "difficulty": "medium", "doc_id": "17"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 19 nodes numbered from 0 to 18:\nnode 0 should be visited before node 18\nnode 0 should be visited before node 3\nnode 1 should be visited before node 6\nnode 1 should be visited before node 13\nnode 1 should be visited before node 5\nnode 1 should be visited before node 4\nnode 1 should be visited before node 17\nnode 1 should be visited before node 9\nnode 1 should be visited before node 10\nnode 1 should be visited before node 3\nnode 2 should be visited before node 12\nnode 2 should be visited before node 1\nnode 2 should be visited before node 11\nnode 2 should be visited before node 16\nnode 2 should be visited before node 5\nnode 2 should be visited before node 4\nnode 2 should be visited before node 17\nnode 2 should be visited before node 18\nnode 2 should be visited before node 14\nnode 4 should be visited before node 9\nnode 4 should be visited before node 10\nnode 4 should be visited before node 14\nnode 4 should be visited before node 3\nnode 4 should be visited before node 15\nnode 5 should be visited before node 4\nnode 5 should be visited before node 17\nnode 5 should be visited before node 0\nnode 5 should be visited before node 18\nnode 5 should be visited before node 14\nnode 5 should be visited before node 3\nnode 6 should be visited before node 11\nnode 6 should be visited before node 16\nnode 6 should be visited before node 13\nnode 6 should be visited before node 17\nnode 6 should be visited before node 9\nnode 6 should be visited before node 0\nnode 6 should be visited before node 18\nnode 6 should be visited before node 14\nnode 6 should be visited before node 15\nnode 7 should be visited before node 2\nnode 7 should be visited before node 1\nnode 7 should be visited before node 6\nnode 7 should be visited before node 11\nnode 7 should be visited before node 16\nnode 7 should be visited before node 17\nnode 7 should be visited before node 9\nnode 7 should be visited before node 18\nnode 7 should be visited before node 10\nnode 7 should be visited before node 14\nnode 7 should be visited before node 3\nnode 7 should be visited before node 15\nnode 8 should be visited before node 2\nnode 8 should be visited before node 12\nnode 8 should be visited before node 1\nnode 8 should be visited before node 11\nnode 8 should be visited before node 16\nnode 8 should be visited before node 13\nnode 8 should be visited before node 5\nnode 8 should be visited before node 18\nnode 8 should be visited before node 14\nnode 8 should be visited before node 3\nnode 8 should be visited before node 15\nnode 9 should be visited before node 18\nnode 9 should be visited before node 10\nnode 9 should be visited before node 14\nnode 9 should be visited before node 15\nnode 11 should be visited before node 16\nnode 11 should be visited before node 4\nnode 11 should be visited before node 9\nnode 11 should be visited before node 18\nnode 11 should be visited before node 10\nnode 11 should be visited before node 3\nnode 12 should be visited before node 16\nnode 12 should be visited before node 5\nnode 12 should be visited before node 17\nnode 12 should be visited before node 9\nnode 12 should be visited before node 0\nnode 12 should be visited before node 14\nnode 12 should be visited before node 3\nnode 12 should be visited before node 15\nnode 13 should be visited before node 5\nnode 13 should be visited before node 4\nnode 13 should be visited before node 17\nnode 13 should be visited before node 0\nnode 13 should be visited before node 18\nnode 13 should be visited before node 14\nnode 13 should be visited before node 15\nnode 16 should be visited before node 13\nnode 16 should be visited before node 5\nnode 16 should be visited before node 4\nnode 16 should be visited before node 9\nnode 16 should be visited before node 0\nnode 16 should be visited before node 3\nnode 16 should be visited before node 15\nnode 17 should be visited before node 9\nnode 17 should be visited before node 10\nnode 17 should be visited before node 15\nnode 18 should be visited before node 10\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 7,8,2,12,1,6,11,16,13,5,4,17,0,9,3,18,14,15,10.", "difficulty": "medium", "doc_id": "18"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 1 should be visited before node 0\nnode 2 should be visited before node 3\nnode 2 should be visited before node 1\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 2,4,3,1,0.", "difficulty": "easy", "doc_id": "19"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 22 nodes numbered from 0 to 21:\nnode 0 should be visited before node 16\nnode 0 should be visited before node 6\nnode 0 should be visited before node 17\nnode 0 should be visited before node 7\nnode 0 should be visited before node 20\nnode 0 should be visited before node 11\nnode 0 should be visited before node 10\nnode 0 should be visited before node 1\nnode 0 should be visited before node 9\nnode 0 should be visited before node 4\nnode 0 should be visited before node 15\nnode 1 should be visited before node 19\nnode 1 should be visited before node 3\nnode 1 should be visited before node 9\nnode 1 should be visited before node 4\nnode 2 should be visited before node 0\nnode 2 should be visited before node 6\nnode 2 should be visited before node 8\nnode 2 should be visited before node 17\nnode 2 should be visited before node 20\nnode 2 should be visited before node 11\nnode 2 should be visited before node 10\nnode 2 should be visited before node 1\nnode 2 should be visited before node 4\nnode 2 should be visited before node 14\nnode 3 should be visited before node 9\nnode 4 should be visited before node 15\nnode 5 should be visited before node 1\nnode 5 should be visited before node 19\nnode 5 should be visited before node 14\nnode 6 should be visited before node 13\nnode 6 should be visited before node 8\nnode 6 should be visited before node 17\nnode 6 should be visited before node 5\nnode 6 should be visited before node 1\nnode 6 should be visited before node 19\nnode 6 should be visited before node 3\nnode 6 should be visited before node 9\nnode 6 should be visited before node 4\nnode 6 should be visited before node 14\nnode 7 should be visited before node 10\nnode 7 should be visited before node 19\nnode 7 should be visited before node 21\nnode 7 should be visited before node 14\nnode 8 should be visited before node 17\nnode 8 should be visited before node 5\nnode 8 should be visited before node 11\nnode 8 should be visited before node 19\nnode 8 should be visited before node 21\nnode 8 should be visited before node 15\nnode 8 should be visited before node 14\nnode 10 should be visited before node 19\nnode 10 should be visited before node 3\nnode 10 should be visited before node 9\nnode 10 should be visited before node 21\nnode 10 should be visited before node 4\nnode 10 should be visited before node 15\nnode 10 should be visited before node 14\nnode 11 should be visited before node 9\nnode 11 should be visited before node 21\nnode 11 should be visited before node 15\nnode 11 should be visited before node 14\nnode 12 should be visited before node 18\nnode 12 should be visited before node 0\nnode 12 should be visited before node 17\nnode 12 should be visited before node 7\nnode 12 should be visited before node 1\nnode 12 should be visited before node 19\nnode 12 should be visited before node 3\nnode 12 should be visited before node 9\nnode 12 should be visited before node 21\nnode 12 should be visited before node 4\nnode 12 should be visited before node 15\nnode 12 should be visited before node 14\nnode 13 should be visited before node 8\nnode 13 should be visited before node 7\nnode 13 should be visited before node 5\nnode 13 should be visited before node 10\nnode 13 should be visited before node 3\nnode 13 should be visited before node 21\nnode 13 should be visited before node 15\nnode 15 should be visited before node 14\nnode 16 should be visited before node 6\nnode 16 should be visited before node 8\nnode 16 should be visited before node 17\nnode 16 should be visited before node 5\nnode 16 should be visited before node 20\nnode 16 should be visited before node 1\nnode 16 should be visited before node 19\nnode 16 should be visited before node 14\nnode 17 should be visited before node 7\nnode 17 should be visited before node 5\nnode 17 should be visited before node 19\nnode 17 should be visited before node 3\nnode 17 should be visited before node 4\nnode 17 should be visited before node 15\nnode 18 should be visited before node 0\nnode 18 should be visited before node 17\nnode 18 should be visited before node 10\nnode 18 should be visited before node 1\nnode 18 should be visited before node 19\nnode 18 should be visited before node 3\nnode 18 should be visited before node 9\nnode 19 should be visited before node 3\nnode 19 should be visited before node 9\nnode 19 should be visited before node 21\nnode 20 should be visited before node 11\nnode 20 should be visited before node 10\nnode 20 should be visited before node 19\nnode 20 should be visited before node 9\nnode 20 should be visited before node 21\nnode 20 should be visited before node 14\nnode 21 should be visited before node 4\nnode 21 should be visited before node 15\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 2,12,18,0,16,6,20,13,8,17,11,7,5,10,1,19,3,21,9,4,15,14.", "difficulty": "medium", "doc_id": "20"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 1 should be visited before node 4\nnode 1 should be visited before node 3\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 2 should be visited before node 0\nnode 3 should be visited before node 2\nnode 3 should be visited before node 0\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nnode 5 should be visited before node 1\nnode 5 should be visited before node 4\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 5,1,4,3,2,0.", "difficulty": "easy", "doc_id": "21"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 30 nodes numbered from 0 to 29:\nnode 0 should be visited before node 24\nnode 1 should be visited before node 0\nnode 2 should be visited before node 4\nnode 2 should be visited before node 17\nnode 2 should be visited before node 23\nnode 2 should be visited before node 11\nnode 2 should be visited before node 24\nnode 2 should be visited before node 29\nnode 3 should be visited before node 10\nnode 3 should be visited before node 17\nnode 3 should be visited before node 28\nnode 3 should be visited before node 23\nnode 3 should be visited before node 1\nnode 3 should be visited before node 25\nnode 3 should be visited before node 0\nnode 3 should be visited before node 26\nnode 3 should be visited before node 29\nnode 4 should be visited before node 10\nnode 4 should be visited before node 27\nnode 4 should be visited before node 17\nnode 4 should be visited before node 23\nnode 4 should be visited before node 1\nnode 4 should be visited before node 25\nnode 4 should be visited before node 0\nnode 4 should be visited before node 24\nnode 4 should be visited before node 29\nnode 5 should be visited before node 2\nnode 5 should be visited before node 28\nnode 5 should be visited before node 19\nnode 5 should be visited before node 11\nnode 6 should be visited before node 14\nnode 6 should be visited before node 3\nnode 6 should be visited before node 2\nnode 6 should be visited before node 4\nnode 6 should be visited before node 28\nnode 6 should be visited before node 15\nnode 6 should be visited before node 29\nnode 7 should be visited before node 8\nnode 7 should be visited before node 13\nnode 7 should be visited before node 5\nnode 7 should be visited before node 22\nnode 7 should be visited before node 6\nnode 7 should be visited before node 2\nnode 7 should be visited before node 4\nnode 7 should be visited before node 19\nnode 7 should be visited before node 1\nnode 8 should be visited before node 6\nnode 8 should be visited before node 3\nnode 8 should be visited before node 4\nnode 8 should be visited before node 10\nnode 8 should be visited before node 17\nnode 8 should be visited before node 23\nnode 8 should be visited before node 29\nnode 9 should be visited before node 20\nnode 9 should be visited before node 22\nnode 9 should be visited before node 2\nnode 9 should be visited before node 10\nnode 9 should be visited before node 28\nnode 9 should be visited before node 19\nnode 9 should be visited before node 1\nnode 9 should be visited before node 24\nnode 9 should be visited before node 15\nnode 9 should be visited before node 29\nnode 10 should be visited before node 21\nnode 10 should be visited before node 28\nnode 10 should be visited before node 23\nnode 10 should be visited before node 1\nnode 10 should be visited before node 24\nnode 10 should be visited before node 29\nnode 11 should be visited before node 15\nnode 11 should be visited before node 29\nnode 12 should be visited before node 2\nnode 12 should be visited before node 4\nnode 12 should be visited before node 25\nnode 12 should be visited before node 0\nnode 13 should be visited before node 22\nnode 13 should be visited before node 12\nnode 13 should be visited before node 18\nnode 13 should be visited before node 17\nnode 13 should be visited before node 25\nnode 14 should be visited before node 17\nnode 14 should be visited before node 21\nnode 14 should be visited before node 1\nnode 14 should be visited before node 24\nnode 14 should be visited before node 15\nnode 14 should be visited before node 29\nnode 16 should be visited before node 6\nnode 16 should be visited before node 3\nnode 16 should be visited before node 4\nnode 17 should be visited before node 28\nnode 17 should be visited before node 0\nnode 17 should be visited before node 24\nnode 17 should be visited before node 26\nnode 18 should be visited before node 3\nnode 18 should be visited before node 27\nnode 18 should be visited before node 23\nnode 18 should be visited before node 19\nnode 20 should be visited before node 8\nnode 20 should be visited before node 22\nnode 20 should be visited before node 6\nnode 20 should be visited before node 27\nnode 20 should be visited before node 28\nnode 20 should be visited before node 23\nnode 20 should be visited before node 25\nnode 20 should be visited before node 0\nnode 21 should be visited before node 23\nnode 21 should be visited before node 11\nnode 21 should be visited before node 25\nnode 21 should be visited before node 0\nnode 21 should be visited before node 26\nnode 21 should be visited before node 29\nnode 22 should be visited before node 12\nnode 22 should be visited before node 18\nnode 22 should be visited before node 16\nnode 22 should be visited before node 6\nnode 22 should be visited before node 2\nnode 22 should be visited before node 17\nnode 22 should be visited before node 25\nnode 23 should be visited before node 25\nnode 23 should be visited before node 0\nnode 25 should be visited before node 0\nnode 27 should be visited before node 23\nnode 27 should be visited before node 19\nnode 28 should be visited before node 23\nnode 28 should be visited before node 11\nnode 28 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 7,9,13,5,20,8,22,12,18,16,6,14,3,2,4,10,27,17,21,1,19,28,26,23,11,25,15,29,0,24.", "difficulty": "hard", "doc_id": "22"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 8 nodes numbered from 0 to 7:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 6\nnode 0 should be visited before node 2\nnode 0 should be visited before node 1\nnode 2 should be visited before node 7\nnode 2 should be visited before node 1\nnode 3 should be visited before node 4\nnode 3 should be visited before node 2\nnode 3 should be visited before node 7\nnode 3 should be visited before node 1\nnode 4 should be visited before node 6\nnode 4 should be visited before node 2\nnode 4 should be visited before node 7\nnode 4 should be visited before node 1\nnode 5 should be visited before node 3\nnode 5 should be visited before node 2\nnode 5 should be visited before node 7\nnode 5 should be visited before node 1\nnode 6 should be visited before node 2\nnode 6 should be visited before node 7\nnode 7 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 0,5,3,4,6,2,7,1.", "difficulty": "easy", "doc_id": "23"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 2 should be visited before node 3\nnode 2 should be visited before node 5\nnode 2 should be visited before node 6\nnode 2 should be visited before node 4\nnode 3 should be visited before node 5\nnode 3 should be visited before node 4\nnode 3 should be visited before node 0\nnode 4 should be visited before node 1\nnode 4 should be visited before node 0\nnode 5 should be visited before node 6\nnode 5 should be visited before node 4\nnode 5 should be visited before node 1\nnode 5 should be visited before node 0\nnode 6 should be visited before node 4\nnode 6 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 2,3,5,6,4,1,0.", "difficulty": "easy", "doc_id": "24"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 8 nodes numbered from 0 to 7:\nnode 1 should be visited before node 6\nnode 1 should be visited before node 4\nnode 1 should be visited before node 3\nnode 1 should be visited before node 0\nnode 1 should be visited before node 7\nnode 2 should be visited before node 6\nnode 2 should be visited before node 4\nnode 2 should be visited before node 0\nnode 2 should be visited before node 7\nnode 3 should be visited before node 5\nnode 3 should be visited before node 0\nnode 4 should be visited before node 3\nnode 4 should be visited before node 5\nnode 5 should be visited before node 7\nnode 6 should be visited before node 4\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nnode 6 should be visited before node 7\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 1,2,6,4,3,5,0,7.", "difficulty": "easy", "doc_id": "25"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 0\nnode 2 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 0\nnode 4 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 2,3,4,1,0,5.", "difficulty": "easy", "doc_id": "26"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 18 nodes numbered from 0 to 17:\nnode 1 should be visited before node 4\nnode 1 should be visited before node 16\nnode 1 should be visited before node 17\nnode 1 should be visited before node 13\nnode 1 should be visited before node 8\nnode 1 should be visited before node 3\nnode 1 should be visited before node 11\nnode 1 should be visited before node 0\nnode 2 should be visited before node 15\nnode 2 should be visited before node 4\nnode 2 should be visited before node 10\nnode 2 should be visited before node 16\nnode 2 should be visited before node 13\nnode 2 should be visited before node 8\nnode 2 should be visited before node 14\nnode 3 should be visited before node 0\nnode 4 should be visited before node 16\nnode 4 should be visited before node 13\nnode 4 should be visited before node 12\nnode 4 should be visited before node 7\nnode 5 should be visited before node 4\nnode 5 should be visited before node 16\nnode 5 should be visited before node 17\nnode 5 should be visited before node 14\nnode 5 should be visited before node 12\nnode 5 should be visited before node 3\nnode 5 should be visited before node 0\nnode 6 should be visited before node 9\nnode 6 should be visited before node 1\nnode 6 should be visited before node 15\nnode 6 should be visited before node 4\nnode 6 should be visited before node 10\nnode 6 should be visited before node 13\nnode 6 should be visited before node 8\nnode 6 should be visited before node 7\nnode 6 should be visited before node 11\nnode 6 should be visited before node 0\nnode 7 should be visited before node 3\nnode 8 should be visited before node 14\nnode 8 should be visited before node 12\nnode 8 should be visited before node 7\nnode 9 should be visited before node 1\nnode 9 should be visited before node 5\nnode 9 should be visited before node 4\nnode 9 should be visited before node 13\nnode 9 should be visited before node 8\nnode 9 should be visited before node 7\nnode 10 should be visited before node 16\nnode 10 should be visited before node 17\nnode 10 should be visited before node 13\nnode 10 should be visited before node 14\nnode 10 should be visited before node 12\nnode 10 should be visited before node 7\nnode 10 should be visited before node 3\nnode 10 should be visited before node 11\nnode 12 should be visited before node 3\nnode 12 should be visited before node 11\nnode 13 should be visited before node 8\nnode 13 should be visited before node 14\nnode 13 should be visited before node 12\nnode 13 should be visited before node 7\nnode 13 should be visited before node 3\nnode 13 should be visited before node 11\nnode 13 should be visited before node 0\nnode 14 should be visited before node 7\nnode 14 should be visited before node 3\nnode 15 should be visited before node 4\nnode 15 should be visited before node 10\nnode 15 should be visited before node 17\nnode 15 should be visited before node 8\nnode 15 should be visited before node 14\nnode 15 should be visited before node 7\nnode 15 should be visited before node 3\nnode 15 should be visited before node 0\nnode 16 should be visited before node 17\nnode 16 should be visited before node 14\nnode 16 should be visited before node 7\nnode 16 should be visited before node 3\nnode 16 should be visited before node 11\nnode 16 should be visited before node 0\nnode 17 should be visited before node 13\nnode 17 should be visited before node 8\nnode 17 should be visited before node 14\nnode 17 should be visited before node 3\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 2,6,9,15,1,5,10,4,16,17,13,8,14,12,7,11,3,0.", "difficulty": "medium", "doc_id": "27"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 25 nodes numbered from 0 to 24:\nnode 0 should be visited before node 21\nnode 0 should be visited before node 11\nnode 1 should be visited before node 23\nnode 1 should be visited before node 7\nnode 1 should be visited before node 0\nnode 1 should be visited before node 10\nnode 1 should be visited before node 8\nnode 1 should be visited before node 14\nnode 2 should be visited before node 19\nnode 3 should be visited before node 24\nnode 3 should be visited before node 21\nnode 3 should be visited before node 8\nnode 4 should be visited before node 23\nnode 4 should be visited before node 9\nnode 4 should be visited before node 7\nnode 4 should be visited before node 13\nnode 4 should be visited before node 0\nnode 4 should be visited before node 21\nnode 4 should be visited before node 20\nnode 4 should be visited before node 10\nnode 4 should be visited before node 2\nnode 4 should be visited before node 11\nnode 5 should be visited before node 3\nnode 5 should be visited before node 14\nnode 5 should be visited before node 19\nnode 6 should be visited before node 7\nnode 6 should be visited before node 5\nnode 6 should be visited before node 15\nnode 6 should be visited before node 20\nnode 6 should be visited before node 10\nnode 6 should be visited before node 14\nnode 7 should be visited before node 0\nnode 7 should be visited before node 15\nnode 7 should be visited before node 24\nnode 7 should be visited before node 22\nnode 7 should be visited before node 10\nnode 7 should be visited before node 11\nnode 8 should be visited before node 11\nnode 9 should be visited before node 15\nnode 9 should be visited before node 2\nnode 10 should be visited before node 8\nnode 10 should be visited before node 14\nnode 10 should be visited before node 19\nnode 11 should be visited before node 19\nnode 12 should be visited before node 3\nnode 12 should be visited before node 22\nnode 12 should be visited before node 2\nnode 12 should be visited before node 19\nnode 13 should be visited before node 15\nnode 13 should be visited before node 21\nnode 13 should be visited before node 20\nnode 13 should be visited before node 11\nnode 15 should be visited before node 21\nnode 15 should be visited before node 10\nnode 15 should be visited before node 8\nnode 15 should be visited before node 14\nnode 15 should be visited before node 11\nnode 16 should be visited before node 23\nnode 16 should be visited before node 13\nnode 16 should be visited before node 10\nnode 16 should be visited before node 2\nnode 17 should be visited before node 4\nnode 17 should be visited before node 16\nnode 17 should be visited before node 23\nnode 17 should be visited before node 12\nnode 17 should be visited before node 0\nnode 17 should be visited before node 21\nnode 17 should be visited before node 14\nnode 18 should be visited before node 10\nnode 18 should be visited before node 2\nnode 20 should be visited before node 19\nnode 21 should be visited before node 10\nnode 22 should be visited before node 8\nnode 22 should be visited before node 14\nnode 23 should be visited before node 9\nnode 23 should be visited before node 14\nnode 24 should be visited before node 21\nnode 24 should be visited before node 18\nnode 24 should be visited before node 8\nnode 24 should be visited before node 11\nnode 24 should be visited before node 19\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 1,6,17,5,4,16,12,7,23,13,3,0,22,9,20,24,15,18,21,2,10,8,14,11,19.", "difficulty": "medium", "doc_id": "28"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 12 nodes numbered from 0 to 11:\nnode 0 should be visited before node 1\nnode 0 should be visited before node 10\nnode 1 should be visited before node 4\nnode 1 should be visited before node 3\nnode 1 should be visited before node 10\nnode 4 should be visited before node 10\nnode 4 should be visited before node 2\nnode 5 should be visited before node 2\nnode 6 should be visited before node 11\nnode 6 should be visited before node 4\nnode 6 should be visited before node 5\nnode 6 should be visited before node 2\nnode 7 should be visited before node 8\nnode 7 should be visited before node 11\nnode 7 should be visited before node 4\nnode 7 should be visited before node 5\nnode 7 should be visited before node 2\nnode 8 should be visited before node 11\nnode 8 should be visited before node 9\nnode 8 should be visited before node 0\nnode 8 should be visited before node 1\nnode 8 should be visited before node 4\nnode 8 should be visited before node 3\nnode 8 should be visited before node 10\nnode 9 should be visited before node 0\nnode 9 should be visited before node 10\nnode 9 should be visited before node 5\nnode 9 should be visited before node 2\nnode 10 should be visited before node 5\nnode 10 should be visited before node 2\nnode 11 should be visited before node 1\nnode 11 should be visited before node 4\nnode 11 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 6,7,8,11,9,0,1,4,3,10,5,2.", "difficulty": "medium", "doc_id": "29"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 20 nodes numbered from 0 to 19:\nnode 0 should be visited before node 19\nnode 0 should be visited before node 6\nnode 0 should be visited before node 18\nnode 1 should be visited before node 0\nnode 1 should be visited before node 18\nnode 2 should be visited before node 18\nnode 3 should be visited before node 17\nnode 3 should be visited before node 1\nnode 3 should be visited before node 14\nnode 3 should be visited before node 2\nnode 4 should be visited before node 16\nnode 4 should be visited before node 2\nnode 5 should be visited before node 13\nnode 5 should be visited before node 7\nnode 5 should be visited before node 9\nnode 5 should be visited before node 15\nnode 5 should be visited before node 1\nnode 5 should be visited before node 19\nnode 5 should be visited before node 6\nnode 6 should be visited before node 18\nnode 7 should be visited before node 16\nnode 7 should be visited before node 9\nnode 7 should be visited before node 3\nnode 7 should be visited before node 15\nnode 7 should be visited before node 17\nnode 7 should be visited before node 10\nnode 8 should be visited before node 1\nnode 8 should be visited before node 14\nnode 8 should be visited before node 0\nnode 9 should be visited before node 3\nnode 9 should be visited before node 1\nnode 9 should be visited before node 14\nnode 9 should be visited before node 18\nnode 10 should be visited before node 0\nnode 10 should be visited before node 19\nnode 10 should be visited before node 2\nnode 10 should be visited before node 6\nnode 11 should be visited before node 8\nnode 11 should be visited before node 17\nnode 11 should be visited before node 1\nnode 11 should be visited before node 19\nnode 12 should be visited before node 11\nnode 12 should be visited before node 5\nnode 12 should be visited before node 16\nnode 13 should be visited before node 16\nnode 13 should be visited before node 3\nnode 13 should be visited before node 15\nnode 13 should be visited before node 1\nnode 13 should be visited before node 6\nnode 14 should be visited before node 10\nnode 15 should be visited before node 17\nnode 15 should be visited before node 1\nnode 15 should be visited before node 10\nnode 15 should be visited before node 0\nnode 15 should be visited before node 2\nnode 15 should be visited before node 18\nnode 16 should be visited before node 3\nnode 16 should be visited before node 17\nnode 16 should be visited before node 14\nnode 16 should be visited before node 10\nnode 16 should be visited before node 18\nnode 17 should be visited before node 0\nnode 19 should be visited before node 6\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 4,12,11,5,8,13,7,16,9,15,3,17,1,14,10,0,2,19,6,18.", "difficulty": "medium", "doc_id": "30"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 20 nodes numbered from 0 to 19:\nnode 0 should be visited before node 13\nnode 0 should be visited before node 2\nnode 0 should be visited before node 10\nnode 0 should be visited before node 1\nnode 0 should be visited before node 11\nnode 0 should be visited before node 12\nnode 0 should be visited before node 17\nnode 0 should be visited before node 18\nnode 0 should be visited before node 5\nnode 0 should be visited before node 4\nnode 1 should be visited before node 9\nnode 1 should be visited before node 8\nnode 1 should be visited before node 12\nnode 1 should be visited before node 3\nnode 1 should be visited before node 5\nnode 1 should be visited before node 6\nnode 2 should be visited before node 19\nnode 2 should be visited before node 9\nnode 2 should be visited before node 11\nnode 2 should be visited before node 8\nnode 2 should be visited before node 17\nnode 2 should be visited before node 18\nnode 2 should be visited before node 4\nnode 5 should be visited before node 6\nnode 5 should be visited before node 4\nnode 6 should be visited before node 4\nnode 7 should be visited before node 14\nnode 7 should be visited before node 0\nnode 7 should be visited before node 13\nnode 7 should be visited before node 2\nnode 7 should be visited before node 10\nnode 7 should be visited before node 19\nnode 7 should be visited before node 11\nnode 7 should be visited before node 12\nnode 8 should be visited before node 12\nnode 8 should be visited before node 17\nnode 8 should be visited before node 18\nnode 8 should be visited before node 3\nnode 8 should be visited before node 5\nnode 8 should be visited before node 6\nnode 8 should be visited before node 4\nnode 9 should be visited before node 8\nnode 9 should be visited before node 3\nnode 9 should be visited before node 6\nnode 9 should be visited before node 4\nnode 10 should be visited before node 1\nnode 10 should be visited before node 9\nnode 10 should be visited before node 11\nnode 10 should be visited before node 8\nnode 10 should be visited before node 6\nnode 11 should be visited before node 8\nnode 11 should be visited before node 12\nnode 11 should be visited before node 17\nnode 11 should be visited before node 18\nnode 11 should be visited before node 3\nnode 11 should be visited before node 5\nnode 12 should be visited before node 17\nnode 12 should be visited before node 18\nnode 12 should be visited before node 3\nnode 12 should be visited before node 5\nnode 13 should be visited before node 8\nnode 13 should be visited before node 5\nnode 13 should be visited before node 6\nnode 13 should be visited before node 4\nnode 14 should be visited before node 0\nnode 14 should be visited before node 19\nnode 14 should be visited before node 9\nnode 14 should be visited before node 8\nnode 14 should be visited before node 12\nnode 14 should be visited before node 17\nnode 15 should be visited before node 19\nnode 15 should be visited before node 9\nnode 15 should be visited before node 11\nnode 15 should be visited before node 5\nnode 15 should be visited before node 6\nnode 15 should be visited before node 4\nnode 16 should be visited before node 15\nnode 16 should be visited before node 1\nnode 16 should be visited before node 11\nnode 16 should be visited before node 17\nnode 16 should be visited before node 18\nnode 17 should be visited before node 3\nnode 17 should be visited before node 5\nnode 17 should be visited before node 6\nnode 18 should be visited before node 3\nnode 18 should be visited before node 5\nnode 18 should be visited before node 6\nnode 18 should be visited before node 4\nnode 19 should be visited before node 9\nnode 19 should be visited before node 8\nnode 19 should be visited before node 17\nnode 19 should be visited before node 4\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 7,16,14,15,0,13,2,10,19,1,11,9,8,12,17,18,3,5,6,4.", "difficulty": "medium", "doc_id": "31"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 14 nodes numbered from 0 to 13:\nnode 0 should be visited before node 10\nnode 0 should be visited before node 13\nnode 0 should be visited before node 1\nnode 1 should be visited before node 11\nnode 1 should be visited before node 9\nnode 1 should be visited before node 6\nnode 2 should be visited before node 13\nnode 2 should be visited before node 5\nnode 3 should be visited before node 9\nnode 4 should be visited before node 8\nnode 4 should be visited before node 13\nnode 4 should be visited before node 7\nnode 4 should be visited before node 11\nnode 5 should be visited before node 3\nnode 5 should be visited before node 9\nnode 5 should be visited before node 6\nnode 7 should be visited before node 11\nnode 8 should be visited before node 12\nnode 8 should be visited before node 3\nnode 10 should be visited before node 13\nnode 10 should be visited before node 1\nnode 10 should be visited before node 5\nnode 10 should be visited before node 3\nnode 10 should be visited before node 11\nnode 12 should be visited before node 7\nnode 12 should be visited before node 11\nnode 12 should be visited before node 9\nnode 13 should be visited before node 1\nnode 13 should be visited before node 12\nnode 13 should be visited before node 9\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 0,2,4,10,8,13,5,1,12,3,6,7,9,11.", "difficulty": "medium", "doc_id": "32"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 23 nodes numbered from 0 to 22:\nnode 0 should be visited before node 10\nnode 0 should be visited before node 12\nnode 0 should be visited before node 14\nnode 0 should be visited before node 18\nnode 0 should be visited before node 9\nnode 0 should be visited before node 16\nnode 0 should be visited before node 5\nnode 0 should be visited before node 15\nnode 0 should be visited before node 11\nnode 0 should be visited before node 22\nnode 0 should be visited before node 2\nnode 0 should be visited before node 13\nnode 0 should be visited before node 3\nnode 1 should be visited before node 15\nnode 1 should be visited before node 19\nnode 1 should be visited before node 11\nnode 1 should be visited before node 22\nnode 1 should be visited before node 2\nnode 1 should be visited before node 13\nnode 1 should be visited before node 3\nnode 2 should be visited before node 13\nnode 4 should be visited before node 0\nnode 4 should be visited before node 12\nnode 4 should be visited before node 14\nnode 4 should be visited before node 18\nnode 4 should be visited before node 9\nnode 4 should be visited before node 1\nnode 4 should be visited before node 5\nnode 4 should be visited before node 15\nnode 4 should be visited before node 19\nnode 4 should be visited before node 11\nnode 4 should be visited before node 22\nnode 4 should be visited before node 17\nnode 4 should be visited before node 2\nnode 4 should be visited before node 13\nnode 4 should be visited before node 3\nnode 5 should be visited before node 15\nnode 5 should be visited before node 19\nnode 5 should be visited before node 11\nnode 5 should be visited before node 17\nnode 5 should be visited before node 3\nnode 6 should be visited before node 4\nnode 6 should be visited before node 0\nnode 6 should be visited before node 12\nnode 6 should be visited before node 18\nnode 6 should be visited before node 9\nnode 6 should be visited before node 1\nnode 6 should be visited before node 16\nnode 6 should be visited before node 7\nnode 6 should be visited before node 5\nnode 6 should be visited before node 15\nnode 6 should be visited before node 19\nnode 6 should be visited before node 17\nnode 6 should be visited before node 2\nnode 6 should be visited before node 3\nnode 7 should be visited before node 5\nnode 7 should be visited before node 15\nnode 7 should be visited before node 22\nnode 7 should be visited before node 17\nnode 7 should be visited before node 2\nnode 7 should be visited before node 3\nnode 8 should be visited before node 20\nnode 8 should be visited before node 4\nnode 8 should be visited before node 10\nnode 8 should be visited before node 12\nnode 8 should be visited before node 14\nnode 8 should be visited before node 18\nnode 8 should be visited before node 9\nnode 8 should be visited before node 1\nnode 8 should be visited before node 7\nnode 8 should be visited before node 5\nnode 8 should be visited before node 15\nnode 8 should be visited before node 19\nnode 8 should be visited before node 11\nnode 8 should be visited before node 2\nnode 8 should be visited before node 13\nnode 8 should be visited before node 3\nnode 9 should be visited before node 1\nnode 9 should be visited before node 16\nnode 9 should be visited before node 7\nnode 9 should be visited before node 15\nnode 9 should be visited before node 11\nnode 9 should be visited before node 22\nnode 9 should be visited before node 2\nnode 9 should be visited before node 13\nnode 10 should be visited before node 12\nnode 10 should be visited before node 14\nnode 10 should be visited before node 18\nnode 10 should be visited before node 1\nnode 10 should be visited before node 16\nnode 10 should be visited before node 5\nnode 10 should be visited before node 15\nnode 10 should be visited before node 19\nnode 10 should be visited before node 11\nnode 10 should be visited before node 13\nnode 10 should be visited before node 3\nnode 11 should be visited before node 22\nnode 11 should be visited before node 3\nnode 12 should be visited before node 14\nnode 12 should be visited before node 16\nnode 12 should be visited before node 7\nnode 12 should be visited before node 5\nnode 12 should be visited before node 19\nnode 12 should be visited before node 11\nnode 12 should be visited before node 22\nnode 12 should be visited before node 17\nnode 12 should be visited before node 2\nnode 12 should be visited before node 13\nnode 12 should be visited before node 3\nnode 13 should be visited before node 3\nnode 14 should be visited before node 18\nnode 14 should be visited before node 9\nnode 14 should be visited before node 16\nnode 14 should be visited before node 7\nnode 14 should be visited before node 5\nnode 14 should be visited before node 15\nnode 14 should be visited before node 11\nnode 14 should be visited before node 22\nnode 14 should be visited before node 17\nnode 14 should be visited before node 2\nnode 15 should be visited before node 19\nnode 15 should be visited before node 11\nnode 15 should be visited before node 22\nnode 15 should be visited before node 17\nnode 15 should be visited before node 13\nnode 15 should be visited before node 3\nnode 16 should be visited before node 5\nnode 16 should be visited before node 15\nnode 16 should be visited before node 19\nnode 16 should be visited before node 11\nnode 16 should be visited before node 3\nnode 17 should be visited before node 2\nnode 17 should be visited before node 13\nnode 17 should be visited before node 3\nnode 18 should be visited before node 9\nnode 18 should be visited before node 16\nnode 18 should be visited before node 7\nnode 18 should be visited before node 5\nnode 18 should be visited before node 15\nnode 18 should be visited before node 19\nnode 18 should be visited before node 11\nnode 18 should be visited before node 22\nnode 18 should be visited before node 17\nnode 18 should be visited before node 2\nnode 18 should be visited before node 13\nnode 18 should be visited before node 3\nnode 19 should be visited before node 17\nnode 19 should be visited before node 13\nnode 19 should be visited before node 3\nnode 20 should be visited before node 4\nnode 20 should be visited before node 10\nnode 20 should be visited before node 12\nnode 20 should be visited before node 14\nnode 20 should be visited before node 9\nnode 20 should be visited before node 1\nnode 20 should be visited before node 16\nnode 20 should be visited before node 7\nnode 20 should be visited before node 5\nnode 20 should be visited before node 15\nnode 20 should be visited before node 11\nnode 20 should be visited before node 22\nnode 20 should be visited before node 17\nnode 20 should be visited before node 13\nnode 21 should be visited before node 20\nnode 21 should be visited before node 4\nnode 21 should be visited before node 0\nnode 21 should be visited before node 10\nnode 21 should be visited before node 12\nnode 21 should be visited before node 18\nnode 21 should be visited before node 16\nnode 21 should be visited before node 7\nnode 21 should be visited before node 5\nnode 21 should be visited before node 11\nnode 21 should be visited before node 22\nnode 21 should be visited before node 2\nnode 21 should be visited before node 3\nnode 22 should be visited before node 17\nnode 22 should be visited before node 2\nnode 22 should be visited before node 3\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 6,8,21,20,4,0,10,12,14,18,9,1,16,7,5,15,19,11,22,17,2,13,3.", "difficulty": "medium", "doc_id": "33"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 14 nodes numbered from 0 to 13:\nnode 0 should be visited before node 8\nnode 0 should be visited before node 6\nnode 0 should be visited before node 2\nnode 0 should be visited before node 12\nnode 0 should be visited before node 9\nnode 0 should be visited before node 10\nnode 0 should be visited before node 5\nnode 0 should be visited before node 11\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 12\nnode 2 should be visited before node 9\nnode 2 should be visited before node 10\nnode 2 should be visited before node 5\nnode 2 should be visited before node 4\nnode 2 should be visited before node 1\nnode 3 should be visited before node 13\nnode 3 should be visited before node 6\nnode 3 should be visited before node 2\nnode 3 should be visited before node 12\nnode 3 should be visited before node 9\nnode 3 should be visited before node 11\nnode 4 should be visited before node 1\nnode 5 should be visited before node 11\nnode 5 should be visited before node 1\nnode 6 should be visited before node 9\nnode 7 should be visited before node 6\nnode 7 should be visited before node 2\nnode 7 should be visited before node 10\nnode 7 should be visited before node 11\nnode 7 should be visited before node 1\nnode 8 should be visited before node 7\nnode 8 should be visited before node 6\nnode 8 should be visited before node 2\nnode 8 should be visited before node 12\nnode 8 should be visited before node 9\nnode 8 should be visited before node 1\nnode 9 should be visited before node 5\nnode 9 should be visited before node 1\nnode 10 should be visited before node 11\nnode 10 should be visited before node 1\nnode 11 should be visited before node 4\nnode 12 should be visited before node 9\nnode 12 should be visited before node 5\nnode 12 should be visited before node 11\nnode 12 should be visited before node 4\nnode 12 should be visited before node 1\nnode 13 should be visited before node 8\nnode 13 should be visited before node 6\nnode 13 should be visited before node 2\nnode 13 should be visited before node 11\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 0,3,13,8,7,6,2,12,10,9,5,11,4,1.", "difficulty": "medium", "doc_id": "34"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 10 nodes numbered from 0 to 9:\nnode 0 should be visited before node 5\nnode 0 should be visited before node 7\nnode 0 should be visited before node 9\nnode 2 should be visited before node 1\nnode 2 should be visited before node 9\nnode 3 should be visited before node 5\nnode 4 should be visited before node 9\nnode 5 should be visited before node 2\nnode 6 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 3,4,6,8,0,5,7,2,1,9.", "difficulty": "easy", "doc_id": "35"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 17 nodes numbered from 0 to 16:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 6\nnode 2 should be visited before node 4\nnode 3 should be visited before node 2\nnode 3 should be visited before node 1\nnode 4 should be visited before node 8\nnode 4 should be visited before node 5\nnode 4 should be visited before node 10\nnode 4 should be visited before node 1\nnode 5 should be visited before node 6\nnode 7 should be visited before node 0\nnode 7 should be visited before node 4\nnode 7 should be visited before node 13\nnode 7 should be visited before node 5\nnode 7 should be visited before node 10\nnode 8 should be visited before node 12\nnode 9 should be visited before node 16\nnode 9 should be visited before node 15\nnode 9 should be visited before node 4\nnode 9 should be visited before node 13\nnode 9 should be visited before node 10\nnode 9 should be visited before node 6\nnode 10 should be visited before node 1\nnode 11 should be visited before node 16\nnode 11 should be visited before node 15\nnode 11 should be visited before node 12\nnode 11 should be visited before node 13\nnode 11 should be visited before node 6\nnode 12 should be visited before node 5\nnode 12 should be visited before node 10\nnode 12 should be visited before node 6\nnode 14 should be visited before node 3\nnode 14 should be visited before node 12\nnode 14 should be visited before node 13\nnode 14 should be visited before node 10\nnode 15 should be visited before node 1\nnode 16 should be visited before node 15\nnode 16 should be visited before node 12\nnode 16 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 7,9,11,14,0,16,3,13,15,2,4,8,12,5,10,1,6.", "difficulty": "medium", "doc_id": "36"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 30 nodes numbered from 0 to 29:\nnode 0 should be visited before node 12\nnode 2 should be visited before node 25\nnode 2 should be visited before node 26\nnode 2 should be visited before node 23\nnode 2 should be visited before node 21\nnode 2 should be visited before node 0\nnode 4 should be visited before node 2\nnode 4 should be visited before node 25\nnode 4 should be visited before node 3\nnode 4 should be visited before node 18\nnode 5 should be visited before node 21\nnode 5 should be visited before node 0\nnode 6 should be visited before node 11\nnode 6 should be visited before node 24\nnode 6 should be visited before node 2\nnode 6 should be visited before node 3\nnode 6 should be visited before node 21\nnode 6 should be visited before node 8\nnode 6 should be visited before node 0\nnode 6 should be visited before node 12\nnode 7 should be visited before node 10\nnode 7 should be visited before node 11\nnode 7 should be visited before node 2\nnode 7 should be visited before node 13\nnode 7 should be visited before node 29\nnode 7 should be visited before node 26\nnode 7 should be visited before node 5\nnode 7 should be visited before node 1\nnode 7 should be visited before node 8\nnode 7 should be visited before node 9\nnode 8 should be visited before node 9\nnode 8 should be visited before node 0\nnode 10 should be visited before node 24\nnode 10 should be visited before node 19\nnode 10 should be visited before node 16\nnode 10 should be visited before node 22\nnode 10 should be visited before node 4\nnode 10 should be visited before node 29\nnode 10 should be visited before node 26\nnode 10 should be visited before node 3\nnode 10 should be visited before node 23\nnode 10 should be visited before node 20\nnode 11 should be visited before node 19\nnode 11 should be visited before node 22\nnode 11 should be visited before node 13\nnode 11 should be visited before node 29\nnode 11 should be visited before node 26\nnode 11 should be visited before node 3\nnode 11 should be visited before node 23\nnode 11 should be visited before node 18\nnode 11 should be visited before node 9\nnode 11 should be visited before node 0\nnode 14 should be visited before node 11\nnode 14 should be visited before node 24\nnode 14 should be visited before node 2\nnode 14 should be visited before node 25\nnode 14 should be visited before node 26\nnode 14 should be visited before node 28\nnode 14 should be visited before node 5\nnode 14 should be visited before node 21\nnode 14 should be visited before node 18\nnode 14 should be visited before node 1\nnode 14 should be visited before node 12\nnode 15 should be visited before node 19\nnode 15 should be visited before node 22\nnode 15 should be visited before node 25\nnode 15 should be visited before node 26\nnode 15 should be visited before node 23\nnode 15 should be visited before node 17\nnode 15 should be visited before node 8\nnode 15 should be visited before node 9\nnode 15 should be visited before node 0\nnode 16 should be visited before node 22\nnode 16 should be visited before node 13\nnode 16 should be visited before node 29\nnode 16 should be visited before node 28\nnode 16 should be visited before node 5\nnode 16 should be visited before node 21\nnode 16 should be visited before node 18\nnode 16 should be visited before node 0\nnode 17 should be visited before node 20\nnode 17 should be visited before node 1\nnode 17 should be visited before node 0\nnode 17 should be visited before node 12\nnode 18 should be visited before node 12\nnode 19 should be visited before node 16\nnode 19 should be visited before node 2\nnode 19 should be visited before node 29\nnode 19 should be visited before node 26\nnode 19 should be visited before node 3\nnode 19 should be visited before node 23\nnode 19 should be visited before node 21\nnode 19 should be visited before node 18\nnode 19 should be visited before node 1\nnode 21 should be visited before node 1\nnode 21 should be visited before node 8\nnode 21 should be visited before node 0\nnode 22 should be visited before node 23\nnode 22 should be visited before node 21\nnode 22 should be visited before node 1\nnode 23 should be visited before node 17\nnode 23 should be visited before node 1\nnode 23 should be visited before node 8\nnode 23 should be visited before node 0\nnode 23 should be visited before node 12\nnode 24 should be visited before node 16\nnode 24 should be visited before node 22\nnode 24 should be visited before node 4\nnode 24 should be visited before node 29\nnode 24 should be visited before node 3\nnode 24 should be visited before node 23\nnode 24 should be visited before node 18\nnode 24 should be visited before node 20\nnode 25 should be visited before node 26\nnode 25 should be visited before node 3\nnode 26 should be visited before node 5\nnode 26 should be visited before node 18\nnode 26 should be visited before node 20\nnode 27 should be visited before node 24\nnode 27 should be visited before node 19\nnode 27 should be visited before node 16\nnode 27 should be visited before node 4\nnode 27 should be visited before node 2\nnode 27 should be visited before node 25\nnode 27 should be visited before node 26\nnode 27 should be visited before node 5\nnode 27 should be visited before node 21\nnode 27 should be visited before node 12\nnode 28 should be visited before node 17\nnode 28 should be visited before node 20\nnode 28 should be visited before node 9\nnode 29 should be visited before node 26\nnode 29 should be visited before node 3\nnode 29 should be visited before node 28\nnode 29 should be visited before node 18\nnode 29 should be visited before node 20\nnode 29 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 6,7,14,15,27,10,11,24,19,4,16,2,22,13,29,25,23,28,26,3,17,5,18,20,21,1,8,9,0,12.", "difficulty": "hard", "doc_id": "37"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 8 nodes numbered from 0 to 7:\nnode 0 should be visited before node 7\nnode 0 should be visited before node 6\nnode 0 should be visited before node 3\nnode 0 should be visited before node 5\nnode 0 should be visited before node 1\nnode 0 should be visited before node 4\nnode 1 should be visited before node 4\nnode 2 should be visited before node 3\nnode 2 should be visited before node 1\nnode 2 should be visited before node 4\nnode 3 should be visited before node 5\nnode 3 should be visited before node 1\nnode 3 should be visited before node 4\nnode 5 should be visited before node 1\nnode 6 should be visited before node 2\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nnode 6 should be visited before node 1\nnode 6 should be visited before node 4\nnode 7 should be visited before node 6\nnode 7 should be visited before node 2\nnode 7 should be visited before node 3\nnode 7 should be visited before node 5\nnode 7 should be visited before node 1\nnode 7 should be visited before node 4\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 0,7,6,2,3,5,1,4.", "difficulty": "easy", "doc_id": "38"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 26 nodes numbered from 0 to 25:\nnode 0 should be visited before node 13\nnode 0 should be visited before node 12\nnode 0 should be visited before node 22\nnode 1 should be visited before node 3\nnode 1 should be visited before node 23\nnode 1 should be visited before node 19\nnode 1 should be visited before node 8\nnode 1 should be visited before node 5\nnode 1 should be visited before node 20\nnode 1 should be visited before node 10\nnode 2 should be visited before node 12\nnode 3 should be visited before node 23\nnode 3 should be visited before node 4\nnode 3 should be visited before node 19\nnode 3 should be visited before node 11\nnode 3 should be visited before node 14\nnode 3 should be visited before node 7\nnode 3 should be visited before node 10\nnode 3 should be visited before node 24\nnode 3 should be visited before node 15\nnode 3 should be visited before node 0\nnode 3 should be visited before node 13\nnode 4 should be visited before node 7\nnode 4 should be visited before node 25\nnode 4 should be visited before node 2\nnode 4 should be visited before node 22\nnode 4 should be visited before node 16\nnode 5 should be visited before node 7\nnode 6 should be visited before node 15\nnode 7 should be visited before node 20\nnode 7 should be visited before node 15\nnode 7 should be visited before node 22\nnode 8 should be visited before node 20\nnode 8 should be visited before node 2\nnode 8 should be visited before node 10\nnode 8 should be visited before node 24\nnode 8 should be visited before node 22\nnode 9 should be visited before node 21\nnode 9 should be visited before node 5\nnode 9 should be visited before node 2\nnode 9 should be visited before node 10\nnode 9 should be visited before node 24\nnode 9 should be visited before node 0\nnode 9 should be visited before node 12\nnode 10 should be visited before node 13\nnode 11 should be visited before node 8\nnode 11 should be visited before node 5\nnode 11 should be visited before node 20\nnode 11 should be visited before node 12\nnode 11 should be visited before node 22\nnode 11 should be visited before node 16\nnode 14 should be visited before node 2\nnode 14 should be visited before node 15\nnode 14 should be visited before node 22\nnode 14 should be visited before node 16\nnode 15 should be visited before node 0\nnode 17 should be visited before node 18\nnode 17 should be visited before node 24\nnode 17 should be visited before node 15\nnode 17 should be visited before node 0\nnode 18 should be visited before node 7\nnode 18 should be visited before node 13\nnode 19 should be visited before node 8\nnode 19 should be visited before node 20\nnode 19 should be visited before node 2\nnode 19 should be visited before node 10\nnode 19 should be visited before node 0\nnode 19 should be visited before node 13\nnode 19 should be visited before node 12\nnode 19 should be visited before node 16\nnode 20 should be visited before node 24\nnode 20 should be visited before node 15\nnode 20 should be visited before node 22\nnode 21 should be visited before node 19\nnode 21 should be visited before node 18\nnode 21 should be visited before node 24\nnode 21 should be visited before node 15\nnode 21 should be visited before node 0\nnode 21 should be visited before node 13\nnode 21 should be visited before node 12\nnode 22 should be visited before node 16\nnode 23 should be visited before node 21\nnode 23 should be visited before node 18\nnode 23 should be visited before node 5\nnode 23 should be visited before node 7\nnode 23 should be visited before node 20\nnode 23 should be visited before node 24\nnode 23 should be visited before node 6\nnode 24 should be visited before node 6\nnode 24 should be visited before node 15\nnode 24 should be visited before node 13\nnode 24 should be visited before node 16\nnode 25 should be visited before node 2\nnode 25 should be visited before node 10\nnode 25 should be visited before node 22\nnode 25 should be visited before node 16\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 1,9,17,3,23,4,11,14,21,25,5,19,18,8,7,2,10,20,24,6,15,0,13,12,22,16.", "difficulty": "hard", "doc_id": "39"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 24 nodes numbered from 0 to 23:\nnode 0 should be visited before node 15\nnode 0 should be visited before node 1\nnode 0 should be visited before node 5\nnode 0 should be visited before node 3\nnode 0 should be visited before node 13\nnode 1 should be visited before node 5\nnode 1 should be visited before node 3\nnode 2 should be visited before node 0\nnode 2 should be visited before node 10\nnode 2 should be visited before node 1\nnode 2 should be visited before node 5\nnode 2 should be visited before node 3\nnode 2 should be visited before node 13\nnode 3 should be visited before node 13\nnode 4 should be visited before node 11\nnode 4 should be visited before node 0\nnode 4 should be visited before node 10\nnode 4 should be visited before node 15\nnode 4 should be visited before node 12\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 4 should be visited before node 13\nnode 5 should be visited before node 13\nnode 6 should be visited before node 4\nnode 6 should be visited before node 2\nnode 6 should be visited before node 0\nnode 6 should be visited before node 10\nnode 6 should be visited before node 15\nnode 6 should be visited before node 1\nnode 6 should be visited before node 5\nnode 6 should be visited before node 3\nnode 6 should be visited before node 13\nnode 7 should be visited before node 17\nnode 7 should be visited before node 23\nnode 7 should be visited before node 4\nnode 7 should be visited before node 22\nnode 7 should be visited before node 2\nnode 7 should be visited before node 0\nnode 7 should be visited before node 10\nnode 7 should be visited before node 15\nnode 7 should be visited before node 1\nnode 7 should be visited before node 5\nnode 7 should be visited before node 3\nnode 7 should be visited before node 13\nnode 8 should be visited before node 7\nnode 8 should be visited before node 17\nnode 8 should be visited before node 23\nnode 8 should be visited before node 6\nnode 8 should be visited before node 22\nnode 8 should be visited before node 11\nnode 8 should be visited before node 2\nnode 8 should be visited before node 0\nnode 8 should be visited before node 10\nnode 8 should be visited before node 15\nnode 8 should be visited before node 12\nnode 8 should be visited before node 1\nnode 8 should be visited before node 3\nnode 8 should be visited before node 13\nnode 9 should be visited before node 20\nnode 9 should be visited before node 14\nnode 9 should be visited before node 18\nnode 9 should be visited before node 17\nnode 9 should be visited before node 6\nnode 9 should be visited before node 4\nnode 9 should be visited before node 22\nnode 9 should be visited before node 11\nnode 9 should be visited before node 0\nnode 9 should be visited before node 10\nnode 9 should be visited before node 1\nnode 9 should be visited before node 3\nnode 10 should be visited before node 15\nnode 10 should be visited before node 12\nnode 10 should be visited before node 1\nnode 10 should be visited before node 5\nnode 11 should be visited before node 10\nnode 11 should be visited before node 15\nnode 11 should be visited before node 12\nnode 11 should be visited before node 1\nnode 11 should be visited before node 5\nnode 11 should be visited before node 13\nnode 12 should be visited before node 1\nnode 12 should be visited before node 5\nnode 12 should be visited before node 3\nnode 12 should be visited before node 13\nnode 14 should be visited before node 18\nnode 14 should be visited before node 8\nnode 14 should be visited before node 7\nnode 14 should be visited before node 17\nnode 14 should be visited before node 6\nnode 14 should be visited before node 22\nnode 14 should be visited before node 11\nnode 14 should be visited before node 2\nnode 14 should be visited before node 0\nnode 14 should be visited before node 10\nnode 14 should be visited before node 15\nnode 14 should be visited before node 12\nnode 14 should be visited before node 1\nnode 15 should be visited before node 12\nnode 15 should be visited before node 1\nnode 15 should be visited before node 5\nnode 15 should be visited before node 3\nnode 15 should be visited before node 13\nnode 16 should be visited before node 9\nnode 16 should be visited before node 20\nnode 16 should be visited before node 18\nnode 16 should be visited before node 8\nnode 16 should be visited before node 7\nnode 16 should be visited before node 17\nnode 16 should be visited before node 6\nnode 16 should be visited before node 4\nnode 16 should be visited before node 22\nnode 16 should be visited before node 11\nnode 16 should be visited before node 2\nnode 16 should be visited before node 0\nnode 16 should be visited before node 10\nnode 16 should be visited before node 15\nnode 16 should be visited before node 12\nnode 16 should be visited before node 3\nnode 17 should be visited before node 6\nnode 17 should be visited before node 2\nnode 17 should be visited before node 10\nnode 17 should be visited before node 12\nnode 17 should be visited before node 3\nnode 17 should be visited before node 13\nnode 18 should be visited before node 8\nnode 18 should be visited before node 7\nnode 18 should be visited before node 17\nnode 18 should be visited before node 6\nnode 18 should be visited before node 4\nnode 18 should be visited before node 22\nnode 18 should be visited before node 2\nnode 18 should be visited before node 0\nnode 18 should be visited before node 10\nnode 18 should be visited before node 12\nnode 18 should be visited before node 1\nnode 18 should be visited before node 3\nnode 18 should be visited before node 13\nnode 19 should be visited before node 21\nnode 19 should be visited before node 16\nnode 19 should be visited before node 9\nnode 19 should be visited before node 14\nnode 19 should be visited before node 8\nnode 19 should be visited before node 7\nnode 19 should be visited before node 17\nnode 19 should be visited before node 23\nnode 19 should be visited before node 6\nnode 19 should be visited before node 4\nnode 19 should be visited before node 22\nnode 19 should be visited before node 11\nnode 19 should be visited before node 2\nnode 19 should be visited before node 0\nnode 19 should be visited before node 10\nnode 19 should be visited before node 12\nnode 19 should be visited before node 5\nnode 19 should be visited before node 3\nnode 19 should be visited before node 13\nnode 20 should be visited before node 14\nnode 20 should be visited before node 18\nnode 20 should be visited before node 8\nnode 20 should be visited before node 17\nnode 20 should be visited before node 23\nnode 20 should be visited before node 6\nnode 20 should be visited before node 4\nnode 20 should be visited before node 22\nnode 20 should be visited before node 2\nnode 20 should be visited before node 0\nnode 20 should be visited before node 10\nnode 20 should be visited before node 15\nnode 20 should be visited before node 12\nnode 20 should be visited before node 1\nnode 21 should be visited before node 16\nnode 21 should be visited before node 20\nnode 21 should be visited before node 14\nnode 21 should be visited before node 18\nnode 21 should be visited before node 8\nnode 21 should be visited before node 7\nnode 21 should be visited before node 17\nnode 21 should be visited before node 6\nnode 21 should be visited before node 22\nnode 21 should be visited before node 2\nnode 21 should be visited before node 10\nnode 21 should be visited before node 15\nnode 21 should be visited before node 1\nnode 21 should be visited before node 5\nnode 21 should be visited before node 3\nnode 22 should be visited before node 11\nnode 22 should be visited before node 2\nnode 22 should be visited before node 0\nnode 22 should be visited before node 15\nnode 22 should be visited before node 12\nnode 22 should be visited before node 13\nnode 23 should be visited before node 6\nnode 23 should be visited before node 4\nnode 23 should be visited before node 22\nnode 23 should be visited before node 2\nnode 23 should be visited before node 0\nnode 23 should be visited before node 10\nnode 23 should be visited before node 15\nnode 23 should be visited before node 12\nnode 23 should be visited before node 1\nnode 23 should be visited before node 3\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 19,21,16,9,20,14,18,8,7,17,23,6,22,4,2,11,0,10,15,12,1,5,3,13.", "difficulty": "medium", "doc_id": "40"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 18 nodes numbered from 0 to 17:\nnode 0 should be visited before node 12\nnode 0 should be visited before node 13\nnode 1 should be visited before node 10\nnode 1 should be visited before node 4\nnode 1 should be visited before node 8\nnode 1 should be visited before node 0\nnode 1 should be visited before node 12\nnode 2 should be visited before node 8\nnode 2 should be visited before node 14\nnode 2 should be visited before node 0\nnode 2 should be visited before node 12\nnode 2 should be visited before node 5\nnode 3 should be visited before node 17\nnode 3 should be visited before node 7\nnode 3 should be visited before node 13\nnode 4 should be visited before node 2\nnode 4 should be visited before node 14\nnode 4 should be visited before node 7\nnode 4 should be visited before node 15\nnode 4 should be visited before node 13\nnode 5 should be visited before node 15\nnode 5 should be visited before node 13\nnode 6 should be visited before node 5\nnode 6 should be visited before node 15\nnode 7 should be visited before node 5\nnode 7 should be visited before node 11\nnode 7 should be visited before node 13\nnode 8 should be visited before node 3\nnode 8 should be visited before node 17\nnode 8 should be visited before node 5\nnode 9 should be visited before node 15\nnode 10 should be visited before node 2\nnode 10 should be visited before node 8\nnode 10 should be visited before node 3\nnode 10 should be visited before node 12\nnode 10 should be visited before node 5\nnode 10 should be visited before node 15\nnode 11 should be visited before node 15\nnode 12 should be visited before node 6\nnode 14 should be visited before node 12\nnode 14 should be visited before node 9\nnode 15 should be visited before node 13\nnode 16 should be visited before node 12\nnode 16 should be visited before node 5\nnode 16 should be visited before node 15\nnode 16 should be visited before node 13\nnode 17 should be visited before node 0\nnode 17 should be visited before node 7\nnode 17 should be visited before node 13\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 1,16,10,4,2,8,14,3,9,17,0,7,12,11,6,5,15,13.", "difficulty": "medium", "doc_id": "41"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 34 nodes numbered from 0 to 33:\nnode 0 should be visited before node 32\nnode 0 should be visited before node 5\nnode 0 should be visited before node 24\nnode 0 should be visited before node 9\nnode 0 should be visited before node 19\nnode 0 should be visited before node 11\nnode 0 should be visited before node 22\nnode 0 should be visited before node 26\nnode 1 should be visited before node 13\nnode 1 should be visited before node 15\nnode 1 should be visited before node 30\nnode 2 should be visited before node 9\nnode 2 should be visited before node 3\nnode 2 should be visited before node 17\nnode 2 should be visited before node 23\nnode 2 should be visited before node 18\nnode 2 should be visited before node 7\nnode 2 should be visited before node 11\nnode 2 should be visited before node 26\nnode 2 should be visited before node 30\nnode 3 should be visited before node 17\nnode 3 should be visited before node 12\nnode 3 should be visited before node 21\nnode 3 should be visited before node 27\nnode 3 should be visited before node 7\nnode 3 should be visited before node 11\nnode 3 should be visited before node 30\nnode 4 should be visited before node 33\nnode 4 should be visited before node 31\nnode 4 should be visited before node 6\nnode 4 should be visited before node 2\nnode 4 should be visited before node 24\nnode 4 should be visited before node 9\nnode 4 should be visited before node 16\nnode 4 should be visited before node 20\nnode 4 should be visited before node 17\nnode 4 should be visited before node 23\nnode 4 should be visited before node 1\nnode 4 should be visited before node 21\nnode 4 should be visited before node 27\nnode 4 should be visited before node 11\nnode 4 should be visited before node 26\nnode 4 should be visited before node 30\nnode 5 should be visited before node 2\nnode 5 should be visited before node 16\nnode 5 should be visited before node 17\nnode 5 should be visited before node 15\nnode 5 should be visited before node 21\nnode 5 should be visited before node 22\nnode 5 should be visited before node 26\nnode 6 should be visited before node 5\nnode 6 should be visited before node 24\nnode 6 should be visited before node 10\nnode 6 should be visited before node 16\nnode 6 should be visited before node 20\nnode 6 should be visited before node 19\nnode 6 should be visited before node 15\nnode 6 should be visited before node 11\nnode 6 should be visited before node 22\nnode 7 should be visited before node 30\nnode 8 should be visited before node 33\nnode 8 should be visited before node 31\nnode 8 should be visited before node 10\nnode 8 should be visited before node 3\nnode 8 should be visited before node 1\nnode 8 should be visited before node 27\nnode 8 should be visited before node 7\nnode 9 should be visited before node 16\nnode 9 should be visited before node 13\nnode 9 should be visited before node 26\nnode 9 should be visited before node 30\nnode 10 should be visited before node 20\nnode 10 should be visited before node 18\nnode 10 should be visited before node 30\nnode 11 should be visited before node 30\nnode 12 should be visited before node 18\nnode 12 should be visited before node 13\nnode 12 should be visited before node 15\nnode 12 should be visited before node 21\nnode 12 should be visited before node 27\nnode 12 should be visited before node 22\nnode 12 should be visited before node 30\nnode 13 should be visited before node 7\nnode 13 should be visited before node 28\nnode 13 should be visited before node 11\nnode 13 should be visited before node 26\nnode 14 should be visited before node 2\nnode 14 should be visited before node 3\nnode 14 should be visited before node 16\nnode 14 should be visited before node 20\nnode 14 should be visited before node 17\nnode 14 should be visited before node 12\nnode 14 should be visited before node 21\nnode 14 should be visited before node 27\nnode 14 should be visited before node 7\nnode 14 should be visited before node 28\nnode 14 should be visited before node 30\nnode 15 should be visited before node 7\nnode 16 should be visited before node 23\nnode 16 should be visited before node 19\nnode 16 should be visited before node 1\nnode 16 should be visited before node 18\nnode 16 should be visited before node 15\nnode 16 should be visited before node 27\nnode 16 should be visited before node 7\nnode 16 should be visited before node 11\nnode 16 should be visited before node 22\nnode 17 should be visited before node 23\nnode 17 should be visited before node 21\nnode 17 should be visited before node 22\nnode 17 should be visited before node 26\nnode 18 should be visited before node 13\nnode 18 should be visited before node 21\nnode 18 should be visited before node 7\nnode 18 should be visited before node 11\nnode 18 should be visited before node 26\nnode 19 should be visited before node 1\nnode 20 should be visited before node 17\nnode 20 should be visited before node 13\nnode 20 should be visited before node 27\nnode 20 should be visited before node 7\nnode 21 should be visited before node 22\nnode 23 should be visited before node 19\nnode 23 should be visited before node 18\nnode 23 should be visited before node 13\nnode 23 should be visited before node 15\nnode 23 should be visited before node 7\nnode 23 should be visited before node 30\nnode 24 should be visited before node 20\nnode 24 should be visited before node 18\nnode 24 should be visited before node 15\nnode 24 should be visited before node 28\nnode 24 should be visited before node 22\nnode 24 should be visited before node 26\nnode 25 should be visited before node 31\nnode 25 should be visited before node 2\nnode 25 should be visited before node 10\nnode 25 should be visited before node 9\nnode 25 should be visited before node 3\nnode 25 should be visited before node 23\nnode 25 should be visited before node 27\nnode 25 should be visited before node 26\nnode 27 should be visited before node 30\nnode 29 should be visited before node 32\nnode 29 should be visited before node 33\nnode 29 should be visited before node 31\nnode 29 should be visited before node 5\nnode 29 should be visited before node 2\nnode 29 should be visited before node 24\nnode 29 should be visited before node 9\nnode 29 should be visited before node 16\nnode 29 should be visited before node 23\nnode 29 should be visited before node 19\nnode 29 should be visited before node 22\nnode 31 should be visited before node 24\nnode 31 should be visited before node 10\nnode 31 should be visited before node 9\nnode 31 should be visited before node 17\nnode 31 should be visited before node 12\nnode 31 should be visited before node 18\nnode 31 should be visited before node 21\nnode 31 should be visited before node 11\nnode 31 should be visited before node 22\nnode 32 should be visited before node 31\nnode 32 should be visited before node 16\nnode 32 should be visited before node 13\nnode 32 should be visited before node 27\nnode 32 should be visited before node 11\nnode 32 should be visited before node 22\nnode 33 should be visited before node 31\nnode 33 should be visited before node 10\nnode 33 should be visited before node 9\nnode 33 should be visited before node 3\nnode 33 should be visited before node 23\nnode 33 should be visited before node 18\nnode 33 should be visited before node 28\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 0,4,8,14,25,29,6,32,33,5,31,2,24,10,9,3,20,16,12,17,27,23,19,18,1,21,13,15,22,28,11,26,7,30.", "difficulty": "hard", "doc_id": "42"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 10 nodes numbered from 0 to 9:\nnode 1 should be visited before node 5\nnode 1 should be visited before node 0\nnode 1 should be visited before node 4\nnode 1 should be visited before node 3\nnode 2 should be visited before node 8\nnode 4 should be visited before node 3\nnode 5 should be visited before node 4\nnode 6 should be visited before node 2\nnode 6 should be visited before node 5\nnode 7 should be visited before node 3\nnode 8 should be visited before node 5\nnode 9 should be visited before node 4\nnode 9 should be visited before node 3\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 1,6,7,9,0,2,8,5,4,3.", "difficulty": "easy", "doc_id": "43"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 9 nodes numbered from 0 to 8:\nnode 1 should be visited before node 2\nnode 1 should be visited before node 7\nnode 1 should be visited before node 5\nnode 1 should be visited before node 6\nnode 2 should be visited before node 5\nnode 2 should be visited before node 3\nnode 2 should be visited before node 0\nnode 3 should be visited before node 0\nnode 4 should be visited before node 1\nnode 4 should be visited before node 5\nnode 4 should be visited before node 0\nnode 5 should be visited before node 3\nnode 5 should be visited before node 0\nnode 6 should be visited before node 0\nnode 7 should be visited before node 5\nnode 7 should be visited before node 6\nnode 7 should be visited before node 3\nnode 7 should be visited before node 0\nnode 8 should be visited before node 6\nnode 8 should be visited before node 3\nnode 8 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 4,8,1,2,7,5,6,3,0.", "difficulty": "easy", "doc_id": "44"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 12 nodes numbered from 0 to 11:\nnode 0 should be visited before node 3\nnode 2 should be visited before node 5\nnode 2 should be visited before node 0\nnode 2 should be visited before node 3\nnode 4 should be visited before node 9\nnode 4 should be visited before node 11\nnode 4 should be visited before node 2\nnode 4 should be visited before node 5\nnode 5 should be visited before node 10\nnode 5 should be visited before node 1\nnode 6 should be visited before node 8\nnode 6 should be visited before node 9\nnode 6 should be visited before node 2\nnode 6 should be visited before node 10\nnode 6 should be visited before node 1\nnode 6 should be visited before node 3\nnode 7 should be visited before node 2\nnode 7 should be visited before node 5\nnode 7 should be visited before node 0\nnode 7 should be visited before node 3\nnode 8 should be visited before node 4\nnode 8 should be visited before node 10\nnode 8 should be visited before node 1\nnode 8 should be visited before node 0\nnode 9 should be visited before node 11\nnode 9 should be visited before node 2\nnode 9 should be visited before node 5\nnode 9 should be visited before node 1\nnode 9 should be visited before node 0\nnode 10 should be visited before node 0\nnode 10 should be visited before node 3\nnode 11 should be visited before node 5\nnode 11 should be visited before node 10\nnode 11 should be visited before node 1\nnode 11 should be visited before node 3\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 6,7,8,4,9,11,2,5,10,1,0,3.", "difficulty": "medium", "doc_id": "45"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 25 nodes numbered from 0 to 24:\nnode 0 should be visited before node 1\nnode 0 should be visited before node 19\nnode 1 should be visited before node 19\nnode 2 should be visited before node 16\nnode 2 should be visited before node 24\nnode 2 should be visited before node 22\nnode 2 should be visited before node 23\nnode 2 should be visited before node 21\nnode 2 should be visited before node 15\nnode 2 should be visited before node 7\nnode 3 should be visited before node 10\nnode 3 should be visited before node 14\nnode 3 should be visited before node 9\nnode 3 should be visited before node 17\nnode 3 should be visited before node 5\nnode 3 should be visited before node 16\nnode 3 should be visited before node 24\nnode 3 should be visited before node 22\nnode 3 should be visited before node 23\nnode 3 should be visited before node 21\nnode 3 should be visited before node 6\nnode 3 should be visited before node 15\nnode 3 should be visited before node 8\nnode 3 should be visited before node 7\nnode 3 should be visited before node 11\nnode 3 should be visited before node 1\nnode 4 should be visited before node 2\nnode 4 should be visited before node 22\nnode 4 should be visited before node 23\nnode 4 should be visited before node 21\nnode 4 should be visited before node 20\nnode 4 should be visited before node 6\nnode 4 should be visited before node 15\nnode 4 should be visited before node 11\nnode 5 should be visited before node 16\nnode 5 should be visited before node 24\nnode 5 should be visited before node 22\nnode 5 should be visited before node 23\nnode 5 should be visited before node 21\nnode 5 should be visited before node 6\nnode 5 should be visited before node 15\nnode 5 should be visited before node 8\nnode 5 should be visited before node 12\nnode 5 should be visited before node 0\nnode 5 should be visited before node 1\nnode 5 should be visited before node 19\nnode 6 should be visited before node 8\nnode 6 should be visited before node 7\nnode 6 should be visited before node 11\nnode 6 should be visited before node 0\nnode 6 should be visited before node 19\nnode 7 should be visited before node 12\nnode 7 should be visited before node 11\nnode 8 should be visited before node 7\nnode 8 should be visited before node 0\nnode 9 should be visited before node 17\nnode 9 should be visited before node 18\nnode 9 should be visited before node 4\nnode 9 should be visited before node 2\nnode 9 should be visited before node 16\nnode 9 should be visited before node 23\nnode 9 should be visited before node 8\nnode 9 should be visited before node 7\nnode 9 should be visited before node 12\nnode 9 should be visited before node 0\nnode 9 should be visited before node 19\nnode 10 should be visited before node 9\nnode 10 should be visited before node 5\nnode 10 should be visited before node 2\nnode 10 should be visited before node 16\nnode 10 should be visited before node 23\nnode 10 should be visited before node 20\nnode 10 should be visited before node 15\nnode 10 should be visited before node 8\nnode 10 should be visited before node 7\nnode 10 should be visited before node 12\nnode 10 should be visited before node 0\nnode 10 should be visited before node 1\nnode 10 should be visited before node 19\nnode 11 should be visited before node 0\nnode 13 should be visited before node 14\nnode 13 should be visited before node 4\nnode 13 should be visited before node 2\nnode 13 should be visited before node 6\nnode 13 should be visited before node 15\nnode 13 should be visited before node 12\nnode 13 should be visited before node 11\nnode 13 should be visited before node 0\nnode 13 should be visited before node 19\nnode 14 should be visited before node 17\nnode 14 should be visited before node 5\nnode 14 should be visited before node 2\nnode 14 should be visited before node 23\nnode 14 should be visited before node 21\nnode 14 should be visited before node 6\nnode 14 should be visited before node 15\nnode 14 should be visited before node 8\nnode 14 should be visited before node 11\nnode 14 should be visited before node 19\nnode 15 should be visited before node 8\nnode 15 should be visited before node 12\nnode 15 should be visited before node 11\nnode 15 should be visited before node 0\nnode 15 should be visited before node 19\nnode 16 should be visited before node 22\nnode 16 should be visited before node 23\nnode 16 should be visited before node 21\nnode 16 should be visited before node 20\nnode 16 should be visited before node 15\nnode 16 should be visited before node 8\nnode 16 should be visited before node 7\nnode 16 should be visited before node 0\nnode 16 should be visited before node 1\nnode 16 should be visited before node 19\nnode 17 should be visited before node 18\nnode 17 should be visited before node 5\nnode 17 should be visited before node 4\nnode 17 should be visited before node 2\nnode 17 should be visited before node 16\nnode 17 should be visited before node 20\nnode 17 should be visited before node 6\nnode 17 should be visited before node 15\nnode 17 should be visited before node 0\nnode 17 should be visited before node 1\nnode 17 should be visited before node 19\nnode 18 should be visited before node 5\nnode 18 should be visited before node 4\nnode 18 should be visited before node 6\nnode 18 should be visited before node 15\nnode 18 should be visited before node 8\nnode 18 should be visited before node 7\nnode 18 should be visited before node 19\nnode 20 should be visited before node 6\nnode 20 should be visited before node 15\nnode 20 should be visited before node 0\nnode 20 should be visited before node 1\nnode 20 should be visited before node 19\nnode 21 should be visited before node 8\nnode 21 should be visited before node 12\nnode 21 should be visited before node 11\nnode 21 should be visited before node 0\nnode 22 should be visited before node 6\nnode 22 should be visited before node 7\nnode 22 should be visited before node 12\nnode 22 should be visited before node 11\nnode 22 should be visited before node 1\nnode 23 should be visited before node 21\nnode 23 should be visited before node 20\nnode 23 should be visited before node 15\nnode 23 should be visited before node 7\nnode 23 should be visited before node 12\nnode 23 should be visited before node 11\nnode 23 should be visited before node 19\nnode 24 should be visited before node 21\nnode 24 should be visited before node 15\nnode 24 should be visited before node 8\nnode 24 should be visited before node 7\nnode 24 should be visited before node 11\nnode 24 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 3,13,10,14,9,17,18,5,4,2,16,24,22,23,21,20,6,15,8,7,12,11,0,1,19.", "difficulty": "medium", "doc_id": "46"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 34 nodes numbered from 0 to 33:\nnode 0 should be visited before node 29\nnode 0 should be visited before node 18\nnode 1 should be visited before node 24\nnode 1 should be visited before node 16\nnode 1 should be visited before node 10\nnode 1 should be visited before node 33\nnode 1 should be visited before node 19\nnode 1 should be visited before node 6\nnode 1 should be visited before node 2\nnode 1 should be visited before node 7\nnode 1 should be visited before node 17\nnode 1 should be visited before node 21\nnode 1 should be visited before node 29\nnode 2 should be visited before node 9\nnode 2 should be visited before node 7\nnode 2 should be visited before node 17\nnode 2 should be visited before node 21\nnode 2 should be visited before node 18\nnode 3 should be visited before node 25\nnode 3 should be visited before node 28\nnode 3 should be visited before node 1\nnode 3 should be visited before node 16\nnode 3 should be visited before node 33\nnode 3 should be visited before node 32\nnode 3 should be visited before node 4\nnode 3 should be visited before node 19\nnode 3 should be visited before node 27\nnode 3 should be visited before node 11\nnode 3 should be visited before node 6\nnode 3 should be visited before node 20\nnode 3 should be visited before node 9\nnode 3 should be visited before node 12\nnode 3 should be visited before node 13\nnode 3 should be visited before node 8\nnode 3 should be visited before node 21\nnode 3 should be visited before node 0\nnode 3 should be visited before node 29\nnode 4 should be visited before node 27\nnode 4 should be visited before node 2\nnode 4 should be visited before node 9\nnode 4 should be visited before node 17\nnode 4 should be visited before node 8\nnode 4 should be visited before node 21\nnode 4 should be visited before node 15\nnode 4 should be visited before node 0\nnode 5 should be visited before node 26\nnode 5 should be visited before node 4\nnode 5 should be visited before node 11\nnode 5 should be visited before node 6\nnode 5 should be visited before node 2\nnode 5 should be visited before node 9\nnode 5 should be visited before node 7\nnode 5 should be visited before node 13\nnode 5 should be visited before node 22\nnode 5 should be visited before node 21\nnode 5 should be visited before node 15\nnode 5 should be visited before node 29\nnode 5 should be visited before node 18\nnode 6 should be visited before node 2\nnode 6 should be visited before node 7\nnode 6 should be visited before node 12\nnode 6 should be visited before node 13\nnode 6 should be visited before node 17\nnode 6 should be visited before node 8\nnode 6 should be visited before node 22\nnode 6 should be visited before node 0\nnode 6 should be visited before node 29\nnode 6 should be visited before node 18\nnode 7 should be visited before node 12\nnode 7 should be visited before node 13\nnode 7 should be visited before node 17\nnode 7 should be visited before node 8\nnode 7 should be visited before node 22\nnode 7 should be visited before node 21\nnode 7 should be visited before node 29\nnode 8 should be visited before node 22\nnode 8 should be visited before node 21\nnode 8 should be visited before node 15\nnode 8 should be visited before node 0\nnode 8 should be visited before node 18\nnode 9 should be visited before node 22\nnode 9 should be visited before node 21\nnode 10 should be visited before node 5\nnode 10 should be visited before node 26\nnode 10 should be visited before node 32\nnode 10 should be visited before node 4\nnode 10 should be visited before node 19\nnode 10 should be visited before node 27\nnode 10 should be visited before node 6\nnode 10 should be visited before node 20\nnode 10 should be visited before node 2\nnode 10 should be visited before node 9\nnode 10 should be visited before node 12\nnode 10 should be visited before node 17\nnode 10 should be visited before node 22\nnode 10 should be visited before node 18\nnode 11 should be visited before node 6\nnode 11 should be visited before node 2\nnode 11 should be visited before node 7\nnode 11 should be visited before node 12\nnode 11 should be visited before node 13\nnode 11 should be visited before node 8\nnode 11 should be visited before node 22\nnode 11 should be visited before node 21\nnode 11 should be visited before node 0\nnode 11 should be visited before node 29\nnode 12 should be visited before node 13\nnode 12 should be visited before node 0\nnode 12 should be visited before node 29\nnode 12 should be visited before node 18\nnode 13 should be visited before node 22\nnode 13 should be visited before node 21\nnode 13 should be visited before node 29\nnode 13 should be visited before node 18\nnode 14 should be visited before node 25\nnode 14 should be visited before node 30\nnode 14 should be visited before node 24\nnode 14 should be visited before node 16\nnode 14 should be visited before node 10\nnode 14 should be visited before node 33\nnode 14 should be visited before node 4\nnode 14 should be visited before node 19\nnode 14 should be visited before node 27\nnode 14 should be visited before node 11\nnode 14 should be visited before node 6\nnode 14 should be visited before node 2\nnode 14 should be visited before node 9\nnode 14 should be visited before node 12\nnode 14 should be visited before node 17\nnode 14 should be visited before node 8\nnode 14 should be visited before node 21\nnode 14 should be visited before node 15\nnode 14 should be visited before node 0\nnode 14 should be visited before node 29\nnode 14 should be visited before node 18\nnode 15 should be visited before node 0\nnode 15 should be visited before node 29\nnode 15 should be visited before node 18\nnode 16 should be visited before node 10\nnode 16 should be visited before node 33\nnode 16 should be visited before node 4\nnode 16 should be visited before node 19\nnode 16 should be visited before node 11\nnode 16 should be visited before node 17\nnode 16 should be visited before node 8\nnode 16 should be visited before node 21\nnode 16 should be visited before node 0\nnode 16 should be visited before node 29\nnode 17 should be visited before node 8\nnode 17 should be visited before node 21\nnode 17 should be visited before node 0\nnode 19 should be visited before node 27\nnode 19 should be visited before node 12\nnode 19 should be visited before node 17\nnode 19 should be visited before node 22\nnode 19 should be visited before node 21\nnode 19 should be visited before node 15\nnode 19 should be visited before node 18\nnode 20 should be visited before node 13\nnode 20 should be visited before node 8\nnode 20 should be visited before node 22\nnode 20 should be visited before node 15\nnode 20 should be visited before node 18\nnode 21 should be visited before node 15\nnode 21 should be visited before node 18\nnode 22 should be visited before node 21\nnode 22 should be visited before node 29\nnode 22 should be visited before node 18\nnode 23 should be visited before node 14\nnode 23 should be visited before node 25\nnode 23 should be visited before node 1\nnode 23 should be visited before node 30\nnode 23 should be visited before node 24\nnode 23 should be visited before node 26\nnode 23 should be visited before node 32\nnode 23 should be visited before node 27\nnode 23 should be visited before node 6\nnode 23 should be visited before node 20\nnode 23 should be visited before node 2\nnode 23 should be visited before node 12\nnode 23 should be visited before node 13\nnode 23 should be visited before node 17\nnode 23 should be visited before node 8\nnode 23 should be visited before node 22\nnode 23 should be visited before node 21\nnode 24 should be visited before node 10\nnode 24 should be visited before node 5\nnode 24 should be visited before node 2\nnode 24 should be visited before node 9\nnode 24 should be visited before node 7\nnode 24 should be visited before node 12\nnode 24 should be visited before node 8\nnode 24 should be visited before node 0\nnode 24 should be visited before node 29\nnode 24 should be visited before node 18\nnode 25 should be visited before node 1\nnode 25 should be visited before node 24\nnode 25 should be visited before node 33\nnode 25 should be visited before node 19\nnode 25 should be visited before node 11\nnode 25 should be visited before node 2\nnode 25 should be visited before node 9\nnode 25 should be visited before node 21\nnode 25 should be visited before node 15\nnode 25 should be visited before node 0\nnode 25 should be visited before node 29\nnode 25 should be visited before node 18\nnode 26 should be visited before node 32\nnode 26 should be visited before node 19\nnode 26 should be visited before node 27\nnode 26 should be visited before node 11\nnode 26 should be visited before node 6\nnode 26 should be visited before node 2\nnode 26 should be visited before node 9\nnode 26 should be visited before node 12\nnode 26 should be visited before node 13\nnode 26 should be visited before node 21\nnode 26 should be visited before node 0\nnode 27 should be visited before node 9\nnode 27 should be visited before node 8\nnode 27 should be visited before node 15\nnode 27 should be visited before node 0\nnode 28 should be visited before node 24\nnode 28 should be visited before node 16\nnode 28 should be visited before node 10\nnode 28 should be visited before node 33\nnode 28 should be visited before node 32\nnode 28 should be visited before node 4\nnode 28 should be visited before node 19\nnode 28 should be visited before node 27\nnode 28 should be visited before node 20\nnode 28 should be visited before node 2\nnode 28 should be visited before node 9\nnode 28 should be visited before node 7\nnode 28 should be visited before node 12\nnode 28 should be visited before node 13\nnode 28 should be visited before node 8\nnode 28 should be visited before node 21\nnode 28 should be visited before node 18\nnode 30 should be visited before node 16\nnode 30 should be visited before node 10\nnode 30 should be visited before node 5\nnode 30 should be visited before node 32\nnode 30 should be visited before node 20\nnode 30 should be visited before node 12\nnode 30 should be visited before node 22\nnode 30 should be visited before node 21\nnode 30 should be visited before node 15\nnode 30 should be visited before node 0\nnode 30 should be visited before node 18\nnode 31 should be visited before node 3\nnode 31 should be visited before node 1\nnode 31 should be visited before node 33\nnode 31 should be visited before node 5\nnode 31 should be visited before node 26\nnode 31 should be visited before node 19\nnode 31 should be visited before node 27\nnode 31 should be visited before node 11\nnode 31 should be visited before node 6\nnode 31 should be visited before node 20\nnode 31 should be visited before node 17\nnode 31 should be visited before node 15\nnode 31 should be visited before node 0\nnode 31 should be visited before node 18\nnode 32 should be visited before node 4\nnode 32 should be visited before node 27\nnode 32 should be visited before node 20\nnode 32 should be visited before node 9\nnode 32 should be visited before node 7\nnode 32 should be visited before node 13\nnode 32 should be visited before node 17\nnode 32 should be visited before node 21\nnode 32 should be visited before node 15\nnode 33 should be visited before node 26\nnode 33 should be visited before node 32\nnode 33 should be visited before node 19\nnode 33 should be visited before node 27\nnode 33 should be visited before node 20\nnode 33 should be visited before node 2\nnode 33 should be visited before node 13\nnode 33 should be visited before node 17\nnode 33 should be visited before node 8\nnode 33 should be visited before node 21\nnode 33 should be visited before node 15\nnode 33 should be visited before node 18\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 23,31,14,3,30,25,28,1,24,16,10,33,5,26,32,19,11,4,20,6,27,2,9,7,12,17,13,8,22,21,15,0,29,18.", "difficulty": "hard", "doc_id": "47"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 13 nodes numbered from 0 to 12:\nnode 0 should be visited before node 7\nnode 0 should be visited before node 1\nnode 3 should be visited before node 7\nnode 3 should be visited before node 1\nnode 4 should be visited before node 12\nnode 4 should be visited before node 0\nnode 4 should be visited before node 9\nnode 4 should be visited before node 7\nnode 4 should be visited before node 2\nnode 4 should be visited before node 1\nnode 5 should be visited before node 12\nnode 5 should be visited before node 0\nnode 5 should be visited before node 7\nnode 5 should be visited before node 2\nnode 5 should be visited before node 1\nnode 6 should be visited before node 4\nnode 6 should be visited before node 3\nnode 6 should be visited before node 11\nnode 6 should be visited before node 0\nnode 6 should be visited before node 2\nnode 6 should be visited before node 1\nnode 7 should be visited before node 8\nnode 9 should be visited before node 7\nnode 9 should be visited before node 1\nnode 10 should be visited before node 3\nnode 10 should be visited before node 12\nnode 10 should be visited before node 8\nnode 10 should be visited before node 1\nnode 11 should be visited before node 1\nnode 12 should be visited before node 0\nnode 12 should be visited before node 7\nnode 12 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 5,6,10,4,11,3,12,9,2,0,7,1,8.", "difficulty": "medium", "doc_id": "48"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 29 nodes numbered from 0 to 28:\nnode 0 should be visited before node 12\nnode 0 should be visited before node 11\nnode 0 should be visited before node 1\nnode 0 should be visited before node 21\nnode 0 should be visited before node 26\nnode 0 should be visited before node 13\nnode 0 should be visited before node 23\nnode 0 should be visited before node 27\nnode 0 should be visited before node 15\nnode 0 should be visited before node 22\nnode 0 should be visited before node 5\nnode 0 should be visited before node 6\nnode 0 should be visited before node 10\nnode 0 should be visited before node 18\nnode 0 should be visited before node 24\nnode 1 should be visited before node 9\nnode 1 should be visited before node 21\nnode 1 should be visited before node 20\nnode 1 should be visited before node 16\nnode 1 should be visited before node 27\nnode 1 should be visited before node 15\nnode 1 should be visited before node 7\nnode 1 should be visited before node 5\nnode 2 should be visited before node 10\nnode 3 should be visited before node 8\nnode 3 should be visited before node 28\nnode 3 should be visited before node 11\nnode 3 should be visited before node 26\nnode 3 should be visited before node 13\nnode 3 should be visited before node 19\nnode 3 should be visited before node 16\nnode 3 should be visited before node 15\nnode 3 should be visited before node 7\nnode 3 should be visited before node 2\nnode 3 should be visited before node 24\nnode 4 should be visited before node 8\nnode 4 should be visited before node 28\nnode 4 should be visited before node 0\nnode 4 should be visited before node 12\nnode 4 should be visited before node 11\nnode 4 should be visited before node 1\nnode 4 should be visited before node 9\nnode 4 should be visited before node 20\nnode 4 should be visited before node 19\nnode 4 should be visited before node 16\nnode 4 should be visited before node 23\nnode 4 should be visited before node 15\nnode 4 should be visited before node 22\nnode 4 should be visited before node 7\nnode 4 should be visited before node 2\nnode 4 should be visited before node 6\nnode 4 should be visited before node 18\nnode 4 should be visited before node 24\nnode 5 should be visited before node 10\nnode 5 should be visited before node 18\nnode 6 should be visited before node 10\nnode 6 should be visited before node 18\nnode 7 should be visited before node 5\nnode 7 should be visited before node 10\nnode 7 should be visited before node 18\nnode 7 should be visited before node 24\nnode 8 should be visited before node 0\nnode 8 should be visited before node 11\nnode 8 should be visited before node 9\nnode 8 should be visited before node 20\nnode 8 should be visited before node 26\nnode 8 should be visited before node 13\nnode 8 should be visited before node 15\nnode 8 should be visited before node 22\nnode 8 should be visited before node 14\nnode 8 should be visited before node 5\nnode 9 should be visited before node 20\nnode 9 should be visited before node 19\nnode 9 should be visited before node 16\nnode 9 should be visited before node 27\nnode 9 should be visited before node 15\nnode 9 should be visited before node 22\nnode 9 should be visited before node 14\nnode 9 should be visited before node 7\nnode 9 should be visited before node 5\nnode 9 should be visited before node 2\nnode 9 should be visited before node 10\nnode 9 should be visited before node 24\nnode 10 should be visited before node 18\nnode 10 should be visited before node 24\nnode 11 should be visited before node 21\nnode 11 should be visited before node 20\nnode 11 should be visited before node 26\nnode 11 should be visited before node 13\nnode 11 should be visited before node 16\nnode 11 should be visited before node 27\nnode 11 should be visited before node 15\nnode 11 should be visited before node 22\nnode 11 should be visited before node 7\nnode 11 should be visited before node 5\nnode 11 should be visited before node 18\nnode 11 should be visited before node 24\nnode 12 should be visited before node 11\nnode 12 should be visited before node 9\nnode 12 should be visited before node 21\nnode 12 should be visited before node 13\nnode 12 should be visited before node 19\nnode 12 should be visited before node 16\nnode 12 should be visited before node 6\nnode 12 should be visited before node 18\nnode 12 should be visited before node 24\nnode 13 should be visited before node 16\nnode 13 should be visited before node 27\nnode 13 should be visited before node 15\nnode 13 should be visited before node 22\nnode 13 should be visited before node 7\nnode 13 should be visited before node 6\nnode 14 should be visited before node 5\nnode 14 should be visited before node 6\nnode 14 should be visited before node 18\nnode 15 should be visited before node 14\nnode 15 should be visited before node 7\nnode 15 should be visited before node 5\nnode 15 should be visited before node 18\nnode 15 should be visited before node 24\nnode 16 should be visited before node 27\nnode 16 should be visited before node 7\nnode 16 should be visited before node 2\nnode 16 should be visited before node 6\nnode 16 should be visited before node 10\nnode 16 should be visited before node 18\nnode 16 should be visited before node 24\nnode 17 should be visited before node 8\nnode 17 should be visited before node 0\nnode 17 should be visited before node 12\nnode 17 should be visited before node 11\nnode 17 should be visited before node 1\nnode 17 should be visited before node 9\nnode 17 should be visited before node 20\nnode 17 should be visited before node 13\nnode 17 should be visited before node 23\nnode 17 should be visited before node 27\nnode 17 should be visited before node 15\nnode 17 should be visited before node 14\nnode 17 should be visited before node 7\nnode 17 should be visited before node 10\nnode 18 should be visited before node 24\nnode 19 should be visited before node 16\nnode 19 should be visited before node 15\nnode 19 should be visited before node 22\nnode 19 should be visited before node 7\nnode 19 should be visited before node 2\nnode 19 should be visited before node 6\nnode 19 should be visited before node 10\nnode 20 should be visited before node 26\nnode 20 should be visited before node 13\nnode 20 should be visited before node 27\nnode 20 should be visited before node 14\nnode 20 should be visited before node 2\nnode 20 should be visited before node 10\nnode 20 should be visited before node 18\nnode 21 should be visited before node 26\nnode 21 should be visited before node 13\nnode 21 should be visited before node 23\nnode 21 should be visited before node 15\nnode 21 should be visited before node 22\nnode 21 should be visited before node 14\nnode 21 should be visited before node 7\nnode 21 should be visited before node 6\nnode 21 should be visited before node 10\nnode 21 should be visited before node 24\nnode 22 should be visited before node 7\nnode 22 should be visited before node 2\nnode 22 should be visited before node 6\nnode 22 should be visited before node 10\nnode 22 should be visited before node 18\nnode 23 should be visited before node 27\nnode 23 should be visited before node 15\nnode 23 should be visited before node 5\nnode 23 should be visited before node 2\nnode 23 should be visited before node 24\nnode 25 should be visited before node 17\nnode 25 should be visited before node 8\nnode 25 should be visited before node 11\nnode 25 should be visited before node 9\nnode 25 should be visited before node 20\nnode 25 should be visited before node 13\nnode 25 should be visited before node 16\nnode 25 should be visited before node 15\nnode 25 should be visited before node 22\nnode 25 should be visited before node 14\nnode 25 should be visited before node 5\nnode 25 should be visited before node 2\nnode 25 should be visited before node 18\nnode 26 should be visited before node 16\nnode 26 should be visited before node 27\nnode 26 should be visited before node 15\nnode 26 should be visited before node 6\nnode 27 should be visited before node 22\nnode 27 should be visited before node 7\nnode 27 should be visited before node 2\nnode 27 should be visited before node 10\nnode 27 should be visited before node 24\nnode 28 should be visited before node 11\nnode 28 should be visited before node 1\nnode 28 should be visited before node 9\nnode 28 should be visited before node 21\nnode 28 should be visited before node 20\nnode 28 should be visited before node 13\nnode 28 should be visited before node 19\nnode 28 should be visited before node 22\nnode 28 should be visited before node 14\nnode 28 should be visited before node 7\nnode 28 should be visited before node 2\nnode 28 should be visited before node 18\nnode 28 should be visited before node 24\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 3,4,25,28,17,8,0,12,1,11,9,21,20,19,23,26,13,16,15,27,14,22,7,2,6,5,10,18,24.", "difficulty": "hard", "doc_id": "49"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 26 nodes numbered from 0 to 25:\nnode 0 should be visited before node 15\nnode 0 should be visited before node 4\nnode 1 should be visited before node 4\nnode 1 should be visited before node 22\nnode 1 should be visited before node 17\nnode 2 should be visited before node 19\nnode 2 should be visited before node 13\nnode 2 should be visited before node 18\nnode 2 should be visited before node 24\nnode 3 should be visited before node 10\nnode 3 should be visited before node 7\nnode 3 should be visited before node 16\nnode 3 should be visited before node 15\nnode 3 should be visited before node 4\nnode 3 should be visited before node 12\nnode 3 should be visited before node 24\nnode 4 should be visited before node 18\nnode 4 should be visited before node 24\nnode 5 should be visited before node 16\nnode 5 should be visited before node 22\nnode 6 should be visited before node 5\nnode 6 should be visited before node 12\nnode 7 should be visited before node 6\nnode 7 should be visited before node 18\nnode 7 should be visited before node 11\nnode 7 should be visited before node 12\nnode 7 should be visited before node 24\nnode 8 should be visited before node 5\nnode 8 should be visited before node 1\nnode 8 should be visited before node 4\nnode 8 should be visited before node 18\nnode 8 should be visited before node 17\nnode 8 should be visited before node 23\nnode 9 should be visited before node 3\nnode 9 should be visited before node 6\nnode 9 should be visited before node 15\nnode 9 should be visited before node 12\nnode 10 should be visited before node 1\nnode 10 should be visited before node 15\nnode 10 should be visited before node 22\nnode 10 should be visited before node 23\nnode 11 should be visited before node 12\nnode 11 should be visited before node 24\nnode 12 should be visited before node 22\nnode 13 should be visited before node 7\nnode 13 should be visited before node 0\nnode 13 should be visited before node 6\nnode 13 should be visited before node 1\nnode 13 should be visited before node 15\nnode 13 should be visited before node 4\nnode 13 should be visited before node 11\nnode 13 should be visited before node 12\nnode 13 should be visited before node 24\nnode 14 should be visited before node 9\nnode 14 should be visited before node 19\nnode 14 should be visited before node 13\nnode 14 should be visited before node 16\nnode 14 should be visited before node 4\nnode 14 should be visited before node 24\nnode 15 should be visited before node 4\nnode 15 should be visited before node 12\nnode 15 should be visited before node 24\nnode 16 should be visited before node 15\nnode 16 should be visited before node 18\nnode 16 should be visited before node 12\nnode 16 should be visited before node 22\nnode 17 should be visited before node 24\nnode 18 should be visited before node 11\nnode 18 should be visited before node 22\nnode 19 should be visited before node 6\nnode 19 should be visited before node 1\nnode 19 should be visited before node 18\nnode 20 should be visited before node 2\nnode 20 should be visited before node 9\nnode 20 should be visited before node 19\nnode 20 should be visited before node 13\nnode 20 should be visited before node 6\nnode 20 should be visited before node 5\nnode 20 should be visited before node 18\nnode 20 should be visited before node 11\nnode 20 should be visited before node 23\nnode 21 should be visited before node 2\nnode 21 should be visited before node 13\nnode 21 should be visited before node 0\nnode 21 should be visited before node 16\nnode 21 should be visited before node 15\nnode 21 should be visited before node 12\nnode 21 should be visited before node 17\nnode 22 should be visited before node 24\nnode 23 should be visited before node 24\nnode 25 should be visited before node 20\nnode 25 should be visited before node 19\nnode 25 should be visited before node 10\nnode 25 should be visited before node 0\nnode 25 should be visited before node 12\nnode 25 should be visited before node 24\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 8,14,21,25,20,2,9,19,13,3,0,10,7,1,23,6,17,5,16,15,4,18,11,12,22,24.", "difficulty": "hard", "doc_id": "50"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 4\nnode 1 should be visited before node 3\nnode 1 should be visited before node 5\nnode 2 should be visited before node 5\nnode 3 should be visited before node 0\nnode 3 should be visited before node 4\nnode 5 should be visited before node 4\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 1,2,3,5,0,4.", "difficulty": "easy", "doc_id": "51"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 24 nodes numbered from 0 to 23:\nnode 0 should be visited before node 9\nnode 0 should be visited before node 2\nnode 0 should be visited before node 14\nnode 0 should be visited before node 1\nnode 0 should be visited before node 12\nnode 0 should be visited before node 22\nnode 0 should be visited before node 13\nnode 0 should be visited before node 15\nnode 1 should be visited before node 12\nnode 1 should be visited before node 23\nnode 2 should be visited before node 14\nnode 2 should be visited before node 5\nnode 2 should be visited before node 10\nnode 2 should be visited before node 1\nnode 2 should be visited before node 23\nnode 2 should be visited before node 22\nnode 2 should be visited before node 11\nnode 2 should be visited before node 16\nnode 3 should be visited before node 2\nnode 3 should be visited before node 19\nnode 3 should be visited before node 11\nnode 4 should be visited before node 6\nnode 4 should be visited before node 18\nnode 4 should be visited before node 1\nnode 4 should be visited before node 23\nnode 5 should be visited before node 23\nnode 5 should be visited before node 11\nnode 5 should be visited before node 15\nnode 6 should be visited before node 9\nnode 6 should be visited before node 7\nnode 6 should be visited before node 19\nnode 6 should be visited before node 22\nnode 6 should be visited before node 13\nnode 6 should be visited before node 15\nnode 7 should be visited before node 18\nnode 7 should be visited before node 21\nnode 7 should be visited before node 14\nnode 7 should be visited before node 5\nnode 7 should be visited before node 10\nnode 7 should be visited before node 12\nnode 8 should be visited before node 9\nnode 8 should be visited before node 7\nnode 8 should be visited before node 3\nnode 8 should be visited before node 18\nnode 8 should be visited before node 20\nnode 8 should be visited before node 14\nnode 8 should be visited before node 10\nnode 8 should be visited before node 13\nnode 9 should be visited before node 7\nnode 9 should be visited before node 3\nnode 9 should be visited before node 19\nnode 9 should be visited before node 20\nnode 9 should be visited before node 23\nnode 9 should be visited before node 13\nnode 9 should be visited before node 15\nnode 10 should be visited before node 1\nnode 10 should be visited before node 13\nnode 10 should be visited before node 11\nnode 10 should be visited before node 15\nnode 11 should be visited before node 16\nnode 11 should be visited before node 15\nnode 12 should be visited before node 13\nnode 12 should be visited before node 11\nnode 12 should be visited before node 15\nnode 13 should be visited before node 15\nnode 14 should be visited before node 5\nnode 14 should be visited before node 12\nnode 14 should be visited before node 11\nnode 14 should be visited before node 16\nnode 16 should be visited before node 15\nnode 17 should be visited before node 12\nnode 17 should be visited before node 23\nnode 17 should be visited before node 22\nnode 17 should be visited before node 15\nnode 18 should be visited before node 10\nnode 18 should be visited before node 11\nnode 19 should be visited before node 14\nnode 19 should be visited before node 10\nnode 19 should be visited before node 13\nnode 20 should be visited before node 12\nnode 20 should be visited before node 23\nnode 21 should be visited before node 14\nnode 21 should be visited before node 23\nnode 21 should be visited before node 22\nnode 21 should be visited before node 13\nnode 21 should be visited before node 16\nnode 22 should be visited before node 16\nnode 23 should be visited before node 22\nnode 23 should be visited before node 11\nnode 23 should be visited before node 16\nnode 23 should be visited before node 15\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 0,4,8,17,6,9,7,3,20,18,21,2,19,14,10,5,1,12,23,13,22,11,16,15.", "difficulty": "medium", "doc_id": "52"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 18 nodes numbered from 0 to 17:\nnode 0 should be visited before node 15\nnode 1 should be visited before node 7\nnode 1 should be visited before node 4\nnode 1 should be visited before node 14\nnode 1 should be visited before node 17\nnode 1 should be visited before node 11\nnode 1 should be visited before node 15\nnode 2 should be visited before node 0\nnode 2 should be visited before node 11\nnode 3 should be visited before node 14\nnode 3 should be visited before node 2\nnode 3 should be visited before node 0\nnode 4 should be visited before node 14\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nnode 4 should be visited before node 11\nnode 5 should be visited before node 16\nnode 5 should be visited before node 9\nnode 5 should be visited before node 12\nnode 5 should be visited before node 10\nnode 5 should be visited before node 7\nnode 5 should be visited before node 3\nnode 5 should be visited before node 14\nnode 5 should be visited before node 2\nnode 5 should be visited before node 17\nnode 6 should be visited before node 14\nnode 6 should be visited before node 17\nnode 6 should be visited before node 11\nnode 6 should be visited before node 15\nnode 7 should be visited before node 6\nnode 7 should be visited before node 3\nnode 7 should be visited before node 14\nnode 7 should be visited before node 2\nnode 7 should be visited before node 17\nnode 7 should be visited before node 0\nnode 8 should be visited before node 13\nnode 8 should be visited before node 5\nnode 8 should be visited before node 9\nnode 8 should be visited before node 1\nnode 8 should be visited before node 7\nnode 8 should be visited before node 4\nnode 8 should be visited before node 14\nnode 8 should be visited before node 2\nnode 8 should be visited before node 11\nnode 9 should be visited before node 10\nnode 9 should be visited before node 1\nnode 9 should be visited before node 6\nnode 9 should be visited before node 4\nnode 9 should be visited before node 14\nnode 9 should be visited before node 2\nnode 9 should be visited before node 11\nnode 9 should be visited before node 15\nnode 10 should be visited before node 1\nnode 10 should be visited before node 4\nnode 10 should be visited before node 14\nnode 11 should be visited before node 15\nnode 12 should be visited before node 10\nnode 12 should be visited before node 7\nnode 12 should be visited before node 6\nnode 12 should be visited before node 3\nnode 12 should be visited before node 14\nnode 12 should be visited before node 17\nnode 12 should be visited before node 11\nnode 13 should be visited before node 5\nnode 13 should be visited before node 16\nnode 13 should be visited before node 9\nnode 13 should be visited before node 12\nnode 13 should be visited before node 10\nnode 13 should be visited before node 7\nnode 13 should be visited before node 6\nnode 13 should be visited before node 4\nnode 13 should be visited before node 14\nnode 14 should be visited before node 0\nnode 14 should be visited before node 11\nnode 14 should be visited before node 15\nnode 16 should be visited before node 9\nnode 16 should be visited before node 1\nnode 16 should be visited before node 6\nnode 16 should be visited before node 3\nnode 16 should be visited before node 14\nnode 16 should be visited before node 17\nnode 16 should be visited before node 0\nnode 16 should be visited before node 11\nnode 17 should be visited before node 0\nnode 17 should be visited before node 11\nnode 17 should be visited before node 15\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 8,13,5,16,12,9,10,1,7,4,6,3,17,14,2,0,11,15.", "difficulty": "medium", "doc_id": "53"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 29 nodes numbered from 0 to 28:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 14\nnode 0 should be visited before node 18\nnode 0 should be visited before node 3\nnode 0 should be visited before node 6\nnode 0 should be visited before node 16\nnode 0 should be visited before node 17\nnode 0 should be visited before node 28\nnode 0 should be visited before node 1\nnode 0 should be visited before node 20\nnode 0 should be visited before node 27\nnode 0 should be visited before node 15\nnode 0 should be visited before node 10\nnode 0 should be visited before node 13\nnode 1 should be visited before node 20\nnode 1 should be visited before node 5\nnode 1 should be visited before node 10\nnode 1 should be visited before node 19\nnode 1 should be visited before node 23\nnode 2 should be visited before node 17\nnode 2 should be visited before node 1\nnode 2 should be visited before node 12\nnode 2 should be visited before node 20\nnode 2 should be visited before node 5\nnode 2 should be visited before node 10\nnode 2 should be visited before node 13\nnode 2 should be visited before node 23\nnode 3 should be visited before node 2\nnode 3 should be visited before node 28\nnode 3 should be visited before node 1\nnode 3 should be visited before node 20\nnode 3 should be visited before node 11\nnode 3 should be visited before node 5\nnode 3 should be visited before node 10\nnode 3 should be visited before node 24\nnode 4 should be visited before node 25\nnode 4 should be visited before node 14\nnode 4 should be visited before node 18\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 16\nnode 4 should be visited before node 17\nnode 4 should be visited before node 1\nnode 4 should be visited before node 27\nnode 4 should be visited before node 11\nnode 4 should be visited before node 10\nnode 4 should be visited before node 19\nnode 4 should be visited before node 24\nnode 5 should be visited before node 10\nnode 5 should be visited before node 19\nnode 6 should be visited before node 17\nnode 6 should be visited before node 1\nnode 6 should be visited before node 20\nnode 6 should be visited before node 27\nnode 6 should be visited before node 11\nnode 7 should be visited before node 3\nnode 7 should be visited before node 6\nnode 7 should be visited before node 2\nnode 7 should be visited before node 17\nnode 7 should be visited before node 28\nnode 7 should be visited before node 12\nnode 7 should be visited before node 27\nnode 7 should be visited before node 15\nnode 7 should be visited before node 11\nnode 7 should be visited before node 5\nnode 7 should be visited before node 13\nnode 7 should be visited before node 19\nnode 7 should be visited before node 24\nnode 8 should be visited before node 15\nnode 8 should be visited before node 11\nnode 8 should be visited before node 10\nnode 8 should be visited before node 13\nnode 8 should be visited before node 19\nnode 8 should be visited before node 23\nnode 8 should be visited before node 24\nnode 9 should be visited before node 26\nnode 9 should be visited before node 22\nnode 9 should be visited before node 0\nnode 9 should be visited before node 25\nnode 9 should be visited before node 7\nnode 9 should be visited before node 28\nnode 9 should be visited before node 1\nnode 9 should be visited before node 8\nnode 9 should be visited before node 12\nnode 9 should be visited before node 27\nnode 9 should be visited before node 15\nnode 9 should be visited before node 11\nnode 9 should be visited before node 10\nnode 9 should be visited before node 13\nnode 9 should be visited before node 19\nnode 10 should be visited before node 13\nnode 10 should be visited before node 19\nnode 10 should be visited before node 24\nnode 11 should be visited before node 13\nnode 11 should be visited before node 23\nnode 12 should be visited before node 20\nnode 12 should be visited before node 23\nnode 13 should be visited before node 19\nnode 13 should be visited before node 24\nnode 14 should be visited before node 18\nnode 14 should be visited before node 6\nnode 14 should be visited before node 2\nnode 14 should be visited before node 16\nnode 14 should be visited before node 28\nnode 14 should be visited before node 8\nnode 14 should be visited before node 20\nnode 14 should be visited before node 27\nnode 14 should be visited before node 5\nnode 14 should be visited before node 13\nnode 14 should be visited before node 19\nnode 14 should be visited before node 24\nnode 15 should be visited before node 11\nnode 15 should be visited before node 5\nnode 15 should be visited before node 13\nnode 15 should be visited before node 24\nnode 16 should be visited before node 17\nnode 16 should be visited before node 1\nnode 16 should be visited before node 8\nnode 16 should be visited before node 12\nnode 16 should be visited before node 27\nnode 16 should be visited before node 15\nnode 16 should be visited before node 11\nnode 16 should be visited before node 5\nnode 16 should be visited before node 13\nnode 16 should be visited before node 19\nnode 16 should be visited before node 24\nnode 17 should be visited before node 15\nnode 17 should be visited before node 13\nnode 17 should be visited before node 19\nnode 17 should be visited before node 23\nnode 17 should be visited before node 24\nnode 18 should be visited before node 3\nnode 18 should be visited before node 2\nnode 18 should be visited before node 16\nnode 18 should be visited before node 17\nnode 18 should be visited before node 28\nnode 18 should be visited before node 1\nnode 18 should be visited before node 8\nnode 18 should be visited before node 27\nnode 18 should be visited before node 11\nnode 18 should be visited before node 10\nnode 18 should be visited before node 13\nnode 18 should be visited before node 19\nnode 18 should be visited before node 23\nnode 18 should be visited before node 24\nnode 19 should be visited before node 23\nnode 20 should be visited before node 11\nnode 20 should be visited before node 13\nnode 20 should be visited before node 19\nnode 20 should be visited before node 24\nnode 21 should be visited before node 14\nnode 21 should be visited before node 3\nnode 21 should be visited before node 6\nnode 21 should be visited before node 16\nnode 21 should be visited before node 27\nnode 21 should be visited before node 5\nnode 21 should be visited before node 10\nnode 21 should be visited before node 23\nnode 22 should be visited before node 0\nnode 22 should be visited before node 4\nnode 22 should be visited before node 25\nnode 22 should be visited before node 21\nnode 22 should be visited before node 7\nnode 22 should be visited before node 14\nnode 22 should be visited before node 3\nnode 22 should be visited before node 2\nnode 22 should be visited before node 28\nnode 22 should be visited before node 20\nnode 22 should be visited before node 27\nnode 22 should be visited before node 15\nnode 22 should be visited before node 5\nnode 22 should be visited before node 23\nnode 23 should be visited before node 24\nnode 25 should be visited before node 21\nnode 25 should be visited before node 7\nnode 25 should be visited before node 3\nnode 25 should be visited before node 6\nnode 25 should be visited before node 2\nnode 25 should be visited before node 1\nnode 25 should be visited before node 8\nnode 25 should be visited before node 27\nnode 25 should be visited before node 11\nnode 25 should be visited before node 5\nnode 25 should be visited before node 10\nnode 25 should be visited before node 24\nnode 26 should be visited before node 22\nnode 26 should be visited before node 0\nnode 26 should be visited before node 4\nnode 26 should be visited before node 25\nnode 26 should be visited before node 7\nnode 26 should be visited before node 14\nnode 26 should be visited before node 18\nnode 26 should be visited before node 2\nnode 26 should be visited before node 16\nnode 26 should be visited before node 28\nnode 26 should be visited before node 12\nnode 26 should be visited before node 20\nnode 26 should be visited before node 15\nnode 26 should be visited before node 11\nnode 26 should be visited before node 19\nnode 26 should be visited before node 23\nnode 27 should be visited before node 15\nnode 27 should be visited before node 11\nnode 27 should be visited before node 5\nnode 27 should be visited before node 10\nnode 27 should be visited before node 13\nnode 28 should be visited before node 1\nnode 28 should be visited before node 8\nnode 28 should be visited before node 5\nnode 28 should be visited before node 10\nnode 28 should be visited before node 13\nnode 28 should be visited before node 19\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 9,26,22,0,4,25,21,7,14,18,6,3,16,2,28,27,17,12,1,8,20,15,11,5,10,13,19,23,24.", "difficulty": "hard", "doc_id": "54"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 12 nodes numbered from 0 to 11:\nnode 1 should be visited before node 5\nnode 1 should be visited before node 0\nnode 2 should be visited before node 5\nnode 2 should be visited before node 0\nnode 3 should be visited before node 8\nnode 3 should be visited before node 0\nnode 4 should be visited before node 2\nnode 4 should be visited before node 5\nnode 5 should be visited before node 0\nnode 6 should be visited before node 9\nnode 6 should be visited before node 8\nnode 6 should be visited before node 4\nnode 6 should be visited before node 7\nnode 6 should be visited before node 10\nnode 6 should be visited before node 1\nnode 6 should be visited before node 5\nnode 6 should be visited before node 0\nnode 7 should be visited before node 10\nnode 7 should be visited before node 1\nnode 7 should be visited before node 5\nnode 8 should be visited before node 7\nnode 8 should be visited before node 10\nnode 8 should be visited before node 2\nnode 8 should be visited before node 1\nnode 8 should be visited before node 5\nnode 8 should be visited before node 0\nnode 9 should be visited before node 11\nnode 9 should be visited before node 4\nnode 9 should be visited before node 10\nnode 9 should be visited before node 2\nnode 9 should be visited before node 1\nnode 9 should be visited before node 5\nnode 9 should be visited before node 0\nnode 10 should be visited before node 1\nnode 10 should be visited before node 5\nnode 10 should be visited before node 0\nnode 11 should be visited before node 3\nnode 11 should be visited before node 8\nnode 11 should be visited before node 4\nnode 11 should be visited before node 10\nnode 11 should be visited before node 2\nnode 11 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 6,9,11,3,4,8,7,2,10,1,5,0.", "difficulty": "medium", "doc_id": "55"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 19 nodes numbered from 0 to 18:\nnode 0 should be visited before node 10\nnode 0 should be visited before node 4\nnode 0 should be visited before node 12\nnode 0 should be visited before node 13\nnode 1 should be visited before node 16\nnode 1 should be visited before node 13\nnode 2 should be visited before node 4\nnode 2 should be visited before node 18\nnode 2 should be visited before node 3\nnode 2 should be visited before node 13\nnode 3 should be visited before node 16\nnode 4 should be visited before node 12\nnode 4 should be visited before node 18\nnode 5 should be visited before node 15\nnode 5 should be visited before node 8\nnode 5 should be visited before node 7\nnode 5 should be visited before node 1\nnode 5 should be visited before node 4\nnode 5 should be visited before node 3\nnode 5 should be visited before node 16\nnode 6 should be visited before node 15\nnode 6 should be visited before node 8\nnode 6 should be visited before node 1\nnode 6 should be visited before node 4\nnode 7 should be visited before node 0\nnode 7 should be visited before node 1\nnode 7 should be visited before node 9\nnode 7 should be visited before node 16\nnode 8 should be visited before node 14\nnode 8 should be visited before node 4\nnode 8 should be visited before node 11\nnode 8 should be visited before node 3\nnode 8 should be visited before node 9\nnode 8 should be visited before node 16\nnode 9 should be visited before node 16\nnode 10 should be visited before node 3\nnode 10 should be visited before node 13\nnode 11 should be visited before node 12\nnode 11 should be visited before node 13\nnode 12 should be visited before node 9\nnode 14 should be visited before node 4\nnode 14 should be visited before node 12\nnode 14 should be visited before node 16\nnode 15 should be visited before node 8\nnode 15 should be visited before node 7\nnode 15 should be visited before node 10\nnode 15 should be visited before node 1\nnode 15 should be visited before node 11\nnode 15 should be visited before node 12\nnode 15 should be visited before node 13\nnode 17 should be visited before node 6\nnode 17 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 2,5,17,6,15,8,7,14,11,0,1,10,4,3,13,12,18,9,16.", "difficulty": "medium", "doc_id": "56"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 12 nodes numbered from 0 to 11:\nnode 0 should be visited before node 1\nnode 0 should be visited before node 3\nnode 0 should be visited before node 11\nnode 0 should be visited before node 6\nnode 0 should be visited before node 2\nnode 0 should be visited before node 8\nnode 0 should be visited before node 10\nnode 1 should be visited before node 11\nnode 1 should be visited before node 6\nnode 1 should be visited before node 2\nnode 1 should be visited before node 8\nnode 1 should be visited before node 10\nnode 1 should be visited before node 9\nnode 1 should be visited before node 5\nnode 2 should be visited before node 8\nnode 2 should be visited before node 10\nnode 2 should be visited before node 9\nnode 3 should be visited before node 11\nnode 3 should be visited before node 6\nnode 3 should be visited before node 2\nnode 3 should be visited before node 8\nnode 3 should be visited before node 9\nnode 3 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 4 should be visited before node 7\nnode 4 should be visited before node 11\nnode 4 should be visited before node 6\nnode 4 should be visited before node 2\nnode 4 should be visited before node 8\nnode 4 should be visited before node 10\nnode 4 should be visited before node 5\nnode 6 should be visited before node 2\nnode 6 should be visited before node 10\nnode 7 should be visited before node 11\nnode 7 should be visited before node 6\nnode 7 should be visited before node 2\nnode 7 should be visited before node 10\nnode 7 should be visited before node 9\nnode 8 should be visited before node 10\nnode 8 should be visited before node 5\nnode 9 should be visited before node 5\nnode 10 should be visited before node 9\nnode 10 should be visited before node 5\nnode 11 should be visited before node 6\nnode 11 should be visited before node 2\nnode 11 should be visited before node 8\nnode 11 should be visited before node 9\nnode 11 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 0,4,1,3,7,11,6,2,8,10,9,5.", "difficulty": "medium", "doc_id": "57"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 23 nodes numbered from 0 to 22:\nnode 0 should be visited before node 19\nnode 0 should be visited before node 18\nnode 1 should be visited before node 14\nnode 1 should be visited before node 16\nnode 1 should be visited before node 5\nnode 1 should be visited before node 9\nnode 1 should be visited before node 11\nnode 1 should be visited before node 0\nnode 1 should be visited before node 3\nnode 2 should be visited before node 15\nnode 2 should be visited before node 19\nnode 4 should be visited before node 17\nnode 4 should be visited before node 16\nnode 4 should be visited before node 2\nnode 4 should be visited before node 11\nnode 5 should be visited before node 21\nnode 5 should be visited before node 9\nnode 5 should be visited before node 15\nnode 5 should be visited before node 11\nnode 6 should be visited before node 7\nnode 6 should be visited before node 17\nnode 6 should be visited before node 5\nnode 6 should be visited before node 20\nnode 6 should be visited before node 21\nnode 6 should be visited before node 22\nnode 6 should be visited before node 9\nnode 6 should be visited before node 0\nnode 7 should be visited before node 8\nnode 7 should be visited before node 9\nnode 7 should be visited before node 0\nnode 7 should be visited before node 18\nnode 8 should be visited before node 4\nnode 8 should be visited before node 14\nnode 8 should be visited before node 5\nnode 8 should be visited before node 22\nnode 8 should be visited before node 11\nnode 8 should be visited before node 3\nnode 9 should be visited before node 11\nnode 9 should be visited before node 3\nnode 10 should be visited before node 2\nnode 10 should be visited before node 19\nnode 10 should be visited before node 3\nnode 11 should be visited before node 18\nnode 12 should be visited before node 5\nnode 12 should be visited before node 3\nnode 13 should be visited before node 8\nnode 13 should be visited before node 16\nnode 13 should be visited before node 5\nnode 13 should be visited before node 22\nnode 13 should be visited before node 9\nnode 13 should be visited before node 18\nnode 14 should be visited before node 16\nnode 14 should be visited before node 15\nnode 14 should be visited before node 0\nnode 14 should be visited before node 19\nnode 14 should be visited before node 3\nnode 16 should be visited before node 21\nnode 16 should be visited before node 2\nnode 16 should be visited before node 19\nnode 17 should be visited before node 20\nnode 17 should be visited before node 10\nnode 17 should be visited before node 21\nnode 17 should be visited before node 22\nnode 17 should be visited before node 2\nnode 17 should be visited before node 15\nnode 17 should be visited before node 0\nnode 17 should be visited before node 3\nnode 20 should be visited before node 10\nnode 20 should be visited before node 2\nnode 20 should be visited before node 11\nnode 20 should be visited before node 0\nnode 20 should be visited before node 3\nnode 21 should be visited before node 22\nnode 21 should be visited before node 11\nnode 21 should be visited before node 18\nnode 22 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 1,6,12,13,7,8,4,14,5,17,16,9,20,21,10,0,22,11,3,2,18,15,19.", "difficulty": "medium", "doc_id": "58"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 11 nodes numbered from 0 to 10:\nnode 0 should be visited before node 3\nnode 0 should be visited before node 9\nnode 0 should be visited before node 4\nnode 0 should be visited before node 10\nnode 0 should be visited before node 6\nnode 0 should be visited before node 1\nnode 0 should be visited before node 8\nnode 2 should be visited before node 5\nnode 2 should be visited before node 4\nnode 2 should be visited before node 10\nnode 2 should be visited before node 8\nnode 3 should be visited before node 9\nnode 3 should be visited before node 4\nnode 3 should be visited before node 6\nnode 3 should be visited before node 1\nnode 3 should be visited before node 8\nnode 4 should be visited before node 10\nnode 4 should be visited before node 6\nnode 4 should be visited before node 1\nnode 4 should be visited before node 8\nnode 5 should be visited before node 3\nnode 5 should be visited before node 10\nnode 5 should be visited before node 6\nnode 5 should be visited before node 1\nnode 5 should be visited before node 8\nnode 7 should be visited before node 0\nnode 7 should be visited before node 9\nnode 7 should be visited before node 4\nnode 7 should be visited before node 1\nnode 7 should be visited before node 8\nnode 9 should be visited before node 10\nnode 9 should be visited before node 8\nnode 10 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 2,7,5,0,3,9,4,10,6,8,1.", "difficulty": "medium", "doc_id": "59"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 17 nodes numbered from 0 to 16:\nnode 0 should be visited before node 3\nnode 0 should be visited before node 11\nnode 0 should be visited before node 9\nnode 0 should be visited before node 2\nnode 0 should be visited before node 4\nnode 0 should be visited before node 8\nnode 0 should be visited before node 12\nnode 0 should be visited before node 6\nnode 0 should be visited before node 16\nnode 0 should be visited before node 5\nnode 1 should be visited before node 6\nnode 1 should be visited before node 16\nnode 2 should be visited before node 4\nnode 2 should be visited before node 8\nnode 2 should be visited before node 12\nnode 2 should be visited before node 6\nnode 2 should be visited before node 16\nnode 3 should be visited before node 9\nnode 3 should be visited before node 2\nnode 3 should be visited before node 8\nnode 3 should be visited before node 6\nnode 3 should be visited before node 5\nnode 4 should be visited before node 10\nnode 4 should be visited before node 8\nnode 4 should be visited before node 1\nnode 4 should be visited before node 7\nnode 4 should be visited before node 12\nnode 4 should be visited before node 6\nnode 4 should be visited before node 16\nnode 6 should be visited before node 5\nnode 8 should be visited before node 1\nnode 8 should be visited before node 7\nnode 9 should be visited before node 13\nnode 9 should be visited before node 4\nnode 9 should be visited before node 7\nnode 9 should be visited before node 12\nnode 9 should be visited before node 5\nnode 10 should be visited before node 1\nnode 10 should be visited before node 15\nnode 10 should be visited before node 7\nnode 10 should be visited before node 6\nnode 10 should be visited before node 16\nnode 11 should be visited before node 9\nnode 11 should be visited before node 13\nnode 11 should be visited before node 2\nnode 11 should be visited before node 8\nnode 11 should be visited before node 1\nnode 11 should be visited before node 7\nnode 11 should be visited before node 6\nnode 11 should be visited before node 16\nnode 12 should be visited before node 5\nnode 13 should be visited before node 4\nnode 13 should be visited before node 10\nnode 13 should be visited before node 8\nnode 13 should be visited before node 7\nnode 13 should be visited before node 5\nnode 14 should be visited before node 3\nnode 14 should be visited before node 11\nnode 14 should be visited before node 9\nnode 14 should be visited before node 13\nnode 14 should be visited before node 8\nnode 14 should be visited before node 15\nnode 14 should be visited before node 12\nnode 14 should be visited before node 6\nnode 14 should be visited before node 16\nnode 15 should be visited before node 7\nnode 15 should be visited before node 12\nnode 15 should be visited before node 16\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 0,14,3,11,9,2,13,4,10,8,15,1,7,12,6,16,5.", "difficulty": "medium", "doc_id": "60"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 26 nodes numbered from 0 to 25:\nnode 0 should be visited before node 2\nnode 0 should be visited before node 7\nnode 0 should be visited before node 12\nnode 0 should be visited before node 16\nnode 0 should be visited before node 11\nnode 0 should be visited before node 20\nnode 0 should be visited before node 22\nnode 0 should be visited before node 14\nnode 0 should be visited before node 4\nnode 0 should be visited before node 15\nnode 0 should be visited before node 5\nnode 1 should be visited before node 14\nnode 1 should be visited before node 8\nnode 1 should be visited before node 10\nnode 1 should be visited before node 25\nnode 1 should be visited before node 4\nnode 1 should be visited before node 15\nnode 1 should be visited before node 13\nnode 1 should be visited before node 5\nnode 1 should be visited before node 3\nnode 2 should be visited before node 17\nnode 2 should be visited before node 7\nnode 2 should be visited before node 18\nnode 2 should be visited before node 1\nnode 2 should be visited before node 22\nnode 2 should be visited before node 15\nnode 4 should be visited before node 13\nnode 4 should be visited before node 5\nnode 5 should be visited before node 3\nnode 6 should be visited before node 17\nnode 6 should be visited before node 7\nnode 6 should be visited before node 18\nnode 6 should be visited before node 11\nnode 6 should be visited before node 22\nnode 6 should be visited before node 15\nnode 6 should be visited before node 13\nnode 6 should be visited before node 5\nnode 6 should be visited before node 3\nnode 7 should be visited before node 18\nnode 7 should be visited before node 20\nnode 7 should be visited before node 14\nnode 7 should be visited before node 24\nnode 7 should be visited before node 8\nnode 7 should be visited before node 10\nnode 7 should be visited before node 9\nnode 7 should be visited before node 13\nnode 7 should be visited before node 5\nnode 7 should be visited before node 3\nnode 8 should be visited before node 25\nnode 8 should be visited before node 13\nnode 8 should be visited before node 5\nnode 8 should be visited before node 3\nnode 9 should be visited before node 13\nnode 10 should be visited before node 15\nnode 10 should be visited before node 5\nnode 11 should be visited before node 20\nnode 11 should be visited before node 22\nnode 11 should be visited before node 19\nnode 11 should be visited before node 24\nnode 11 should be visited before node 8\nnode 11 should be visited before node 10\nnode 11 should be visited before node 9\nnode 11 should be visited before node 15\nnode 11 should be visited before node 13\nnode 11 should be visited before node 3\nnode 12 should be visited before node 19\nnode 12 should be visited before node 8\nnode 12 should be visited before node 9\nnode 13 should be visited before node 5\nnode 14 should be visited before node 4\nnode 14 should be visited before node 15\nnode 14 should be visited before node 5\nnode 14 should be visited before node 3\nnode 15 should be visited before node 13\nnode 16 should be visited before node 19\nnode 16 should be visited before node 10\nnode 16 should be visited before node 25\nnode 16 should be visited before node 4\nnode 16 should be visited before node 15\nnode 16 should be visited before node 5\nnode 16 should be visited before node 3\nnode 17 should be visited before node 7\nnode 17 should be visited before node 12\nnode 17 should be visited before node 16\nnode 17 should be visited before node 18\nnode 17 should be visited before node 1\nnode 17 should be visited before node 20\nnode 17 should be visited before node 22\nnode 17 should be visited before node 14\nnode 17 should be visited before node 8\nnode 17 should be visited before node 10\nnode 17 should be visited before node 5\nnode 17 should be visited before node 3\nnode 18 should be visited before node 1\nnode 18 should be visited before node 11\nnode 18 should be visited before node 20\nnode 18 should be visited before node 14\nnode 18 should be visited before node 24\nnode 18 should be visited before node 10\nnode 18 should be visited before node 3\nnode 19 should be visited before node 14\nnode 19 should be visited before node 24\nnode 19 should be visited before node 15\nnode 19 should be visited before node 3\nnode 20 should be visited before node 22\nnode 20 should be visited before node 14\nnode 20 should be visited before node 4\nnode 20 should be visited before node 3\nnode 21 should be visited before node 7\nnode 21 should be visited before node 12\nnode 21 should be visited before node 11\nnode 21 should be visited before node 19\nnode 21 should be visited before node 14\nnode 21 should be visited before node 24\nnode 21 should be visited before node 9\nnode 21 should be visited before node 15\nnode 21 should be visited before node 13\nnode 21 should be visited before node 3\nnode 22 should be visited before node 19\nnode 22 should be visited before node 4\nnode 22 should be visited before node 15\nnode 22 should be visited before node 5\nnode 23 should be visited before node 21\nnode 23 should be visited before node 2\nnode 23 should be visited before node 7\nnode 23 should be visited before node 1\nnode 23 should be visited before node 11\nnode 23 should be visited before node 20\nnode 23 should be visited before node 22\nnode 23 should be visited before node 19\nnode 23 should be visited before node 24\nnode 23 should be visited before node 8\nnode 23 should be visited before node 10\nnode 23 should be visited before node 4\nnode 23 should be visited before node 15\nnode 23 should be visited before node 13\nnode 23 should be visited before node 5\nnode 24 should be visited before node 9\nnode 24 should be visited before node 25\nnode 24 should be visited before node 4\nnode 24 should be visited before node 15\nnode 24 should be visited before node 5\nnode 25 should be visited before node 4\nnode 25 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 0,6,23,21,2,17,7,12,16,18,1,11,20,8,10,22,19,14,24,9,25,15,4,13,5,3.", "difficulty": "hard", "doc_id": "61"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 15 nodes numbered from 0 to 14:\nnode 0 should be visited before node 10\nnode 0 should be visited before node 7\nnode 0 should be visited before node 14\nnode 0 should be visited before node 6\nnode 0 should be visited before node 1\nnode 2 should be visited before node 6\nnode 3 should be visited before node 10\nnode 3 should be visited before node 8\nnode 3 should be visited before node 4\nnode 3 should be visited before node 14\nnode 3 should be visited before node 6\nnode 3 should be visited before node 1\nnode 4 should be visited before node 14\nnode 4 should be visited before node 12\nnode 4 should be visited before node 1\nnode 5 should be visited before node 10\nnode 5 should be visited before node 8\nnode 5 should be visited before node 7\nnode 5 should be visited before node 14\nnode 5 should be visited before node 12\nnode 5 should be visited before node 6\nnode 5 should be visited before node 1\nnode 7 should be visited before node 4\nnode 7 should be visited before node 12\nnode 7 should be visited before node 6\nnode 8 should be visited before node 2\nnode 8 should be visited before node 4\nnode 8 should be visited before node 6\nnode 9 should be visited before node 13\nnode 9 should be visited before node 0\nnode 9 should be visited before node 5\nnode 9 should be visited before node 14\nnode 10 should be visited before node 8\nnode 10 should be visited before node 2\nnode 10 should be visited before node 1\nnode 11 should be visited before node 9\nnode 11 should be visited before node 13\nnode 11 should be visited before node 3\nnode 11 should be visited before node 0\nnode 11 should be visited before node 8\nnode 11 should be visited before node 14\nnode 11 should be visited before node 12\nnode 12 should be visited before node 1\nnode 13 should be visited before node 5\nnode 13 should be visited before node 10\nnode 13 should be visited before node 8\nnode 13 should be visited before node 6\nnode 13 should be visited before node 1\nnode 14 should be visited before node 12\nnode 14 should be visited before node 6\nnode 14 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 11,9,3,13,0,5,10,7,8,2,4,14,12,6,1.", "difficulty": "medium", "doc_id": "62"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 18 nodes numbered from 0 to 17:\nnode 0 should be visited before node 8\nnode 0 should be visited before node 4\nnode 0 should be visited before node 12\nnode 0 should be visited before node 14\nnode 0 should be visited before node 2\nnode 0 should be visited before node 16\nnode 0 should be visited before node 13\nnode 0 should be visited before node 11\nnode 0 should be visited before node 3\nnode 0 should be visited before node 1\nnode 0 should be visited before node 10\nnode 1 should be visited before node 15\nnode 2 should be visited before node 17\nnode 2 should be visited before node 5\nnode 2 should be visited before node 11\nnode 2 should be visited before node 3\nnode 2 should be visited before node 10\nnode 4 should be visited before node 12\nnode 4 should be visited before node 17\nnode 4 should be visited before node 16\nnode 4 should be visited before node 10\nnode 4 should be visited before node 15\nnode 5 should be visited before node 3\nnode 5 should be visited before node 1\nnode 5 should be visited before node 15\nnode 6 should be visited before node 0\nnode 6 should be visited before node 8\nnode 6 should be visited before node 9\nnode 6 should be visited before node 4\nnode 6 should be visited before node 2\nnode 6 should be visited before node 17\nnode 6 should be visited before node 5\nnode 6 should be visited before node 15\nnode 7 should be visited before node 0\nnode 7 should be visited before node 4\nnode 7 should be visited before node 12\nnode 7 should be visited before node 14\nnode 7 should be visited before node 2\nnode 7 should be visited before node 5\nnode 7 should be visited before node 13\nnode 7 should be visited before node 11\nnode 7 should be visited before node 1\nnode 7 should be visited before node 15\nnode 8 should be visited before node 4\nnode 8 should be visited before node 12\nnode 8 should be visited before node 5\nnode 8 should be visited before node 13\nnode 8 should be visited before node 11\nnode 8 should be visited before node 1\nnode 8 should be visited before node 10\nnode 9 should be visited before node 4\nnode 9 should be visited before node 12\nnode 9 should be visited before node 5\nnode 9 should be visited before node 16\nnode 9 should be visited before node 13\nnode 9 should be visited before node 3\nnode 9 should be visited before node 1\nnode 9 should be visited before node 15\nnode 11 should be visited before node 3\nnode 11 should be visited before node 1\nnode 11 should be visited before node 10\nnode 11 should be visited before node 15\nnode 12 should be visited before node 17\nnode 12 should be visited before node 5\nnode 12 should be visited before node 16\nnode 12 should be visited before node 3\nnode 12 should be visited before node 1\nnode 12 should be visited before node 10\nnode 12 should be visited before node 15\nnode 13 should be visited before node 3\nnode 13 should be visited before node 1\nnode 13 should be visited before node 10\nnode 13 should be visited before node 15\nnode 14 should be visited before node 2\nnode 14 should be visited before node 13\nnode 14 should be visited before node 11\nnode 14 should be visited before node 3\nnode 14 should be visited before node 1\nnode 14 should be visited before node 10\nnode 14 should be visited before node 15\nnode 16 should be visited before node 3\nnode 16 should be visited before node 1\nnode 16 should be visited before node 10\nnode 16 should be visited before node 15\nnode 17 should be visited before node 13\nnode 17 should be visited before node 15\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 6,7,9,0,8,14,4,2,12,11,17,5,16,13,3,1,10,15.", "difficulty": "medium", "doc_id": "63"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 21 nodes numbered from 0 to 20:\nnode 1 should be visited before node 17\nnode 1 should be visited before node 13\nnode 1 should be visited before node 4\nnode 1 should be visited before node 2\nnode 1 should be visited before node 10\nnode 1 should be visited before node 12\nnode 1 should be visited before node 19\nnode 1 should be visited before node 8\nnode 1 should be visited before node 11\nnode 2 should be visited before node 10\nnode 2 should be visited before node 19\nnode 2 should be visited before node 8\nnode 2 should be visited before node 0\nnode 3 should be visited before node 5\nnode 3 should be visited before node 1\nnode 3 should be visited before node 17\nnode 3 should be visited before node 13\nnode 3 should be visited before node 4\nnode 3 should be visited before node 2\nnode 3 should be visited before node 10\nnode 3 should be visited before node 12\nnode 3 should be visited before node 19\nnode 3 should be visited before node 8\nnode 3 should be visited before node 15\nnode 3 should be visited before node 11\nnode 3 should be visited before node 0\nnode 4 should be visited before node 2\nnode 4 should be visited before node 19\nnode 4 should be visited before node 8\nnode 4 should be visited before node 15\nnode 4 should be visited before node 11\nnode 5 should be visited before node 1\nnode 5 should be visited before node 13\nnode 5 should be visited before node 10\nnode 5 should be visited before node 12\nnode 5 should be visited before node 8\nnode 5 should be visited before node 15\nnode 5 should be visited before node 11\nnode 6 should be visited before node 16\nnode 6 should be visited before node 5\nnode 6 should be visited before node 1\nnode 6 should be visited before node 17\nnode 6 should be visited before node 13\nnode 6 should be visited before node 4\nnode 6 should be visited before node 7\nnode 6 should be visited before node 2\nnode 6 should be visited before node 10\nnode 6 should be visited before node 12\nnode 6 should be visited before node 0\nnode 7 should be visited before node 2\nnode 7 should be visited before node 10\nnode 7 should be visited before node 19\nnode 7 should be visited before node 8\nnode 7 should be visited before node 15\nnode 7 should be visited before node 11\nnode 8 should be visited before node 15\nnode 8 should be visited before node 0\nnode 9 should be visited before node 20\nnode 9 should be visited before node 6\nnode 9 should be visited before node 16\nnode 9 should be visited before node 3\nnode 9 should be visited before node 1\nnode 9 should be visited before node 13\nnode 9 should be visited before node 4\nnode 9 should be visited before node 7\nnode 9 should be visited before node 10\nnode 9 should be visited before node 12\nnode 9 should be visited before node 19\nnode 9 should be visited before node 15\nnode 10 should be visited before node 19\nnode 10 should be visited before node 8\nnode 10 should be visited before node 11\nnode 10 should be visited before node 0\nnode 12 should be visited before node 19\nnode 12 should be visited before node 11\nnode 12 should be visited before node 0\nnode 13 should be visited before node 4\nnode 13 should be visited before node 7\nnode 13 should be visited before node 2\nnode 13 should be visited before node 10\nnode 13 should be visited before node 12\nnode 13 should be visited before node 19\nnode 13 should be visited before node 11\nnode 13 should be visited before node 0\nnode 14 should be visited before node 20\nnode 14 should be visited before node 6\nnode 14 should be visited before node 3\nnode 14 should be visited before node 5\nnode 14 should be visited before node 4\nnode 14 should be visited before node 7\nnode 14 should be visited before node 2\nnode 14 should be visited before node 10\nnode 14 should be visited before node 12\nnode 14 should be visited before node 19\nnode 14 should be visited before node 8\nnode 14 should be visited before node 15\nnode 14 should be visited before node 11\nnode 16 should be visited before node 17\nnode 16 should be visited before node 4\nnode 16 should be visited before node 7\nnode 16 should be visited before node 10\nnode 16 should be visited before node 12\nnode 16 should be visited before node 19\nnode 16 should be visited before node 8\nnode 16 should be visited before node 0\nnode 17 should be visited before node 13\nnode 17 should be visited before node 4\nnode 17 should be visited before node 7\nnode 17 should be visited before node 2\nnode 17 should be visited before node 10\nnode 17 should be visited before node 12\nnode 17 should be visited before node 8\nnode 18 should be visited before node 14\nnode 18 should be visited before node 20\nnode 18 should be visited before node 5\nnode 18 should be visited before node 17\nnode 18 should be visited before node 13\nnode 18 should be visited before node 7\nnode 18 should be visited before node 10\nnode 18 should be visited before node 8\nnode 18 should be visited before node 11\nnode 19 should be visited before node 8\nnode 19 should be visited before node 15\nnode 20 should be visited before node 16\nnode 20 should be visited before node 3\nnode 20 should be visited before node 5\nnode 20 should be visited before node 1\nnode 20 should be visited before node 17\nnode 20 should be visited before node 4\nnode 20 should be visited before node 7\nnode 20 should be visited before node 10\nnode 20 should be visited before node 19\nnode 20 should be visited before node 8\nnode 20 should be visited before node 15\nnode 20 should be visited before node 11\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 9,18,14,20,6,3,16,5,1,17,13,4,7,12,2,10,19,11,8,15,0.", "difficulty": "medium", "doc_id": "64"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 1\nnode 2 should be visited before node 0\nnode 2 should be visited before node 1\nnode 3 should be visited before node 5\nnode 3 should be visited before node 1\nnode 4 should be visited before node 1\nnode 5 should be visited before node 2\nnode 5 should be visited before node 0\nnode 5 should be visited before node 4\nnode 5 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 3,5,2,4,0,1.", "difficulty": "easy", "doc_id": "65"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 3\nnode 2 should be visited before node 0\nnode 2 should be visited before node 3\nnode 2 should be visited before node 1\nnode 3 should be visited before node 1\nnode 4 should be visited before node 2\nnode 4 should be visited before node 3\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 4,2,0,3,1.", "difficulty": "easy", "doc_id": "66"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 16 nodes numbered from 0 to 15:\nnode 1 should be visited before node 10\nnode 1 should be visited before node 4\nnode 1 should be visited before node 12\nnode 1 should be visited before node 8\nnode 1 should be visited before node 5\nnode 1 should be visited before node 11\nnode 1 should be visited before node 6\nnode 1 should be visited before node 7\nnode 1 should be visited before node 0\nnode 2 should be visited before node 13\nnode 2 should be visited before node 1\nnode 2 should be visited before node 12\nnode 2 should be visited before node 9\nnode 2 should be visited before node 5\nnode 2 should be visited before node 14\nnode 2 should be visited before node 11\nnode 2 should be visited before node 6\nnode 2 should be visited before node 7\nnode 2 should be visited before node 15\nnode 2 should be visited before node 0\nnode 3 should be visited before node 11\nnode 3 should be visited before node 6\nnode 3 should be visited before node 7\nnode 3 should be visited before node 15\nnode 4 should be visited before node 12\nnode 4 should be visited before node 5\nnode 4 should be visited before node 14\nnode 4 should be visited before node 3\nnode 4 should be visited before node 15\nnode 5 should be visited before node 14\nnode 5 should be visited before node 3\nnode 5 should be visited before node 6\nnode 5 should be visited before node 7\nnode 5 should be visited before node 15\nnode 6 should be visited before node 15\nnode 6 should be visited before node 0\nnode 8 should be visited before node 3\nnode 8 should be visited before node 11\nnode 8 should be visited before node 6\nnode 8 should be visited before node 7\nnode 8 should be visited before node 0\nnode 9 should be visited before node 8\nnode 9 should be visited before node 5\nnode 9 should be visited before node 11\nnode 9 should be visited before node 6\nnode 9 should be visited before node 7\nnode 9 should be visited before node 15\nnode 9 should be visited before node 0\nnode 10 should be visited before node 4\nnode 10 should be visited before node 6\nnode 10 should be visited before node 7\nnode 10 should be visited before node 15\nnode 10 should be visited before node 0\nnode 11 should be visited before node 7\nnode 11 should be visited before node 15\nnode 11 should be visited before node 0\nnode 12 should be visited before node 9\nnode 12 should be visited before node 8\nnode 12 should be visited before node 5\nnode 12 should be visited before node 14\nnode 12 should be visited before node 3\nnode 12 should be visited before node 11\nnode 12 should be visited before node 6\nnode 12 should be visited before node 7\nnode 12 should be visited before node 15\nnode 12 should be visited before node 0\nnode 13 should be visited before node 1\nnode 13 should be visited before node 4\nnode 13 should be visited before node 12\nnode 13 should be visited before node 9\nnode 13 should be visited before node 5\nnode 13 should be visited before node 3\nnode 13 should be visited before node 11\nnode 13 should be visited before node 6\nnode 13 should be visited before node 7\nnode 13 should be visited before node 15\nnode 13 should be visited before node 0\nnode 14 should be visited before node 6\nnode 14 should be visited before node 15\nnode 15 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 2,13,1,10,4,12,9,8,5,14,3,11,6,7,15,0.", "difficulty": "medium", "doc_id": "67"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 12 nodes numbered from 0 to 11:\nnode 1 should be visited before node 0\nnode 3 should be visited before node 9\nnode 3 should be visited before node 7\nnode 3 should be visited before node 2\nnode 3 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 4 should be visited before node 5\nnode 6 should be visited before node 10\nnode 6 should be visited before node 2\nnode 6 should be visited before node 5\nnode 8 should be visited before node 7\nnode 8 should be visited before node 2\nnode 9 should be visited before node 7\nnode 9 should be visited before node 10\nnode 10 should be visited before node 0\nnode 11 should be visited before node 3\nnode 11 should be visited before node 8\nnode 11 should be visited before node 4\nnode 11 should be visited before node 6\nnode 11 should be visited before node 1\nnode 11 should be visited before node 2\nnode 11 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 11,3,8,4,6,9,1,2,5,7,10,0.", "difficulty": "medium", "doc_id": "68"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 16 nodes numbered from 0 to 15:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 8\nnode 0 should be visited before node 14\nnode 1 should be visited before node 8\nnode 2 should be visited before node 13\nnode 3 should be visited before node 8\nnode 4 should be visited before node 3\nnode 4 should be visited before node 14\nnode 5 should be visited before node 13\nnode 5 should be visited before node 4\nnode 5 should be visited before node 3\nnode 5 should be visited before node 8\nnode 5 should be visited before node 14\nnode 6 should be visited before node 13\nnode 6 should be visited before node 0\nnode 6 should be visited before node 1\nnode 6 should be visited before node 14\nnode 7 should be visited before node 0\nnode 7 should be visited before node 4\nnode 7 should be visited before node 3\nnode 7 should be visited before node 14\nnode 9 should be visited before node 12\nnode 9 should be visited before node 5\nnode 9 should be visited before node 6\nnode 9 should be visited before node 2\nnode 9 should be visited before node 13\nnode 9 should be visited before node 4\nnode 9 should be visited before node 1\nnode 10 should be visited before node 15\nnode 10 should be visited before node 5\nnode 10 should be visited before node 6\nnode 10 should be visited before node 2\nnode 10 should be visited before node 0\nnode 10 should be visited before node 4\nnode 10 should be visited before node 3\nnode 10 should be visited before node 8\nnode 11 should be visited before node 9\nnode 11 should be visited before node 12\nnode 11 should be visited before node 6\nnode 11 should be visited before node 7\nnode 11 should be visited before node 4\nnode 11 should be visited before node 3\nnode 11 should be visited before node 8\nnode 11 should be visited before node 14\nnode 12 should be visited before node 5\nnode 12 should be visited before node 13\nnode 12 should be visited before node 4\nnode 12 should be visited before node 3\nnode 12 should be visited before node 8\nnode 12 should be visited before node 14\nnode 13 should be visited before node 4\nnode 13 should be visited before node 1\nnode 13 should be visited before node 3\nnode 15 should be visited before node 12\nnode 15 should be visited before node 5\nnode 15 should be visited before node 7\nnode 15 should be visited before node 13\nnode 15 should be visited before node 4\nnode 15 should be visited before node 1\nnode 15 should be visited before node 8\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 10,11,15,9,7,12,6,2,5,0,13,4,1,3,14,8.", "difficulty": "medium", "doc_id": "69"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 34 nodes numbered from 0 to 33:\nnode 0 should be visited before node 5\nnode 0 should be visited before node 3\nnode 0 should be visited before node 33\nnode 0 should be visited before node 4\nnode 0 should be visited before node 31\nnode 0 should be visited before node 17\nnode 0 should be visited before node 20\nnode 0 should be visited before node 26\nnode 1 should be visited before node 28\nnode 1 should be visited before node 21\nnode 1 should be visited before node 0\nnode 1 should be visited before node 16\nnode 1 should be visited before node 13\nnode 1 should be visited before node 30\nnode 1 should be visited before node 33\nnode 1 should be visited before node 4\nnode 1 should be visited before node 11\nnode 1 should be visited before node 31\nnode 1 should be visited before node 17\nnode 1 should be visited before node 26\nnode 1 should be visited before node 2\nnode 1 should be visited before node 29\nnode 3 should be visited before node 33\nnode 3 should be visited before node 4\nnode 3 should be visited before node 2\nnode 3 should be visited before node 29\nnode 4 should be visited before node 11\nnode 4 should be visited before node 31\nnode 4 should be visited before node 20\nnode 4 should be visited before node 26\nnode 4 should be visited before node 2\nnode 5 should be visited before node 33\nnode 5 should be visited before node 4\nnode 5 should be visited before node 11\nnode 5 should be visited before node 17\nnode 5 should be visited before node 20\nnode 5 should be visited before node 26\nnode 5 should be visited before node 2\nnode 6 should be visited before node 14\nnode 6 should be visited before node 25\nnode 6 should be visited before node 9\nnode 6 should be visited before node 28\nnode 6 should be visited before node 10\nnode 6 should be visited before node 30\nnode 6 should be visited before node 3\nnode 6 should be visited before node 4\nnode 6 should be visited before node 11\nnode 6 should be visited before node 17\nnode 6 should be visited before node 20\nnode 6 should be visited before node 26\nnode 6 should be visited before node 2\nnode 7 should be visited before node 23\nnode 7 should be visited before node 15\nnode 7 should be visited before node 22\nnode 7 should be visited before node 14\nnode 7 should be visited before node 12\nnode 7 should be visited before node 1\nnode 7 should be visited before node 28\nnode 7 should be visited before node 21\nnode 7 should be visited before node 0\nnode 7 should be visited before node 16\nnode 7 should be visited before node 13\nnode 7 should be visited before node 3\nnode 7 should be visited before node 33\nnode 7 should be visited before node 11\nnode 7 should be visited before node 31\nnode 7 should be visited before node 2\nnode 7 should be visited before node 29\nnode 8 should be visited before node 18\nnode 8 should be visited before node 23\nnode 8 should be visited before node 19\nnode 8 should be visited before node 15\nnode 8 should be visited before node 22\nnode 8 should be visited before node 14\nnode 8 should be visited before node 25\nnode 8 should be visited before node 9\nnode 8 should be visited before node 27\nnode 8 should be visited before node 1\nnode 8 should be visited before node 16\nnode 8 should be visited before node 13\nnode 8 should be visited before node 5\nnode 8 should be visited before node 30\nnode 8 should be visited before node 33\nnode 8 should be visited before node 31\nnode 9 should be visited before node 27\nnode 9 should be visited before node 1\nnode 9 should be visited before node 28\nnode 9 should be visited before node 0\nnode 9 should be visited before node 16\nnode 9 should be visited before node 10\nnode 9 should be visited before node 13\nnode 9 should be visited before node 30\nnode 9 should be visited before node 31\nnode 9 should be visited before node 20\nnode 9 should be visited before node 29\nnode 10 should be visited before node 33\nnode 10 should be visited before node 20\nnode 10 should be visited before node 26\nnode 10 should be visited before node 2\nnode 10 should be visited before node 29\nnode 11 should be visited before node 17\nnode 11 should be visited before node 20\nnode 11 should be visited before node 29\nnode 12 should be visited before node 28\nnode 12 should be visited before node 21\nnode 12 should be visited before node 0\nnode 12 should be visited before node 10\nnode 12 should be visited before node 13\nnode 12 should be visited before node 4\nnode 12 should be visited before node 11\nnode 12 should be visited before node 31\nnode 12 should be visited before node 17\nnode 12 should be visited before node 20\nnode 13 should be visited before node 5\nnode 13 should be visited before node 30\nnode 13 should be visited before node 3\nnode 13 should be visited before node 33\nnode 13 should be visited before node 31\nnode 13 should be visited before node 17\nnode 13 should be visited before node 20\nnode 13 should be visited before node 26\nnode 14 should be visited before node 25\nnode 14 should be visited before node 27\nnode 14 should be visited before node 1\nnode 14 should be visited before node 30\nnode 14 should be visited before node 4\nnode 14 should be visited before node 11\nnode 14 should be visited before node 31\nnode 14 should be visited before node 17\nnode 14 should be visited before node 20\nnode 14 should be visited before node 2\nnode 15 should be visited before node 6\nnode 15 should be visited before node 14\nnode 15 should be visited before node 1\nnode 15 should be visited before node 21\nnode 15 should be visited before node 0\nnode 15 should be visited before node 30\nnode 15 should be visited before node 3\nnode 15 should be visited before node 11\nnode 15 should be visited before node 31\nnode 15 should be visited before node 17\nnode 15 should be visited before node 2\nnode 16 should be visited before node 10\nnode 16 should be visited before node 13\nnode 16 should be visited before node 5\nnode 16 should be visited before node 3\nnode 16 should be visited before node 33\nnode 16 should be visited before node 4\nnode 16 should be visited before node 31\nnode 16 should be visited before node 17\nnode 16 should be visited before node 26\nnode 16 should be visited before node 2\nnode 18 should be visited before node 23\nnode 18 should be visited before node 19\nnode 18 should be visited before node 15\nnode 18 should be visited before node 32\nnode 18 should be visited before node 14\nnode 18 should be visited before node 27\nnode 18 should be visited before node 12\nnode 18 should be visited before node 1\nnode 18 should be visited before node 28\nnode 18 should be visited before node 21\nnode 18 should be visited before node 0\nnode 18 should be visited before node 13\nnode 18 should be visited before node 30\nnode 18 should be visited before node 33\nnode 18 should be visited before node 4\nnode 18 should be visited before node 31\nnode 18 should be visited before node 20\nnode 18 should be visited before node 2\nnode 19 should be visited before node 15\nnode 19 should be visited before node 22\nnode 19 should be visited before node 25\nnode 19 should be visited before node 27\nnode 19 should be visited before node 12\nnode 19 should be visited before node 1\nnode 19 should be visited before node 28\nnode 19 should be visited before node 0\nnode 19 should be visited before node 13\nnode 19 should be visited before node 5\nnode 19 should be visited before node 30\nnode 19 should be visited before node 3\nnode 19 should be visited before node 33\nnode 19 should be visited before node 11\nnode 19 should be visited before node 20\nnode 19 should be visited before node 29\nnode 20 should be visited before node 26\nnode 20 should be visited before node 2\nnode 21 should be visited before node 0\nnode 21 should be visited before node 13\nnode 21 should be visited before node 5\nnode 21 should be visited before node 30\nnode 21 should be visited before node 3\nnode 21 should be visited before node 33\nnode 21 should be visited before node 17\nnode 21 should be visited before node 26\nnode 21 should be visited before node 29\nnode 22 should be visited before node 14\nnode 22 should be visited before node 25\nnode 22 should be visited before node 21\nnode 22 should be visited before node 0\nnode 22 should be visited before node 13\nnode 22 should be visited before node 30\nnode 22 should be visited before node 33\nnode 22 should be visited before node 29\nnode 23 should be visited before node 19\nnode 23 should be visited before node 25\nnode 23 should be visited before node 9\nnode 23 should be visited before node 21\nnode 23 should be visited before node 0\nnode 23 should be visited before node 16\nnode 23 should be visited before node 13\nnode 23 should be visited before node 3\nnode 23 should be visited before node 33\nnode 23 should be visited before node 20\nnode 23 should be visited before node 29\nnode 24 should be visited before node 8\nnode 24 should be visited before node 18\nnode 24 should be visited before node 19\nnode 24 should be visited before node 15\nnode 24 should be visited before node 32\nnode 24 should be visited before node 22\nnode 24 should be visited before node 27\nnode 24 should be visited before node 5\nnode 24 should be visited before node 30\nnode 24 should be visited before node 33\nnode 24 should be visited before node 4\nnode 24 should be visited before node 2\nnode 24 should be visited before node 29\nnode 25 should be visited before node 9\nnode 25 should be visited before node 27\nnode 25 should be visited before node 28\nnode 25 should be visited before node 21\nnode 25 should be visited before node 5\nnode 25 should be visited before node 3\nnode 25 should be visited before node 11\nnode 25 should be visited before node 26\nnode 25 should be visited before node 29\nnode 26 should be visited before node 2\nnode 26 should be visited before node 29\nnode 27 should be visited before node 1\nnode 27 should be visited before node 21\nnode 27 should be visited before node 16\nnode 27 should be visited before node 13\nnode 27 should be visited before node 3\nnode 27 should be visited before node 11\nnode 27 should be visited before node 31\nnode 27 should be visited before node 2\nnode 28 should be visited before node 16\nnode 28 should be visited before node 10\nnode 28 should be visited before node 13\nnode 28 should be visited before node 4\nnode 28 should be visited before node 11\nnode 28 should be visited before node 31\nnode 28 should be visited before node 17\nnode 30 should be visited before node 33\nnode 30 should be visited before node 4\nnode 30 should be visited before node 11\nnode 30 should be visited before node 17\nnode 30 should be visited before node 20\nnode 31 should be visited before node 17\nnode 31 should be visited before node 20\nnode 31 should be visited before node 26\nnode 31 should be visited before node 2\nnode 31 should be visited before node 29\nnode 32 should be visited before node 25\nnode 32 should be visited before node 9\nnode 32 should be visited before node 1\nnode 32 should be visited before node 21\nnode 32 should be visited before node 0\nnode 32 should be visited before node 16\nnode 32 should be visited before node 13\nnode 32 should be visited before node 30\nnode 32 should be visited before node 3\nnode 32 should be visited before node 4\nnode 32 should be visited before node 31\nnode 32 should be visited before node 20\nnode 32 should be visited before node 2\nnode 32 should be visited before node 29\nnode 33 should be visited before node 29\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 7,24,8,18,23,32,19,15,22,12,6,14,25,9,27,1,28,21,16,0,10,13,5,30,3,33,4,11,31,17,20,26,2,29.", "difficulty": "hard", "doc_id": "70"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 33 nodes numbered from 0 to 32:\nnode 0 should be visited before node 28\nnode 0 should be visited before node 2\nnode 0 should be visited before node 26\nnode 0 should be visited before node 23\nnode 0 should be visited before node 5\nnode 0 should be visited before node 6\nnode 0 should be visited before node 20\nnode 0 should be visited before node 16\nnode 0 should be visited before node 4\nnode 0 should be visited before node 21\nnode 0 should be visited before node 9\nnode 2 should be visited before node 5\nnode 2 should be visited before node 6\nnode 2 should be visited before node 19\nnode 2 should be visited before node 30\nnode 2 should be visited before node 20\nnode 2 should be visited before node 7\nnode 2 should be visited before node 21\nnode 2 should be visited before node 24\nnode 2 should be visited before node 1\nnode 3 should be visited before node 30\nnode 3 should be visited before node 20\nnode 3 should be visited before node 4\nnode 3 should be visited before node 21\nnode 3 should be visited before node 9\nnode 3 should be visited before node 24\nnode 3 should be visited before node 1\nnode 4 should be visited before node 24\nnode 4 should be visited before node 1\nnode 5 should be visited before node 11\nnode 5 should be visited before node 32\nnode 5 should be visited before node 16\nnode 5 should be visited before node 4\nnode 5 should be visited before node 21\nnode 5 should be visited before node 9\nnode 5 should be visited before node 24\nnode 5 should be visited before node 1\nnode 6 should be visited before node 32\nnode 6 should be visited before node 3\nnode 6 should be visited before node 16\nnode 6 should be visited before node 4\nnode 6 should be visited before node 21\nnode 6 should be visited before node 24\nnode 6 should be visited before node 1\nnode 7 should be visited before node 9\nnode 8 should be visited before node 29\nnode 8 should be visited before node 18\nnode 8 should be visited before node 31\nnode 8 should be visited before node 22\nnode 8 should be visited before node 15\nnode 8 should be visited before node 0\nnode 8 should be visited before node 12\nnode 8 should be visited before node 2\nnode 8 should be visited before node 5\nnode 8 should be visited before node 6\nnode 8 should be visited before node 11\nnode 8 should be visited before node 20\nnode 8 should be visited before node 4\nnode 8 should be visited before node 9\nnode 8 should be visited before node 24\nnode 10 should be visited before node 27\nnode 10 should be visited before node 29\nnode 10 should be visited before node 0\nnode 10 should be visited before node 14\nnode 10 should be visited before node 2\nnode 10 should be visited before node 26\nnode 10 should be visited before node 32\nnode 10 should be visited before node 30\nnode 10 should be visited before node 20\nnode 10 should be visited before node 7\nnode 10 should be visited before node 21\nnode 10 should be visited before node 9\nnode 11 should be visited before node 19\nnode 11 should be visited before node 30\nnode 11 should be visited before node 20\nnode 11 should be visited before node 7\nnode 11 should be visited before node 4\nnode 11 should be visited before node 21\nnode 11 should be visited before node 24\nnode 12 should be visited before node 2\nnode 12 should be visited before node 26\nnode 12 should be visited before node 23\nnode 12 should be visited before node 5\nnode 12 should be visited before node 6\nnode 12 should be visited before node 11\nnode 12 should be visited before node 32\nnode 12 should be visited before node 19\nnode 12 should be visited before node 30\nnode 12 should be visited before node 20\nnode 12 should be visited before node 7\nnode 12 should be visited before node 9\nnode 12 should be visited before node 24\nnode 12 should be visited before node 1\nnode 13 should be visited before node 23\nnode 13 should be visited before node 6\nnode 13 should be visited before node 32\nnode 13 should be visited before node 3\nnode 13 should be visited before node 19\nnode 13 should be visited before node 20\nnode 13 should be visited before node 16\nnode 13 should be visited before node 4\nnode 13 should be visited before node 21\nnode 13 should be visited before node 9\nnode 13 should be visited before node 24\nnode 13 should be visited before node 1\nnode 14 should be visited before node 28\nnode 14 should be visited before node 12\nnode 14 should be visited before node 26\nnode 14 should be visited before node 23\nnode 14 should be visited before node 32\nnode 14 should be visited before node 19\nnode 14 should be visited before node 30\nnode 14 should be visited before node 16\nnode 14 should be visited before node 7\nnode 14 should be visited before node 4\nnode 14 should be visited before node 9\nnode 14 should be visited before node 24\nnode 15 should be visited before node 0\nnode 15 should be visited before node 14\nnode 15 should be visited before node 13\nnode 15 should be visited before node 12\nnode 15 should be visited before node 2\nnode 15 should be visited before node 26\nnode 15 should be visited before node 5\nnode 15 should be visited before node 11\nnode 15 should be visited before node 19\nnode 15 should be visited before node 30\nnode 15 should be visited before node 7\nnode 15 should be visited before node 4\nnode 15 should be visited before node 9\nnode 15 should be visited before node 24\nnode 16 should be visited before node 7\nnode 16 should be visited before node 4\nnode 16 should be visited before node 21\nnode 16 should be visited before node 1\nnode 17 should be visited before node 31\nnode 17 should be visited before node 25\nnode 17 should be visited before node 0\nnode 17 should be visited before node 5\nnode 17 should be visited before node 6\nnode 17 should be visited before node 32\nnode 17 should be visited before node 7\nnode 17 should be visited before node 21\nnode 17 should be visited before node 24\nnode 17 should be visited before node 1\nnode 18 should be visited before node 17\nnode 18 should be visited before node 31\nnode 18 should be visited before node 25\nnode 18 should be visited before node 15\nnode 18 should be visited before node 28\nnode 18 should be visited before node 13\nnode 18 should be visited before node 26\nnode 18 should be visited before node 6\nnode 18 should be visited before node 11\nnode 18 should be visited before node 19\nnode 18 should be visited before node 20\nnode 18 should be visited before node 7\nnode 18 should be visited before node 9\nnode 19 should be visited before node 30\nnode 19 should be visited before node 16\nnode 19 should be visited before node 7\nnode 19 should be visited before node 4\nnode 20 should be visited before node 16\nnode 20 should be visited before node 7\nnode 20 should be visited before node 9\nnode 21 should be visited before node 9\nnode 21 should be visited before node 1\nnode 22 should be visited before node 0\nnode 22 should be visited before node 28\nnode 22 should be visited before node 2\nnode 22 should be visited before node 23\nnode 22 should be visited before node 5\nnode 22 should be visited before node 11\nnode 22 should be visited before node 3\nnode 22 should be visited before node 16\nnode 22 should be visited before node 4\nnode 22 should be visited before node 9\nnode 22 should be visited before node 1\nnode 23 should be visited before node 11\nnode 23 should be visited before node 3\nnode 23 should be visited before node 20\nnode 23 should be visited before node 16\nnode 23 should be visited before node 7\nnode 23 should be visited before node 4\nnode 23 should be visited before node 24\nnode 23 should be visited before node 1\nnode 25 should be visited before node 14\nnode 25 should be visited before node 28\nnode 25 should be visited before node 13\nnode 25 should be visited before node 32\nnode 25 should be visited before node 19\nnode 25 should be visited before node 30\nnode 25 should be visited before node 9\nnode 26 should be visited before node 23\nnode 26 should be visited before node 6\nnode 26 should be visited before node 11\nnode 26 should be visited before node 3\nnode 26 should be visited before node 20\nnode 26 should be visited before node 16\nnode 26 should be visited before node 7\nnode 26 should be visited before node 21\nnode 26 should be visited before node 9\nnode 26 should be visited before node 24\nnode 27 should be visited before node 8\nnode 27 should be visited before node 18\nnode 27 should be visited before node 31\nnode 27 should be visited before node 15\nnode 27 should be visited before node 0\nnode 27 should be visited before node 14\nnode 27 should be visited before node 2\nnode 27 should be visited before node 23\nnode 27 should be visited before node 6\nnode 27 should be visited before node 3\nnode 27 should be visited before node 30\nnode 27 should be visited before node 16\nnode 27 should be visited before node 7\nnode 27 should be visited before node 4\nnode 27 should be visited before node 21\nnode 27 should be visited before node 24\nnode 28 should be visited before node 12\nnode 28 should be visited before node 2\nnode 28 should be visited before node 26\nnode 28 should be visited before node 23\nnode 28 should be visited before node 5\nnode 28 should be visited before node 11\nnode 28 should be visited before node 30\nnode 28 should be visited before node 20\nnode 28 should be visited before node 7\nnode 28 should be visited before node 9\nnode 28 should be visited before node 24\nnode 29 should be visited before node 15\nnode 29 should be visited before node 0\nnode 29 should be visited before node 28\nnode 29 should be visited before node 12\nnode 29 should be visited before node 23\nnode 29 should be visited before node 5\nnode 29 should be visited before node 6\nnode 29 should be visited before node 32\nnode 29 should be visited before node 3\nnode 29 should be visited before node 30\nnode 29 should be visited before node 16\nnode 29 should be visited before node 7\nnode 29 should be visited before node 21\nnode 29 should be visited before node 9\nnode 30 should be visited before node 20\nnode 30 should be visited before node 16\nnode 30 should be visited before node 7\nnode 30 should be visited before node 9\nnode 30 should be visited before node 1\nnode 31 should be visited before node 25\nnode 31 should be visited before node 0\nnode 31 should be visited before node 28\nnode 31 should be visited before node 13\nnode 31 should be visited before node 26\nnode 31 should be visited before node 6\nnode 31 should be visited before node 32\nnode 31 should be visited before node 3\nnode 31 should be visited before node 7\nnode 31 should be visited before node 4\nnode 31 should be visited before node 21\nnode 32 should be visited before node 3\nnode 32 should be visited before node 19\nnode 32 should be visited before node 30\nnode 32 should be visited before node 7\nnode 32 should be visited before node 9\nnode 32 should be visited before node 24\nnode 32 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 10,27,8,29,18,22,17,15,31,25,0,14,13,28,12,2,26,5,23,6,11,32,3,19,30,20,16,7,4,21,24,9,1.", "difficulty": "hard", "doc_id": "71"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 20 nodes numbered from 0 to 19:\nnode 0 should be visited before node 17\nnode 1 should be visited before node 14\nnode 1 should be visited before node 15\nnode 2 should be visited before node 16\nnode 2 should be visited before node 3\nnode 2 should be visited before node 8\nnode 2 should be visited before node 0\nnode 2 should be visited before node 6\nnode 2 should be visited before node 17\nnode 3 should be visited before node 11\nnode 3 should be visited before node 6\nnode 4 should be visited before node 8\nnode 4 should be visited before node 7\nnode 5 should be visited before node 11\nnode 5 should be visited before node 6\nnode 7 should be visited before node 17\nnode 7 should be visited before node 9\nnode 8 should be visited before node 11\nnode 8 should be visited before node 0\nnode 8 should be visited before node 9\nnode 10 should be visited before node 1\nnode 10 should be visited before node 14\nnode 10 should be visited before node 4\nnode 11 should be visited before node 7\nnode 12 should be visited before node 16\nnode 12 should be visited before node 8\nnode 12 should be visited before node 17\nnode 13 should be visited before node 18\nnode 13 should be visited before node 15\nnode 13 should be visited before node 17\nnode 14 should be visited before node 18\nnode 14 should be visited before node 11\nnode 14 should be visited before node 0\nnode 14 should be visited before node 7\nnode 14 should be visited before node 15\nnode 14 should be visited before node 17\nnode 16 should be visited before node 13\nnode 16 should be visited before node 3\nnode 16 should be visited before node 19\nnode 16 should be visited before node 0\nnode 16 should be visited before node 15\nnode 18 should be visited before node 0\nnode 18 should be visited before node 6\nnode 18 should be visited before node 17\nnode 19 should be visited before node 11\nnode 19 should be visited before node 6\nnode 19 should be visited before node 17\nnode 19 should be visited before node 9\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 2,5,10,12,1,4,16,14,8,13,3,19,18,15,11,0,6,7,17,9.", "difficulty": "medium", "doc_id": "72"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 19 nodes numbered from 0 to 18:\nnode 0 should be visited before node 9\nnode 0 should be visited before node 15\nnode 0 should be visited before node 17\nnode 0 should be visited before node 5\nnode 0 should be visited before node 18\nnode 0 should be visited before node 14\nnode 1 should be visited before node 8\nnode 1 should be visited before node 10\nnode 1 should be visited before node 16\nnode 1 should be visited before node 2\nnode 1 should be visited before node 9\nnode 1 should be visited before node 15\nnode 1 should be visited before node 17\nnode 1 should be visited before node 5\nnode 1 should be visited before node 3\nnode 2 should be visited before node 9\nnode 2 should be visited before node 15\nnode 2 should be visited before node 17\nnode 2 should be visited before node 18\nnode 3 should be visited before node 14\nnode 4 should be visited before node 10\nnode 4 should be visited before node 2\nnode 4 should be visited before node 9\nnode 4 should be visited before node 15\nnode 4 should be visited before node 17\nnode 4 should be visited before node 18\nnode 4 should be visited before node 3\nnode 4 should be visited before node 14\nnode 5 should be visited before node 3\nnode 6 should be visited before node 13\nnode 6 should be visited before node 11\nnode 6 should be visited before node 8\nnode 6 should be visited before node 4\nnode 6 should be visited before node 16\nnode 6 should be visited before node 0\nnode 6 should be visited before node 2\nnode 6 should be visited before node 9\nnode 6 should be visited before node 15\nnode 6 should be visited before node 5\nnode 6 should be visited before node 18\nnode 6 should be visited before node 3\nnode 7 should be visited before node 13\nnode 7 should be visited before node 1\nnode 7 should be visited before node 8\nnode 7 should be visited before node 4\nnode 7 should be visited before node 10\nnode 7 should be visited before node 2\nnode 7 should be visited before node 15\nnode 7 should be visited before node 17\nnode 7 should be visited before node 14\nnode 8 should be visited before node 4\nnode 8 should be visited before node 10\nnode 8 should be visited before node 16\nnode 8 should be visited before node 2\nnode 8 should be visited before node 9\nnode 8 should be visited before node 15\nnode 8 should be visited before node 5\nnode 8 should be visited before node 18\nnode 8 should be visited before node 14\nnode 9 should be visited before node 15\nnode 9 should be visited before node 17\nnode 9 should be visited before node 5\nnode 9 should be visited before node 18\nnode 10 should be visited before node 16\nnode 10 should be visited before node 0\nnode 10 should be visited before node 2\nnode 10 should be visited before node 9\nnode 10 should be visited before node 15\nnode 10 should be visited before node 17\nnode 10 should be visited before node 3\nnode 10 should be visited before node 14\nnode 11 should be visited before node 4\nnode 11 should be visited before node 10\nnode 11 should be visited before node 16\nnode 11 should be visited before node 0\nnode 11 should be visited before node 2\nnode 11 should be visited before node 15\nnode 11 should be visited before node 17\nnode 11 should be visited before node 18\nnode 11 should be visited before node 3\nnode 11 should be visited before node 14\nnode 12 should be visited before node 11\nnode 12 should be visited before node 8\nnode 12 should be visited before node 4\nnode 12 should be visited before node 10\nnode 12 should be visited before node 0\nnode 12 should be visited before node 2\nnode 12 should be visited before node 9\nnode 12 should be visited before node 15\nnode 12 should be visited before node 17\nnode 12 should be visited before node 5\nnode 12 should be visited before node 18\nnode 12 should be visited before node 3\nnode 12 should be visited before node 14\nnode 13 should be visited before node 11\nnode 13 should be visited before node 8\nnode 13 should be visited before node 4\nnode 13 should be visited before node 10\nnode 13 should be visited before node 0\nnode 13 should be visited before node 9\nnode 13 should be visited before node 15\nnode 13 should be visited before node 17\nnode 13 should be visited before node 5\nnode 13 should be visited before node 3\nnode 13 should be visited before node 14\nnode 15 should be visited before node 17\nnode 15 should be visited before node 18\nnode 15 should be visited before node 3\nnode 15 should be visited before node 14\nnode 16 should be visited before node 2\nnode 16 should be visited before node 9\nnode 16 should be visited before node 5\nnode 16 should be visited before node 18\nnode 16 should be visited before node 3\nnode 16 should be visited before node 14\nnode 17 should be visited before node 5\nnode 17 should be visited before node 18\nnode 17 should be visited before node 3\nnode 17 should be visited before node 14\nnode 18 should be visited before node 3\nnode 18 should be visited before node 14\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 6,7,12,13,1,11,8,4,10,16,0,2,9,15,17,5,18,3,14.", "difficulty": "medium", "doc_id": "73"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 18 nodes numbered from 0 to 17:\nnode 0 should be visited before node 8\nnode 0 should be visited before node 17\nnode 0 should be visited before node 9\nnode 0 should be visited before node 5\nnode 0 should be visited before node 7\nnode 1 should be visited before node 9\nnode 1 should be visited before node 3\nnode 1 should be visited before node 5\nnode 1 should be visited before node 7\nnode 2 should be visited before node 0\nnode 2 should be visited before node 15\nnode 2 should be visited before node 8\nnode 2 should be visited before node 14\nnode 2 should be visited before node 1\nnode 2 should be visited before node 3\nnode 2 should be visited before node 5\nnode 2 should be visited before node 7\nnode 3 should be visited before node 12\nnode 3 should be visited before node 5\nnode 3 should be visited before node 7\nnode 4 should be visited before node 11\nnode 4 should be visited before node 6\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nnode 4 should be visited before node 8\nnode 4 should be visited before node 17\nnode 4 should be visited before node 1\nnode 4 should be visited before node 9\nnode 4 should be visited before node 3\nnode 4 should be visited before node 12\nnode 4 should be visited before node 5\nnode 4 should be visited before node 7\nnode 5 should be visited before node 7\nnode 6 should be visited before node 0\nnode 6 should be visited before node 15\nnode 6 should be visited before node 14\nnode 6 should be visited before node 1\nnode 6 should be visited before node 9\nnode 6 should be visited before node 12\nnode 6 should be visited before node 7\nnode 8 should be visited before node 14\nnode 8 should be visited before node 17\nnode 8 should be visited before node 3\nnode 9 should be visited before node 12\nnode 9 should be visited before node 5\nnode 9 should be visited before node 7\nnode 10 should be visited before node 2\nnode 10 should be visited before node 0\nnode 10 should be visited before node 8\nnode 10 should be visited before node 1\nnode 10 should be visited before node 3\nnode 10 should be visited before node 12\nnode 11 should be visited before node 13\nnode 11 should be visited before node 16\nnode 11 should be visited before node 6\nnode 11 should be visited before node 2\nnode 11 should be visited before node 0\nnode 11 should be visited before node 8\nnode 11 should be visited before node 14\nnode 11 should be visited before node 1\nnode 11 should be visited before node 9\nnode 11 should be visited before node 5\nnode 12 should be visited before node 5\nnode 13 should be visited before node 10\nnode 13 should be visited before node 6\nnode 13 should be visited before node 2\nnode 13 should be visited before node 0\nnode 13 should be visited before node 15\nnode 13 should be visited before node 8\nnode 13 should be visited before node 3\nnode 13 should be visited before node 7\nnode 14 should be visited before node 1\nnode 14 should be visited before node 3\nnode 14 should be visited before node 12\nnode 14 should be visited before node 7\nnode 15 should be visited before node 14\nnode 15 should be visited before node 17\nnode 15 should be visited before node 1\nnode 15 should be visited before node 9\nnode 15 should be visited before node 5\nnode 15 should be visited before node 7\nnode 16 should be visited before node 10\nnode 16 should be visited before node 0\nnode 16 should be visited before node 15\nnode 16 should be visited before node 17\nnode 16 should be visited before node 1\nnode 16 should be visited before node 12\nnode 16 should be visited before node 7\nnode 17 should be visited before node 1\nnode 17 should be visited before node 3\nnode 17 should be visited before node 12\nnode 17 should be visited before node 5\nnode 17 should be visited before node 7\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 4,11,13,16,6,10,2,0,15,8,14,17,1,9,3,12,5,7.", "difficulty": "medium", "doc_id": "74"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 11 nodes numbered from 0 to 10:\nnode 0 should be visited before node 10\nnode 0 should be visited before node 2\nnode 1 should be visited before node 2\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nnode 5 should be visited before node 7\nnode 5 should be visited before node 3\nnode 6 should be visited before node 10\nnode 7 should be visited before node 3\nnode 8 should be visited before node 0\nnode 8 should be visited before node 7\nnode 8 should be visited before node 3\nnode 8 should be visited before node 2\nnode 9 should be visited before node 4\nnode 9 should be visited before node 3\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 5,6,8,9,7,4,3,0,1,10,2.", "difficulty": "medium", "doc_id": "75"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 2 should be visited before node 0\nnode 2 should be visited before node 3\nnode 4 should be visited before node 5\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 1,4,5,2,0,3.", "difficulty": "easy", "doc_id": "76"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 20 nodes numbered from 0 to 19:\nnode 0 should be visited before node 19\nnode 0 should be visited before node 18\nnode 0 should be visited before node 14\nnode 0 should be visited before node 12\nnode 1 should be visited before node 6\nnode 1 should be visited before node 5\nnode 1 should be visited before node 9\nnode 1 should be visited before node 12\nnode 1 should be visited before node 13\nnode 2 should be visited before node 15\nnode 2 should be visited before node 3\nnode 2 should be visited before node 19\nnode 2 should be visited before node 18\nnode 2 should be visited before node 14\nnode 2 should be visited before node 10\nnode 2 should be visited before node 5\nnode 2 should be visited before node 16\nnode 2 should be visited before node 12\nnode 2 should be visited before node 11\nnode 2 should be visited before node 13\nnode 3 should be visited before node 0\nnode 3 should be visited before node 4\nnode 3 should be visited before node 18\nnode 3 should be visited before node 10\nnode 3 should be visited before node 16\nnode 3 should be visited before node 9\nnode 3 should be visited before node 7\nnode 4 should be visited before node 1\nnode 4 should be visited before node 14\nnode 4 should be visited before node 13\nnode 5 should be visited before node 16\nnode 5 should be visited before node 12\nnode 5 should be visited before node 13\nnode 6 should be visited before node 5\nnode 6 should be visited before node 16\nnode 6 should be visited before node 9\nnode 6 should be visited before node 12\nnode 6 should be visited before node 11\nnode 8 should be visited before node 19\nnode 8 should be visited before node 1\nnode 8 should be visited before node 6\nnode 8 should be visited before node 5\nnode 8 should be visited before node 12\nnode 9 should be visited before node 11\nnode 9 should be visited before node 7\nnode 10 should be visited before node 5\nnode 10 should be visited before node 9\nnode 10 should be visited before node 11\nnode 10 should be visited before node 7\nnode 12 should be visited before node 11\nnode 14 should be visited before node 16\nnode 14 should be visited before node 12\nnode 15 should be visited before node 8\nnode 15 should be visited before node 3\nnode 15 should be visited before node 19\nnode 15 should be visited before node 10\nnode 15 should be visited before node 5\nnode 15 should be visited before node 12\nnode 15 should be visited before node 11\nnode 15 should be visited before node 7\nnode 16 should be visited before node 9\nnode 16 should be visited before node 12\nnode 16 should be visited before node 11\nnode 16 should be visited before node 7\nnode 16 should be visited before node 13\nnode 17 should be visited before node 0\nnode 17 should be visited before node 4\nnode 17 should be visited before node 18\nnode 17 should be visited before node 14\nnode 17 should be visited before node 9\nnode 17 should be visited before node 7\nnode 18 should be visited before node 14\nnode 18 should be visited before node 10\nnode 18 should be visited before node 5\nnode 18 should be visited before node 16\nnode 18 should be visited before node 9\nnode 18 should be visited before node 12\nnode 18 should be visited before node 7\nnode 18 should be visited before node 13\nnode 19 should be visited before node 1\nnode 19 should be visited before node 16\nnode 19 should be visited before node 11\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 2,17,15,8,3,0,4,19,18,1,14,10,6,5,16,9,12,13,7,11.", "difficulty": "medium", "doc_id": "77"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 19 nodes numbered from 0 to 18:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 0 should be visited before node 3\nnode 1 should be visited before node 3\nnode 1 should be visited before node 15\nnode 1 should be visited before node 18\nnode 2 should be visited before node 5\nnode 2 should be visited before node 0\nnode 2 should be visited before node 4\nnode 2 should be visited before node 3\nnode 2 should be visited before node 15\nnode 2 should be visited before node 18\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 4 should be visited before node 15\nnode 4 should be visited before node 18\nnode 5 should be visited before node 4\nnode 5 should be visited before node 3\nnode 5 should be visited before node 15\nnode 5 should be visited before node 18\nnode 6 should be visited before node 8\nnode 6 should be visited before node 9\nnode 6 should be visited before node 12\nnode 6 should be visited before node 2\nnode 6 should be visited before node 5\nnode 6 should be visited before node 0\nnode 6 should be visited before node 3\nnode 6 should be visited before node 15\nnode 6 should be visited before node 18\nnode 7 should be visited before node 14\nnode 7 should be visited before node 6\nnode 7 should be visited before node 8\nnode 7 should be visited before node 9\nnode 7 should be visited before node 5\nnode 7 should be visited before node 0\nnode 7 should be visited before node 4\nnode 7 should be visited before node 3\nnode 7 should be visited before node 15\nnode 7 should be visited before node 18\nnode 8 should be visited before node 11\nnode 8 should be visited before node 16\nnode 8 should be visited before node 12\nnode 8 should be visited before node 2\nnode 8 should be visited before node 5\nnode 8 should be visited before node 0\nnode 8 should be visited before node 4\nnode 8 should be visited before node 15\nnode 9 should be visited before node 2\nnode 9 should be visited before node 0\nnode 9 should be visited before node 1\nnode 9 should be visited before node 18\nnode 10 should be visited before node 7\nnode 10 should be visited before node 14\nnode 10 should be visited before node 11\nnode 10 should be visited before node 16\nnode 10 should be visited before node 9\nnode 10 should be visited before node 12\nnode 10 should be visited before node 3\nnode 10 should be visited before node 18\nnode 11 should be visited before node 16\nnode 11 should be visited before node 9\nnode 11 should be visited before node 2\nnode 11 should be visited before node 5\nnode 11 should be visited before node 1\nnode 11 should be visited before node 3\nnode 11 should be visited before node 15\nnode 12 should be visited before node 2\nnode 12 should be visited before node 0\nnode 12 should be visited before node 4\nnode 12 should be visited before node 3\nnode 12 should be visited before node 15\nnode 12 should be visited before node 18\nnode 13 should be visited before node 17\nnode 13 should be visited before node 7\nnode 13 should be visited before node 14\nnode 13 should be visited before node 6\nnode 13 should be visited before node 11\nnode 13 should be visited before node 16\nnode 13 should be visited before node 2\nnode 13 should be visited before node 5\nnode 13 should be visited before node 0\nnode 13 should be visited before node 4\nnode 13 should be visited before node 15\nnode 13 should be visited before node 18\nnode 14 should be visited before node 6\nnode 14 should be visited before node 8\nnode 14 should be visited before node 11\nnode 14 should be visited before node 16\nnode 14 should be visited before node 9\nnode 14 should be visited before node 12\nnode 14 should be visited before node 0\nnode 14 should be visited before node 3\nnode 14 should be visited before node 15\nnode 14 should be visited before node 18\nnode 15 should be visited before node 18\nnode 16 should be visited before node 2\nnode 16 should be visited before node 0\nnode 16 should be visited before node 4\nnode 16 should be visited before node 1\nnode 16 should be visited before node 3\nnode 16 should be visited before node 15\nnode 16 should be visited before node 18\nnode 17 should be visited before node 10\nnode 17 should be visited before node 7\nnode 17 should be visited before node 14\nnode 17 should be visited before node 6\nnode 17 should be visited before node 11\nnode 17 should be visited before node 16\nnode 17 should be visited before node 9\nnode 17 should be visited before node 12\nnode 17 should be visited before node 2\nnode 17 should be visited before node 0\nnode 17 should be visited before node 1\nnode 17 should be visited before node 15\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 13,17,10,7,14,6,8,11,12,16,9,2,5,0,4,1,3,15,18.", "difficulty": "medium", "doc_id": "78"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 16 nodes numbered from 0 to 15:\nnode 0 should be visited before node 12\nnode 2 should be visited before node 1\nnode 3 should be visited before node 13\nnode 3 should be visited before node 8\nnode 3 should be visited before node 2\nnode 4 should be visited before node 0\nnode 4 should be visited before node 5\nnode 4 should be visited before node 2\nnode 4 should be visited before node 9\nnode 5 should be visited before node 12\nnode 5 should be visited before node 9\nnode 6 should be visited before node 2\nnode 6 should be visited before node 12\nnode 6 should be visited before node 1\nnode 7 should be visited before node 4\nnode 7 should be visited before node 12\nnode 7 should be visited before node 9\nnode 8 should be visited before node 6\nnode 8 should be visited before node 12\nnode 8 should be visited before node 1\nnode 8 should be visited before node 9\nnode 10 should be visited before node 5\nnode 10 should be visited before node 2\nnode 10 should be visited before node 9\nnode 11 should be visited before node 8\nnode 11 should be visited before node 4\nnode 11 should be visited before node 2\nnode 11 should be visited before node 9\nnode 13 should be visited before node 8\nnode 13 should be visited before node 2\nnode 13 should be visited before node 12\nnode 14 should be visited before node 4\nnode 14 should be visited before node 5\nnode 14 should be visited before node 2\nnode 14 should be visited before node 9\nnode 15 should be visited before node 7\nnode 15 should be visited before node 0\nnode 15 should be visited before node 9\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 3,10,11,14,15,13,7,8,4,6,0,5,2,12,9,1.", "difficulty": "medium", "doc_id": "79"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 34 nodes numbered from 0 to 33:\nnode 0 should be visited before node 12\nnode 0 should be visited before node 10\nnode 0 should be visited before node 31\nnode 0 should be visited before node 23\nnode 0 should be visited before node 2\nnode 1 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 22\nnode 3 should be visited before node 23\nnode 3 should be visited before node 2\nnode 4 should be visited before node 6\nnode 4 should be visited before node 9\nnode 4 should be visited before node 12\nnode 4 should be visited before node 3\nnode 4 should be visited before node 10\nnode 4 should be visited before node 31\nnode 4 should be visited before node 22\nnode 4 should be visited before node 2\nnode 5 should be visited before node 13\nnode 5 should be visited before node 24\nnode 5 should be visited before node 19\nnode 5 should be visited before node 29\nnode 5 should be visited before node 20\nnode 5 should be visited before node 4\nnode 5 should be visited before node 1\nnode 5 should be visited before node 10\nnode 5 should be visited before node 31\nnode 5 should be visited before node 22\nnode 6 should be visited before node 0\nnode 6 should be visited before node 12\nnode 6 should be visited before node 3\nnode 6 should be visited before node 10\nnode 6 should be visited before node 31\nnode 6 should be visited before node 22\nnode 6 should be visited before node 23\nnode 6 should be visited before node 2\nnode 7 should be visited before node 29\nnode 7 should be visited before node 8\nnode 7 should be visited before node 9\nnode 7 should be visited before node 0\nnode 7 should be visited before node 22\nnode 8 should be visited before node 26\nnode 8 should be visited before node 6\nnode 8 should be visited before node 0\nnode 8 should be visited before node 10\nnode 8 should be visited before node 31\nnode 8 should be visited before node 22\nnode 8 should be visited before node 2\nnode 9 should be visited before node 10\nnode 9 should be visited before node 31\nnode 9 should be visited before node 22\nnode 10 should be visited before node 31\nnode 10 should be visited before node 23\nnode 11 should be visited before node 18\nnode 11 should be visited before node 5\nnode 11 should be visited before node 17\nnode 11 should be visited before node 25\nnode 11 should be visited before node 13\nnode 11 should be visited before node 28\nnode 11 should be visited before node 24\nnode 11 should be visited before node 19\nnode 11 should be visited before node 7\nnode 11 should be visited before node 29\nnode 11 should be visited before node 20\nnode 11 should be visited before node 4\nnode 11 should be visited before node 26\nnode 11 should be visited before node 6\nnode 11 should be visited before node 12\nnode 11 should be visited before node 3\nnode 12 should be visited before node 10\nnode 12 should be visited before node 31\nnode 12 should be visited before node 2\nnode 13 should be visited before node 28\nnode 13 should be visited before node 24\nnode 13 should be visited before node 19\nnode 13 should be visited before node 7\nnode 13 should be visited before node 29\nnode 13 should be visited before node 4\nnode 13 should be visited before node 8\nnode 13 should be visited before node 9\nnode 13 should be visited before node 0\nnode 13 should be visited before node 3\nnode 13 should be visited before node 22\nnode 13 should be visited before node 23\nnode 13 should be visited before node 2\nnode 14 should be visited before node 21\nnode 14 should be visited before node 16\nnode 14 should be visited before node 15\nnode 14 should be visited before node 27\nnode 14 should be visited before node 11\nnode 14 should be visited before node 25\nnode 14 should be visited before node 30\nnode 14 should be visited before node 7\nnode 14 should be visited before node 20\nnode 14 should be visited before node 4\nnode 14 should be visited before node 8\nnode 14 should be visited before node 26\nnode 14 should be visited before node 9\nnode 14 should be visited before node 12\nnode 14 should be visited before node 3\nnode 14 should be visited before node 10\nnode 14 should be visited before node 31\nnode 14 should be visited before node 2\nnode 15 should be visited before node 18\nnode 15 should be visited before node 5\nnode 15 should be visited before node 28\nnode 15 should be visited before node 19\nnode 15 should be visited before node 32\nnode 15 should be visited before node 7\nnode 15 should be visited before node 29\nnode 15 should be visited before node 20\nnode 15 should be visited before node 8\nnode 15 should be visited before node 1\nnode 15 should be visited before node 12\nnode 16 should be visited before node 15\nnode 16 should be visited before node 11\nnode 16 should be visited before node 17\nnode 16 should be visited before node 25\nnode 16 should be visited before node 28\nnode 16 should be visited before node 19\nnode 16 should be visited before node 7\nnode 16 should be visited before node 29\nnode 16 should be visited before node 4\nnode 16 should be visited before node 9\nnode 16 should be visited before node 1\nnode 16 should be visited before node 0\nnode 16 should be visited before node 12\nnode 16 should be visited before node 3\nnode 16 should be visited before node 22\nnode 16 should be visited before node 23\nnode 17 should be visited before node 25\nnode 17 should be visited before node 13\nnode 17 should be visited before node 24\nnode 17 should be visited before node 30\nnode 17 should be visited before node 19\nnode 17 should be visited before node 32\nnode 17 should be visited before node 29\nnode 17 should be visited before node 26\nnode 17 should be visited before node 9\nnode 17 should be visited before node 10\nnode 17 should be visited before node 22\nnode 18 should be visited before node 5\nnode 18 should be visited before node 25\nnode 18 should be visited before node 13\nnode 18 should be visited before node 28\nnode 18 should be visited before node 24\nnode 18 should be visited before node 30\nnode 18 should be visited before node 19\nnode 18 should be visited before node 32\nnode 18 should be visited before node 7\nnode 18 should be visited before node 8\nnode 18 should be visited before node 26\nnode 18 should be visited before node 9\nnode 18 should be visited before node 1\nnode 18 should be visited before node 12\nnode 18 should be visited before node 3\nnode 18 should be visited before node 22\nnode 18 should be visited before node 23\nnode 18 should be visited before node 2\nnode 19 should be visited before node 20\nnode 19 should be visited before node 4\nnode 19 should be visited before node 8\nnode 19 should be visited before node 6\nnode 19 should be visited before node 1\nnode 19 should be visited before node 10\nnode 19 should be visited before node 23\nnode 20 should be visited before node 4\nnode 20 should be visited before node 26\nnode 20 should be visited before node 1\nnode 20 should be visited before node 12\nnode 20 should be visited before node 23\nnode 21 should be visited before node 15\nnode 21 should be visited before node 11\nnode 21 should be visited before node 18\nnode 21 should be visited before node 30\nnode 21 should be visited before node 19\nnode 21 should be visited before node 8\nnode 21 should be visited before node 26\nnode 21 should be visited before node 6\nnode 21 should be visited before node 1\nnode 21 should be visited before node 10\nnode 21 should be visited before node 22\nnode 21 should be visited before node 2\nnode 22 should be visited before node 2\nnode 24 should be visited before node 32\nnode 24 should be visited before node 7\nnode 24 should be visited before node 4\nnode 24 should be visited before node 6\nnode 24 should be visited before node 12\nnode 24 should be visited before node 2\nnode 25 should be visited before node 13\nnode 25 should be visited before node 28\nnode 25 should be visited before node 30\nnode 25 should be visited before node 19\nnode 25 should be visited before node 32\nnode 25 should be visited before node 20\nnode 25 should be visited before node 4\nnode 25 should be visited before node 8\nnode 25 should be visited before node 1\nnode 25 should be visited before node 12\nnode 25 should be visited before node 3\nnode 25 should be visited before node 10\nnode 25 should be visited before node 31\nnode 25 should be visited before node 23\nnode 26 should be visited before node 1\nnode 26 should be visited before node 0\nnode 26 should be visited before node 12\nnode 26 should be visited before node 3\nnode 26 should be visited before node 31\nnode 26 should be visited before node 22\nnode 27 should be visited before node 11\nnode 27 should be visited before node 18\nnode 27 should be visited before node 17\nnode 27 should be visited before node 25\nnode 27 should be visited before node 30\nnode 27 should be visited before node 32\nnode 27 should be visited before node 7\nnode 27 should be visited before node 20\nnode 27 should be visited before node 26\nnode 27 should be visited before node 1\nnode 27 should be visited before node 12\nnode 27 should be visited before node 31\nnode 27 should be visited before node 22\nnode 27 should be visited before node 23\nnode 27 should be visited before node 2\nnode 28 should be visited before node 24\nnode 28 should be visited before node 30\nnode 28 should be visited before node 19\nnode 28 should be visited before node 29\nnode 28 should be visited before node 20\nnode 28 should be visited before node 4\nnode 28 should be visited before node 8\nnode 28 should be visited before node 26\nnode 28 should be visited before node 6\nnode 28 should be visited before node 0\nnode 28 should be visited before node 12\nnode 28 should be visited before node 23\nnode 28 should be visited before node 2\nnode 29 should be visited before node 20\nnode 29 should be visited before node 6\nnode 29 should be visited before node 0\nnode 29 should be visited before node 3\nnode 29 should be visited before node 10\nnode 29 should be visited before node 23\nnode 30 should be visited before node 19\nnode 30 should be visited before node 20\nnode 30 should be visited before node 26\nnode 30 should be visited before node 9\nnode 30 should be visited before node 3\nnode 30 should be visited before node 10\nnode 30 should be visited before node 31\nnode 31 should be visited before node 23\nnode 32 should be visited before node 0\nnode 32 should be visited before node 12\nnode 32 should be visited before node 3\nnode 32 should be visited before node 10\nnode 32 should be visited before node 31\nnode 32 should be visited before node 2\nnode 33 should be visited before node 15\nnode 33 should be visited before node 27\nnode 33 should be visited before node 11\nnode 33 should be visited before node 17\nnode 33 should be visited before node 13\nnode 33 should be visited before node 28\nnode 33 should be visited before node 30\nnode 33 should be visited before node 19\nnode 33 should be visited before node 32\nnode 33 should be visited before node 29\nnode 33 should be visited before node 20\nnode 33 should be visited before node 4\nnode 33 should be visited before node 26\nnode 33 should be visited before node 6\nnode 33 should be visited before node 12\nnode 33 should be visited before node 10\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 14,33,21,16,27,15,11,18,17,5,25,13,28,24,30,32,7,19,29,8,20,4,26,6,9,1,0,3,12,22,10,2,31,23.", "difficulty": "hard", "doc_id": "80"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 10 nodes numbered from 0 to 9:\nnode 0 should be visited before node 1\nnode 0 should be visited before node 2\nnode 0 should be visited before node 3\nnode 0 should be visited before node 5\nnode 0 should be visited before node 8\nnode 1 should be visited before node 2\nnode 1 should be visited before node 3\nnode 1 should be visited before node 4\nnode 1 should be visited before node 5\nnode 1 should be visited before node 8\nnode 2 should be visited before node 4\nnode 2 should be visited before node 5\nnode 2 should be visited before node 8\nnode 3 should be visited before node 8\nnode 4 should be visited before node 8\nnode 6 should be visited before node 1\nnode 6 should be visited before node 3\nnode 6 should be visited before node 4\nnode 7 should be visited before node 9\nnode 7 should be visited before node 1\nnode 7 should be visited before node 2\nnode 7 should be visited before node 3\nnode 7 should be visited before node 4\nnode 7 should be visited before node 5\nnode 7 should be visited before node 8\nnode 9 should be visited before node 1\nnode 9 should be visited before node 2\nnode 9 should be visited before node 3\nnode 9 should be visited before node 4\nnode 9 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 0,6,7,9,1,2,3,4,5,8.", "difficulty": "easy", "doc_id": "81"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 22 nodes numbered from 0 to 21:\nnode 0 should be visited before node 16\nnode 2 should be visited before node 11\nnode 2 should be visited before node 13\nnode 2 should be visited before node 12\nnode 3 should be visited before node 12\nnode 4 should be visited before node 14\nnode 4 should be visited before node 12\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nnode 5 should be visited before node 2\nnode 5 should be visited before node 18\nnode 5 should be visited before node 19\nnode 6 should be visited before node 7\nnode 6 should be visited before node 14\nnode 6 should be visited before node 13\nnode 6 should be visited before node 0\nnode 6 should be visited before node 19\nnode 7 should be visited before node 2\nnode 7 should be visited before node 3\nnode 7 should be visited before node 0\nnode 7 should be visited before node 18\nnode 8 should be visited before node 18\nnode 8 should be visited before node 19\nnode 8 should be visited before node 1\nnode 9 should be visited before node 10\nnode 9 should be visited before node 6\nnode 9 should be visited before node 7\nnode 9 should be visited before node 4\nnode 9 should be visited before node 2\nnode 9 should be visited before node 12\nnode 9 should be visited before node 19\nnode 9 should be visited before node 1\nnode 10 should be visited before node 11\nnode 10 should be visited before node 3\nnode 10 should be visited before node 8\nnode 10 should be visited before node 18\nnode 10 should be visited before node 19\nnode 11 should be visited before node 3\nnode 11 should be visited before node 12\nnode 11 should be visited before node 1\nnode 12 should be visited before node 0\nnode 12 should be visited before node 16\nnode 12 should be visited before node 19\nnode 12 should be visited before node 1\nnode 13 should be visited before node 3\nnode 13 should be visited before node 19\nnode 13 should be visited before node 1\nnode 14 should be visited before node 2\nnode 14 should be visited before node 11\nnode 14 should be visited before node 19\nnode 14 should be visited before node 1\nnode 15 should be visited before node 13\nnode 15 should be visited before node 3\nnode 15 should be visited before node 0\nnode 15 should be visited before node 18\nnode 15 should be visited before node 19\nnode 15 should be visited before node 1\nnode 16 should be visited before node 19\nnode 17 should be visited before node 20\nnode 17 should be visited before node 5\nnode 17 should be visited before node 14\nnode 17 should be visited before node 13\nnode 17 should be visited before node 8\nnode 18 should be visited before node 19\nnode 19 should be visited before node 1\nnode 20 should be visited before node 5\nnode 20 should be visited before node 14\nnode 20 should be visited before node 2\nnode 20 should be visited before node 12\nnode 20 should be visited before node 0\nnode 20 should be visited before node 19\nnode 21 should be visited before node 17\nnode 21 should be visited before node 7\nnode 21 should be visited before node 4\nnode 21 should be visited before node 2\nnode 21 should be visited before node 3\nnode 21 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 9,15,21,10,6,17,4,7,20,8,5,14,18,2,11,13,3,12,0,16,19,1.", "difficulty": "medium", "doc_id": "82"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 31 nodes numbered from 0 to 30:\nnode 0 should be visited before node 24\nnode 0 should be visited before node 20\nnode 0 should be visited before node 17\nnode 0 should be visited before node 19\nnode 0 should be visited before node 21\nnode 0 should be visited before node 4\nnode 0 should be visited before node 7\nnode 0 should be visited before node 11\nnode 0 should be visited before node 10\nnode 0 should be visited before node 5\nnode 0 should be visited before node 25\nnode 0 should be visited before node 12\nnode 0 should be visited before node 6\nnode 1 should be visited before node 25\nnode 1 should be visited before node 12\nnode 1 should be visited before node 6\nnode 2 should be visited before node 18\nnode 3 should be visited before node 9\nnode 3 should be visited before node 26\nnode 3 should be visited before node 27\nnode 3 should be visited before node 23\nnode 3 should be visited before node 11\nnode 3 should be visited before node 16\nnode 3 should be visited before node 14\nnode 3 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 12\nnode 3 should be visited before node 18\nnode 4 should be visited before node 9\nnode 4 should be visited before node 7\nnode 4 should be visited before node 27\nnode 4 should be visited before node 11\nnode 4 should be visited before node 25\nnode 4 should be visited before node 6\nnode 5 should be visited before node 1\nnode 5 should be visited before node 12\nnode 5 should be visited before node 6\nnode 7 should be visited before node 26\nnode 7 should be visited before node 27\nnode 7 should be visited before node 10\nnode 7 should be visited before node 12\nnode 8 should be visited before node 22\nnode 8 should be visited before node 28\nnode 8 should be visited before node 29\nnode 8 should be visited before node 23\nnode 8 should be visited before node 11\nnode 8 should be visited before node 16\nnode 8 should be visited before node 14\nnode 8 should be visited before node 10\nnode 8 should be visited before node 2\nnode 8 should be visited before node 5\nnode 8 should be visited before node 1\nnode 8 should be visited before node 12\nnode 8 should be visited before node 6\nnode 9 should be visited before node 26\nnode 9 should be visited before node 27\nnode 9 should be visited before node 23\nnode 9 should be visited before node 14\nnode 9 should be visited before node 10\nnode 9 should be visited before node 5\nnode 9 should be visited before node 25\nnode 10 should be visited before node 5\nnode 10 should be visited before node 12\nnode 10 should be visited before node 18\nnode 10 should be visited before node 6\nnode 11 should be visited before node 14\nnode 11 should be visited before node 2\nnode 11 should be visited before node 5\nnode 11 should be visited before node 12\nnode 11 should be visited before node 18\nnode 11 should be visited before node 6\nnode 12 should be visited before node 18\nnode 13 should be visited before node 0\nnode 13 should be visited before node 22\nnode 13 should be visited before node 19\nnode 13 should be visited before node 28\nnode 13 should be visited before node 29\nnode 13 should be visited before node 21\nnode 13 should be visited before node 4\nnode 13 should be visited before node 3\nnode 13 should be visited before node 9\nnode 13 should be visited before node 7\nnode 13 should be visited before node 26\nnode 13 should be visited before node 27\nnode 13 should be visited before node 11\nnode 13 should be visited before node 16\nnode 13 should be visited before node 14\nnode 13 should be visited before node 10\nnode 13 should be visited before node 2\nnode 13 should be visited before node 12\nnode 13 should be visited before node 6\nnode 14 should be visited before node 5\nnode 14 should be visited before node 18\nnode 15 should be visited before node 21\nnode 15 should be visited before node 4\nnode 15 should be visited before node 27\nnode 15 should be visited before node 11\nnode 15 should be visited before node 10\nnode 15 should be visited before node 2\nnode 15 should be visited before node 5\nnode 15 should be visited before node 1\nnode 15 should be visited before node 25\nnode 15 should be visited before node 12\nnode 15 should be visited before node 18\nnode 15 should be visited before node 6\nnode 16 should be visited before node 14\nnode 16 should be visited before node 10\nnode 16 should be visited before node 1\nnode 16 should be visited before node 12\nnode 16 should be visited before node 18\nnode 16 should be visited before node 6\nnode 17 should be visited before node 22\nnode 17 should be visited before node 19\nnode 17 should be visited before node 28\nnode 17 should be visited before node 21\nnode 17 should be visited before node 3\nnode 17 should be visited before node 9\nnode 17 should be visited before node 7\nnode 17 should be visited before node 26\nnode 17 should be visited before node 16\nnode 17 should be visited before node 10\nnode 17 should be visited before node 12\nnode 17 should be visited before node 18\nnode 17 should be visited before node 6\nnode 19 should be visited before node 28\nnode 19 should be visited before node 29\nnode 19 should be visited before node 3\nnode 19 should be visited before node 9\nnode 19 should be visited before node 26\nnode 19 should be visited before node 27\nnode 19 should be visited before node 23\nnode 19 should be visited before node 16\nnode 19 should be visited before node 2\nnode 19 should be visited before node 25\nnode 19 should be visited before node 12\nnode 19 should be visited before node 6\nnode 20 should be visited before node 28\nnode 20 should be visited before node 29\nnode 20 should be visited before node 21\nnode 20 should be visited before node 3\nnode 20 should be visited before node 9\nnode 20 should be visited before node 27\nnode 20 should be visited before node 23\nnode 20 should be visited before node 11\nnode 20 should be visited before node 16\nnode 20 should be visited before node 2\nnode 20 should be visited before node 1\nnode 20 should be visited before node 25\nnode 20 should be visited before node 12\nnode 20 should be visited before node 18\nnode 20 should be visited before node 6\nnode 21 should be visited before node 9\nnode 21 should be visited before node 7\nnode 21 should be visited before node 27\nnode 21 should be visited before node 14\nnode 21 should be visited before node 2\nnode 21 should be visited before node 1\nnode 21 should be visited before node 18\nnode 21 should be visited before node 6\nnode 22 should be visited before node 29\nnode 22 should be visited before node 21\nnode 22 should be visited before node 4\nnode 22 should be visited before node 3\nnode 22 should be visited before node 9\nnode 22 should be visited before node 23\nnode 22 should be visited before node 11\nnode 22 should be visited before node 16\nnode 22 should be visited before node 14\nnode 22 should be visited before node 1\nnode 22 should be visited before node 25\nnode 22 should be visited before node 18\nnode 22 should be visited before node 6\nnode 23 should be visited before node 11\nnode 23 should be visited before node 16\nnode 23 should be visited before node 14\nnode 23 should be visited before node 10\nnode 23 should be visited before node 2\nnode 23 should be visited before node 25\nnode 23 should be visited before node 18\nnode 24 should be visited before node 15\nnode 24 should be visited before node 17\nnode 24 should be visited before node 21\nnode 24 should be visited before node 4\nnode 24 should be visited before node 3\nnode 24 should be visited before node 9\nnode 24 should be visited before node 16\nnode 24 should be visited before node 10\nnode 24 should be visited before node 1\nnode 24 should be visited before node 25\nnode 24 should be visited before node 18\nnode 25 should be visited before node 12\nnode 26 should be visited before node 27\nnode 26 should be visited before node 23\nnode 26 should be visited before node 16\nnode 26 should be visited before node 10\nnode 26 should be visited before node 25\nnode 26 should be visited before node 12\nnode 27 should be visited before node 11\nnode 27 should be visited before node 16\nnode 27 should be visited before node 14\nnode 27 should be visited before node 2\nnode 27 should be visited before node 5\nnode 27 should be visited before node 1\nnode 27 should be visited before node 25\nnode 27 should be visited before node 12\nnode 27 should be visited before node 18\nnode 28 should be visited before node 29\nnode 28 should be visited before node 9\nnode 28 should be visited before node 26\nnode 28 should be visited before node 23\nnode 28 should be visited before node 14\nnode 28 should be visited before node 10\nnode 28 should be visited before node 2\nnode 28 should be visited before node 5\nnode 28 should be visited before node 1\nnode 28 should be visited before node 25\nnode 28 should be visited before node 6\nnode 29 should be visited before node 16\nnode 29 should be visited before node 14\nnode 29 should be visited before node 10\nnode 29 should be visited before node 2\nnode 29 should be visited before node 12\nnode 29 should be visited before node 18\nnode 29 should be visited before node 6\nnode 30 should be visited before node 0\nnode 30 should be visited before node 20\nnode 30 should be visited before node 28\nnode 30 should be visited before node 29\nnode 30 should be visited before node 3\nnode 30 should be visited before node 7\nnode 30 should be visited before node 26\nnode 30 should be visited before node 27\nnode 30 should be visited before node 23\nnode 30 should be visited before node 11\nnode 30 should be visited before node 16\nnode 30 should be visited before node 14\nnode 30 should be visited before node 5\nnode 30 should be visited before node 25\nnode 30 should be visited before node 12\nnode 30 should be visited before node 6\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 8,13,30,0,24,20,15,17,22,19,21,4,28,3,7,29,9,26,27,23,11,16,2,14,10,5,1,25,6,12,18.", "difficulty": "hard", "doc_id": "83"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 2\nnode 0 should be visited before node 1\nnode 0 should be visited before node 3\nnode 1 should be visited before node 5\nnode 1 should be visited before node 3\nnode 2 should be visited before node 1\nnode 2 should be visited before node 3\nnode 4 should be visited before node 5\nnode 4 should be visited before node 3\nnode 5 should be visited before node 3\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 0,4,2,1,5,3.", "difficulty": "easy", "doc_id": "84"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 14 nodes numbered from 0 to 13:\nnode 0 should be visited before node 7\nnode 0 should be visited before node 13\nnode 0 should be visited before node 11\nnode 0 should be visited before node 4\nnode 1 should be visited before node 0\nnode 1 should be visited before node 5\nnode 1 should be visited before node 9\nnode 2 should be visited before node 13\nnode 2 should be visited before node 4\nnode 2 should be visited before node 6\nnode 2 should be visited before node 9\nnode 3 should be visited before node 5\nnode 3 should be visited before node 10\nnode 4 should be visited before node 9\nnode 5 should be visited before node 13\nnode 5 should be visited before node 11\nnode 7 should be visited before node 5\nnode 7 should be visited before node 13\nnode 7 should be visited before node 10\nnode 7 should be visited before node 9\nnode 8 should be visited before node 10\nnode 8 should be visited before node 4\nnode 8 should be visited before node 9\nnode 10 should be visited before node 4\nnode 11 should be visited before node 6\nnode 12 should be visited before node 5\nnode 12 should be visited before node 9\nnode 13 should be visited before node 4\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 1,2,3,8,12,0,7,5,10,13,11,4,6,9.", "difficulty": "medium", "doc_id": "85"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 31 nodes numbered from 0 to 30:\nnode 0 should be visited before node 15\nnode 0 should be visited before node 18\nnode 0 should be visited before node 6\nnode 1 should be visited before node 9\nnode 1 should be visited before node 29\nnode 1 should be visited before node 21\nnode 2 should be visited before node 26\nnode 2 should be visited before node 30\nnode 2 should be visited before node 24\nnode 2 should be visited before node 28\nnode 2 should be visited before node 25\nnode 2 should be visited before node 8\nnode 2 should be visited before node 13\nnode 2 should be visited before node 9\nnode 4 should be visited before node 24\nnode 4 should be visited before node 0\nnode 4 should be visited before node 18\nnode 4 should be visited before node 8\nnode 4 should be visited before node 13\nnode 4 should be visited before node 9\nnode 5 should be visited before node 0\nnode 5 should be visited before node 28\nnode 5 should be visited before node 25\nnode 5 should be visited before node 8\nnode 5 should be visited before node 1\nnode 5 should be visited before node 20\nnode 5 should be visited before node 9\nnode 5 should be visited before node 17\nnode 6 should be visited before node 1\nnode 6 should be visited before node 9\nnode 7 should be visited before node 23\nnode 7 should be visited before node 24\nnode 7 should be visited before node 0\nnode 7 should be visited before node 10\nnode 7 should be visited before node 15\nnode 7 should be visited before node 14\nnode 7 should be visited before node 9\nnode 7 should be visited before node 29\nnode 8 should be visited before node 6\nnode 8 should be visited before node 13\nnode 8 should be visited before node 21\nnode 10 should be visited before node 15\nnode 10 should be visited before node 12\nnode 10 should be visited before node 28\nnode 10 should be visited before node 22\nnode 10 should be visited before node 29\nnode 11 should be visited before node 4\nnode 11 should be visited before node 23\nnode 11 should be visited before node 30\nnode 11 should be visited before node 10\nnode 11 should be visited before node 28\nnode 11 should be visited before node 14\nnode 11 should be visited before node 22\nnode 11 should be visited before node 25\nnode 11 should be visited before node 8\nnode 11 should be visited before node 13\nnode 11 should be visited before node 1\nnode 11 should be visited before node 16\nnode 11 should be visited before node 29\nnode 12 should be visited before node 25\nnode 12 should be visited before node 8\nnode 12 should be visited before node 29\nnode 13 should be visited before node 9\nnode 14 should be visited before node 25\nnode 14 should be visited before node 20\nnode 14 should be visited before node 29\nnode 14 should be visited before node 21\nnode 15 should be visited before node 28\nnode 15 should be visited before node 22\nnode 15 should be visited before node 9\nnode 15 should be visited before node 17\nnode 15 should be visited before node 29\nnode 15 should be visited before node 3\nnode 18 should be visited before node 28\nnode 18 should be visited before node 14\nnode 18 should be visited before node 8\nnode 18 should be visited before node 6\nnode 18 should be visited before node 17\nnode 18 should be visited before node 21\nnode 19 should be visited before node 24\nnode 19 should be visited before node 15\nnode 19 should be visited before node 6\nnode 19 should be visited before node 20\nnode 19 should be visited before node 21\nnode 19 should be visited before node 3\nnode 20 should be visited before node 17\nnode 20 should be visited before node 29\nnode 20 should be visited before node 21\nnode 22 should be visited before node 25\nnode 22 should be visited before node 20\nnode 22 should be visited before node 16\nnode 23 should be visited before node 0\nnode 23 should be visited before node 10\nnode 23 should be visited before node 28\nnode 23 should be visited before node 14\nnode 23 should be visited before node 6\nnode 23 should be visited before node 13\nnode 23 should be visited before node 1\nnode 23 should be visited before node 16\nnode 23 should be visited before node 29\nnode 23 should be visited before node 3\nnode 24 should be visited before node 0\nnode 24 should be visited before node 8\nnode 24 should be visited before node 6\nnode 24 should be visited before node 1\nnode 24 should be visited before node 20\nnode 24 should be visited before node 29\nnode 25 should be visited before node 16\nnode 25 should be visited before node 29\nnode 26 should be visited before node 30\nnode 26 should be visited before node 0\nnode 26 should be visited before node 10\nnode 26 should be visited before node 14\nnode 26 should be visited before node 6\nnode 27 should be visited before node 4\nnode 27 should be visited before node 30\nnode 27 should be visited before node 12\nnode 27 should be visited before node 28\nnode 27 should be visited before node 22\nnode 27 should be visited before node 20\nnode 27 should be visited before node 17\nnode 28 should be visited before node 14\nnode 28 should be visited before node 20\nnode 28 should be visited before node 9\nnode 28 should be visited before node 3\nnode 29 should be visited before node 3\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 2,5,7,11,19,27,26,23,4,30,10,24,12,0,15,18,22,28,8,14,6,13,25,20,1,16,17,9,29,21,3.", "difficulty": "hard", "doc_id": "86"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 23 nodes numbered from 0 to 22:\nnode 1 should be visited before node 9\nnode 1 should be visited before node 6\nnode 1 should be visited before node 11\nnode 1 should be visited before node 14\nnode 1 should be visited before node 5\nnode 1 should be visited before node 7\nnode 1 should be visited before node 12\nnode 1 should be visited before node 21\nnode 1 should be visited before node 22\nnode 1 should be visited before node 3\nnode 1 should be visited before node 18\nnode 1 should be visited before node 20\nnode 2 should be visited before node 12\nnode 2 should be visited before node 21\nnode 2 should be visited before node 22\nnode 2 should be visited before node 18\nnode 3 should be visited before node 18\nnode 3 should be visited before node 0\nnode 4 should be visited before node 11\nnode 4 should be visited before node 13\nnode 4 should be visited before node 5\nnode 4 should be visited before node 7\nnode 4 should be visited before node 12\nnode 4 should be visited before node 21\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 20\nnode 5 should be visited before node 12\nnode 5 should be visited before node 21\nnode 5 should be visited before node 18\nnode 6 should be visited before node 11\nnode 6 should be visited before node 13\nnode 6 should be visited before node 5\nnode 6 should be visited before node 10\nnode 6 should be visited before node 7\nnode 6 should be visited before node 12\nnode 6 should be visited before node 21\nnode 6 should be visited before node 3\nnode 6 should be visited before node 18\nnode 7 should be visited before node 12\nnode 7 should be visited before node 3\nnode 8 should be visited before node 15\nnode 8 should be visited before node 4\nnode 8 should be visited before node 2\nnode 8 should be visited before node 7\nnode 8 should be visited before node 21\nnode 8 should be visited before node 22\nnode 8 should be visited before node 20\nnode 9 should be visited before node 8\nnode 9 should be visited before node 4\nnode 9 should be visited before node 2\nnode 9 should be visited before node 7\nnode 9 should be visited before node 12\nnode 9 should be visited before node 21\nnode 9 should be visited before node 22\nnode 9 should be visited before node 3\nnode 9 should be visited before node 18\nnode 9 should be visited before node 0\nnode 10 should be visited before node 12\nnode 10 should be visited before node 21\nnode 10 should be visited before node 22\nnode 10 should be visited before node 18\nnode 10 should be visited before node 20\nnode 11 should be visited before node 2\nnode 11 should be visited before node 14\nnode 11 should be visited before node 5\nnode 11 should be visited before node 7\nnode 11 should be visited before node 21\nnode 11 should be visited before node 3\nnode 11 should be visited before node 18\nnode 11 should be visited before node 0\nnode 12 should be visited before node 3\nnode 12 should be visited before node 0\nnode 13 should be visited before node 5\nnode 13 should be visited before node 10\nnode 13 should be visited before node 7\nnode 13 should be visited before node 21\nnode 13 should be visited before node 22\nnode 13 should be visited before node 0\nnode 14 should be visited before node 5\nnode 14 should be visited before node 10\nnode 14 should be visited before node 21\nnode 14 should be visited before node 0\nnode 15 should be visited before node 4\nnode 15 should be visited before node 6\nnode 15 should be visited before node 13\nnode 15 should be visited before node 2\nnode 15 should be visited before node 14\nnode 15 should be visited before node 5\nnode 15 should be visited before node 12\nnode 15 should be visited before node 21\nnode 15 should be visited before node 22\nnode 15 should be visited before node 20\nnode 16 should be visited before node 4\nnode 16 should be visited before node 6\nnode 16 should be visited before node 11\nnode 16 should be visited before node 2\nnode 16 should be visited before node 14\nnode 16 should be visited before node 5\nnode 16 should be visited before node 7\nnode 16 should be visited before node 12\nnode 16 should be visited before node 3\nnode 17 should be visited before node 1\nnode 17 should be visited before node 9\nnode 17 should be visited before node 8\nnode 17 should be visited before node 15\nnode 17 should be visited before node 4\nnode 17 should be visited before node 6\nnode 17 should be visited before node 11\nnode 17 should be visited before node 13\nnode 17 should be visited before node 2\nnode 17 should be visited before node 10\nnode 17 should be visited before node 12\nnode 17 should be visited before node 22\nnode 17 should be visited before node 3\nnode 17 should be visited before node 18\nnode 17 should be visited before node 20\nnode 19 should be visited before node 5\nnode 19 should be visited before node 10\nnode 19 should be visited before node 7\nnode 19 should be visited before node 12\nnode 21 should be visited before node 22\nnode 21 should be visited before node 3\nnode 22 should be visited before node 3\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 16,17,19,1,9,8,15,4,6,11,13,2,14,7,5,10,12,21,20,22,3,18,0.", "difficulty": "medium", "doc_id": "87"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 12 nodes numbered from 0 to 11:\nnode 0 should be visited before node 3\nnode 0 should be visited before node 11\nnode 0 should be visited before node 4\nnode 0 should be visited before node 8\nnode 0 should be visited before node 10\nnode 0 should be visited before node 2\nnode 0 should be visited before node 6\nnode 0 should be visited before node 1\nnode 0 should be visited before node 7\nnode 1 should be visited before node 7\nnode 2 should be visited before node 6\nnode 2 should be visited before node 9\nnode 2 should be visited before node 1\nnode 3 should be visited before node 11\nnode 3 should be visited before node 4\nnode 3 should be visited before node 8\nnode 3 should be visited before node 2\nnode 3 should be visited before node 9\nnode 3 should be visited before node 1\nnode 4 should be visited before node 10\nnode 4 should be visited before node 2\nnode 4 should be visited before node 6\nnode 4 should be visited before node 9\nnode 4 should be visited before node 7\nnode 5 should be visited before node 3\nnode 5 should be visited before node 11\nnode 5 should be visited before node 8\nnode 5 should be visited before node 10\nnode 5 should be visited before node 9\nnode 5 should be visited before node 7\nnode 6 should be visited before node 9\nnode 6 should be visited before node 1\nnode 6 should be visited before node 7\nnode 8 should be visited before node 10\nnode 8 should be visited before node 2\nnode 8 should be visited before node 6\nnode 8 should be visited before node 9\nnode 8 should be visited before node 7\nnode 9 should be visited before node 1\nnode 9 should be visited before node 7\nnode 10 should be visited before node 2\nnode 10 should be visited before node 6\nnode 11 should be visited before node 8\nnode 11 should be visited before node 10\nnode 11 should be visited before node 2\nnode 11 should be visited before node 9\nnode 11 should be visited before node 1\nnode 11 should be visited before node 7\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 0,5,3,11,4,8,10,2,6,9,1,7.", "difficulty": "medium", "doc_id": "88"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 21 nodes numbered from 0 to 20:\nnode 0 should be visited before node 10\nnode 0 should be visited before node 11\nnode 0 should be visited before node 20\nnode 0 should be visited before node 14\nnode 0 should be visited before node 13\nnode 0 should be visited before node 6\nnode 0 should be visited before node 19\nnode 0 should be visited before node 5\nnode 1 should be visited before node 4\nnode 1 should be visited before node 18\nnode 1 should be visited before node 16\nnode 1 should be visited before node 12\nnode 1 should be visited before node 2\nnode 1 should be visited before node 11\nnode 1 should be visited before node 20\nnode 1 should be visited before node 3\nnode 1 should be visited before node 14\nnode 1 should be visited before node 13\nnode 1 should be visited before node 6\nnode 1 should be visited before node 7\nnode 1 should be visited before node 5\nnode 2 should be visited before node 11\nnode 2 should be visited before node 3\nnode 2 should be visited before node 14\nnode 2 should be visited before node 6\nnode 2 should be visited before node 7\nnode 2 should be visited before node 19\nnode 3 should be visited before node 13\nnode 3 should be visited before node 6\nnode 3 should be visited before node 7\nnode 3 should be visited before node 19\nnode 4 should be visited before node 16\nnode 4 should be visited before node 9\nnode 4 should be visited before node 20\nnode 4 should be visited before node 17\nnode 4 should be visited before node 3\nnode 4 should be visited before node 14\nnode 4 should be visited before node 13\nnode 4 should be visited before node 6\nnode 4 should be visited before node 19\nnode 6 should be visited before node 7\nnode 8 should be visited before node 16\nnode 8 should be visited before node 10\nnode 8 should be visited before node 12\nnode 8 should be visited before node 9\nnode 8 should be visited before node 2\nnode 8 should be visited before node 17\nnode 8 should be visited before node 3\nnode 8 should be visited before node 14\nnode 8 should be visited before node 15\nnode 8 should be visited before node 13\nnode 8 should be visited before node 7\nnode 9 should be visited before node 2\nnode 9 should be visited before node 11\nnode 9 should be visited before node 17\nnode 9 should be visited before node 14\nnode 9 should be visited before node 13\nnode 9 should be visited before node 19\nnode 10 should be visited before node 12\nnode 10 should be visited before node 2\nnode 10 should be visited before node 11\nnode 10 should be visited before node 14\nnode 10 should be visited before node 15\nnode 10 should be visited before node 13\nnode 10 should be visited before node 6\nnode 10 should be visited before node 19\nnode 10 should be visited before node 5\nnode 11 should be visited before node 20\nnode 11 should be visited before node 17\nnode 11 should be visited before node 3\nnode 11 should be visited before node 14\nnode 11 should be visited before node 15\nnode 11 should be visited before node 6\nnode 11 should be visited before node 19\nnode 12 should be visited before node 9\nnode 12 should be visited before node 20\nnode 12 should be visited before node 3\nnode 12 should be visited before node 15\nnode 12 should be visited before node 6\nnode 12 should be visited before node 5\nnode 13 should be visited before node 7\nnode 13 should be visited before node 19\nnode 14 should be visited before node 15\nnode 14 should be visited before node 13\nnode 14 should be visited before node 6\nnode 14 should be visited before node 5\nnode 15 should be visited before node 13\nnode 15 should be visited before node 19\nnode 15 should be visited before node 5\nnode 16 should be visited before node 10\nnode 16 should be visited before node 11\nnode 16 should be visited before node 3\nnode 16 should be visited before node 19\nnode 16 should be visited before node 5\nnode 17 should be visited before node 6\nnode 17 should be visited before node 7\nnode 17 should be visited before node 19\nnode 18 should be visited before node 16\nnode 18 should be visited before node 10\nnode 18 should be visited before node 9\nnode 18 should be visited before node 2\nnode 18 should be visited before node 11\nnode 18 should be visited before node 6\nnode 18 should be visited before node 7\nnode 20 should be visited before node 17\nnode 20 should be visited before node 3\nnode 20 should be visited before node 14\nnode 20 should be visited before node 6\nnode 20 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 0,1,8,4,18,16,10,12,9,2,11,20,17,3,14,15,6,13,5,7,19.", "difficulty": "medium", "doc_id": "89"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 11 nodes numbered from 0 to 10:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 7\nnode 0 should be visited before node 2\nnode 0 should be visited before node 6\nnode 1 should be visited before node 2\nnode 1 should be visited before node 8\nnode 1 should be visited before node 6\nnode 1 should be visited before node 10\nnode 3 should be visited before node 0\nnode 3 should be visited before node 7\nnode 3 should be visited before node 10\nnode 4 should be visited before node 7\nnode 4 should be visited before node 5\nnode 4 should be visited before node 8\nnode 5 should be visited before node 2\nnode 5 should be visited before node 8\nnode 5 should be visited before node 10\nnode 6 should be visited before node 10\nnode 7 should be visited before node 2\nnode 7 should be visited before node 8\nnode 7 should be visited before node 10\nnode 8 should be visited before node 6\nnode 9 should be visited before node 1\nnode 9 should be visited before node 4\nnode 9 should be visited before node 6\nnode 9 should be visited before node 10\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 3,9,0,1,4,7,5,2,8,6,10.", "difficulty": "medium", "doc_id": "90"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 24 nodes numbered from 0 to 23:\nnode 0 should be visited before node 15\nnode 1 should be visited before node 22\nnode 1 should be visited before node 15\nnode 1 should be visited before node 12\nnode 1 should be visited before node 21\nnode 2 should be visited before node 13\nnode 2 should be visited before node 19\nnode 2 should be visited before node 3\nnode 2 should be visited before node 11\nnode 2 should be visited before node 20\nnode 2 should be visited before node 15\nnode 2 should be visited before node 12\nnode 2 should be visited before node 21\nnode 3 should be visited before node 20\nnode 3 should be visited before node 22\nnode 6 should be visited before node 13\nnode 6 should be visited before node 3\nnode 6 should be visited before node 4\nnode 6 should be visited before node 1\nnode 6 should be visited before node 0\nnode 7 should be visited before node 2\nnode 7 should be visited before node 9\nnode 7 should be visited before node 13\nnode 7 should be visited before node 11\nnode 7 should be visited before node 22\nnode 7 should be visited before node 0\nnode 7 should be visited before node 15\nnode 7 should be visited before node 12\nnode 7 should be visited before node 21\nnode 8 should be visited before node 23\nnode 8 should be visited before node 10\nnode 8 should be visited before node 9\nnode 8 should be visited before node 3\nnode 8 should be visited before node 20\nnode 8 should be visited before node 1\nnode 8 should be visited before node 12\nnode 8 should be visited before node 21\nnode 9 should be visited before node 5\nnode 9 should be visited before node 20\nnode 9 should be visited before node 21\nnode 10 should be visited before node 6\nnode 10 should be visited before node 19\nnode 10 should be visited before node 3\nnode 10 should be visited before node 4\nnode 10 should be visited before node 21\nnode 11 should be visited before node 20\nnode 11 should be visited before node 22\nnode 12 should be visited before node 21\nnode 13 should be visited before node 5\nnode 13 should be visited before node 3\nnode 13 should be visited before node 11\nnode 13 should be visited before node 1\nnode 14 should be visited before node 7\nnode 14 should be visited before node 9\nnode 14 should be visited before node 6\nnode 14 should be visited before node 5\nnode 14 should be visited before node 11\nnode 14 should be visited before node 4\nnode 14 should be visited before node 1\nnode 14 should be visited before node 15\nnode 15 should be visited before node 12\nnode 16 should be visited before node 17\nnode 16 should be visited before node 10\nnode 16 should be visited before node 0\nnode 16 should be visited before node 21\nnode 17 should be visited before node 23\nnode 17 should be visited before node 5\nnode 17 should be visited before node 3\nnode 17 should be visited before node 11\nnode 17 should be visited before node 12\nnode 17 should be visited before node 21\nnode 18 should be visited before node 10\nnode 18 should be visited before node 9\nnode 18 should be visited before node 6\nnode 18 should be visited before node 13\nnode 18 should be visited before node 0\nnode 18 should be visited before node 12\nnode 18 should be visited before node 21\nnode 19 should be visited before node 4\nnode 19 should be visited before node 21\nnode 20 should be visited before node 0\nnode 22 should be visited before node 15\nnode 23 should be visited before node 7\nnode 23 should be visited before node 20\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 8,14,16,18,17,10,23,6,7,2,9,13,19,5,3,11,1,4,20,22,0,15,12,21.", "difficulty": "medium", "doc_id": "91"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 15 nodes numbered from 0 to 14:\nnode 0 should be visited before node 2\nnode 1 should be visited before node 5\nnode 3 should be visited before node 12\nnode 3 should be visited before node 14\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 14\nnode 4 should be visited before node 5\nnode 4 should be visited before node 2\nnode 5 should be visited before node 2\nnode 6 should be visited before node 9\nnode 6 should be visited before node 13\nnode 6 should be visited before node 5\nnode 6 should be visited before node 8\nnode 7 should be visited before node 3\nnode 7 should be visited before node 12\nnode 7 should be visited before node 13\nnode 7 should be visited before node 5\nnode 7 should be visited before node 2\nnode 9 should be visited before node 3\nnode 9 should be visited before node 0\nnode 9 should be visited before node 14\nnode 9 should be visited before node 5\nnode 9 should be visited before node 2\nnode 10 should be visited before node 9\nnode 10 should be visited before node 3\nnode 10 should be visited before node 12\nnode 10 should be visited before node 0\nnode 10 should be visited before node 13\nnode 10 should be visited before node 14\nnode 11 should be visited before node 9\nnode 11 should be visited before node 12\nnode 11 should be visited before node 0\nnode 11 should be visited before node 13\nnode 11 should be visited before node 14\nnode 11 should be visited before node 1\nnode 11 should be visited before node 5\nnode 11 should be visited before node 2\nnode 11 should be visited before node 8\nnode 12 should be visited before node 0\nnode 12 should be visited before node 14\nnode 12 should be visited before node 1\nnode 12 should be visited before node 2\nnode 12 should be visited before node 8\nnode 13 should be visited before node 2\nnode 13 should be visited before node 8\nnode 14 should be visited before node 1\nnode 14 should be visited before node 5\nnode 14 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 4,6,7,10,11,9,13,3,12,0,14,8,1,5,2.", "difficulty": "medium", "doc_id": "92"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 14 nodes numbered from 0 to 13:\nnode 0 should be visited before node 11\nnode 1 should be visited before node 3\nnode 1 should be visited before node 5\nnode 1 should be visited before node 10\nnode 1 should be visited before node 12\nnode 1 should be visited before node 0\nnode 2 should be visited before node 5\nnode 2 should be visited before node 9\nnode 2 should be visited before node 12\nnode 2 should be visited before node 7\nnode 2 should be visited before node 8\nnode 2 should be visited before node 11\nnode 2 should be visited before node 6\nnode 3 should be visited before node 5\nnode 3 should be visited before node 10\nnode 3 should be visited before node 9\nnode 3 should be visited before node 7\nnode 3 should be visited before node 4\nnode 3 should be visited before node 6\nnode 5 should be visited before node 11\nnode 7 should be visited before node 0\nnode 7 should be visited before node 4\nnode 9 should be visited before node 12\nnode 9 should be visited before node 7\nnode 9 should be visited before node 0\nnode 9 should be visited before node 4\nnode 9 should be visited before node 11\nnode 10 should be visited before node 12\nnode 10 should be visited before node 8\nnode 10 should be visited before node 11\nnode 12 should be visited before node 7\nnode 12 should be visited before node 8\nnode 12 should be visited before node 0\nnode 12 should be visited before node 4\nnode 12 should be visited before node 6\nnode 13 should be visited before node 12\nnode 13 should be visited before node 8\nnode 13 should be visited before node 11\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 1,2,13,3,5,10,9,12,7,8,6,0,4,11.", "difficulty": "medium", "doc_id": "93"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 13 nodes numbered from 0 to 12:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 5\nnode 0 should be visited before node 2\nnode 0 should be visited before node 10\nnode 0 should be visited before node 6\nnode 0 should be visited before node 7\nnode 0 should be visited before node 12\nnode 0 should be visited before node 1\nnode 2 should be visited before node 10\nnode 2 should be visited before node 3\nnode 2 should be visited before node 7\nnode 2 should be visited before node 12\nnode 2 should be visited before node 1\nnode 3 should be visited before node 7\nnode 3 should be visited before node 12\nnode 4 should be visited before node 11\nnode 4 should be visited before node 5\nnode 4 should be visited before node 2\nnode 4 should be visited before node 10\nnode 4 should be visited before node 6\nnode 4 should be visited before node 7\nnode 4 should be visited before node 12\nnode 5 should be visited before node 2\nnode 5 should be visited before node 10\nnode 5 should be visited before node 6\nnode 5 should be visited before node 3\nnode 5 should be visited before node 12\nnode 5 should be visited before node 1\nnode 6 should be visited before node 3\nnode 7 should be visited before node 12\nnode 7 should be visited before node 1\nnode 8 should be visited before node 9\nnode 8 should be visited before node 4\nnode 8 should be visited before node 11\nnode 8 should be visited before node 5\nnode 8 should be visited before node 2\nnode 8 should be visited before node 6\nnode 8 should be visited before node 3\nnode 8 should be visited before node 7\nnode 8 should be visited before node 12\nnode 8 should be visited before node 1\nnode 9 should be visited before node 0\nnode 9 should be visited before node 4\nnode 9 should be visited before node 11\nnode 9 should be visited before node 5\nnode 9 should be visited before node 2\nnode 9 should be visited before node 10\nnode 9 should be visited before node 6\nnode 9 should be visited before node 3\nnode 9 should be visited before node 12\nnode 9 should be visited before node 1\nnode 10 should be visited before node 6\nnode 10 should be visited before node 3\nnode 10 should be visited before node 7\nnode 10 should be visited before node 12\nnode 11 should be visited before node 5\nnode 11 should be visited before node 2\nnode 11 should be visited before node 10\nnode 11 should be visited before node 6\nnode 11 should be visited before node 3\nnode 11 should be visited before node 12\nnode 12 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 8,9,0,4,11,5,2,10,6,3,7,12,1.", "difficulty": "medium", "doc_id": "94"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 11 nodes numbered from 0 to 10:\nnode 0 should be visited before node 2\nnode 1 should be visited before node 6\nnode 1 should be visited before node 10\nnode 2 should be visited before node 5\nnode 3 should be visited before node 0\nnode 3 should be visited before node 9\nnode 3 should be visited before node 7\nnode 3 should be visited before node 6\nnode 4 should be visited before node 10\nnode 4 should be visited before node 5\nnode 7 should be visited before node 2\nnode 8 should be visited before node 5\nnode 9 should be visited before node 4\nnode 9 should be visited before node 1\nnode 9 should be visited before node 2\nnode 9 should be visited before node 10\nnode 10 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 3,8,0,9,7,4,1,2,6,10,5.", "difficulty": "medium", "doc_id": "95"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 10 nodes numbered from 0 to 9:\nnode 4 should be visited before node 6\nnode 4 should be visited before node 9\nnode 5 should be visited before node 4\nnode 5 should be visited before node 0\nnode 5 should be visited before node 7\nnode 5 should be visited before node 8\nnode 6 should be visited before node 1\nnode 6 should be visited before node 7\nnode 7 should be visited before node 2\nnode 9 should be visited before node 0\nnode 9 should be visited before node 1\nnode 9 should be visited before node 3\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 5,4,8,6,9,7,0,1,3,2.", "difficulty": "easy", "doc_id": "96"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 16 nodes numbered from 0 to 15:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 3 should be visited before node 2\nnode 3 should be visited before node 0\nnode 4 should be visited before node 10\nnode 4 should be visited before node 11\nnode 5 should be visited before node 3\nnode 5 should be visited before node 1\nnode 5 should be visited before node 10\nnode 5 should be visited before node 0\nnode 7 should be visited before node 8\nnode 7 should be visited before node 9\nnode 7 should be visited before node 4\nnode 7 should be visited before node 15\nnode 7 should be visited before node 3\nnode 7 should be visited before node 1\nnode 7 should be visited before node 6\nnode 8 should be visited before node 12\nnode 8 should be visited before node 9\nnode 8 should be visited before node 3\nnode 8 should be visited before node 13\nnode 8 should be visited before node 6\nnode 9 should be visited before node 5\nnode 9 should be visited before node 2\nnode 9 should be visited before node 13\nnode 9 should be visited before node 1\nnode 9 should be visited before node 0\nnode 9 should be visited before node 6\nnode 10 should be visited before node 6\nnode 11 should be visited before node 6\nnode 12 should be visited before node 9\nnode 12 should be visited before node 4\nnode 12 should be visited before node 5\nnode 12 should be visited before node 15\nnode 12 should be visited before node 3\nnode 12 should be visited before node 10\nnode 12 should be visited before node 0\nnode 12 should be visited before node 6\nnode 13 should be visited before node 10\nnode 13 should be visited before node 11\nnode 13 should be visited before node 6\nnode 14 should be visited before node 8\nnode 14 should be visited before node 12\nnode 14 should be visited before node 5\nnode 14 should be visited before node 3\nnode 14 should be visited before node 2\nnode 14 should be visited before node 13\nnode 14 should be visited before node 0\nnode 14 should be visited before node 11\nnode 15 should be visited before node 13\nnode 15 should be visited before node 0\nnode 15 should be visited before node 11\nnode 15 should be visited before node 6\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 7,14,8,12,9,4,15,5,13,3,1,10,11,2,0,6.", "difficulty": "medium", "doc_id": "97"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 8 nodes numbered from 0 to 7:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 3\nnode 1 should be visited before node 0\nnode 1 should be visited before node 2\nnode 1 should be visited before node 3\nnode 2 should be visited before node 4\nnode 2 should be visited before node 5\nnode 4 should be visited before node 5\nnode 5 should be visited before node 3\nnode 6 should be visited before node 1\nnode 7 should be visited before node 3\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 6,7,1,0,2,4,5,3.", "difficulty": "easy", "doc_id": "98"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 18 nodes numbered from 0 to 17:\nnode 0 should be visited before node 7\nnode 0 should be visited before node 15\nnode 0 should be visited before node 11\nnode 0 should be visited before node 10\nnode 0 should be visited before node 16\nnode 0 should be visited before node 6\nnode 0 should be visited before node 1\nnode 2 should be visited before node 4\nnode 2 should be visited before node 12\nnode 2 should be visited before node 14\nnode 2 should be visited before node 9\nnode 2 should be visited before node 17\nnode 2 should be visited before node 6\nnode 3 should be visited before node 12\nnode 3 should be visited before node 11\nnode 3 should be visited before node 10\nnode 4 should be visited before node 8\nnode 4 should be visited before node 12\nnode 4 should be visited before node 6\nnode 4 should be visited before node 1\nnode 5 should be visited before node 12\nnode 5 should be visited before node 10\nnode 6 should be visited before node 1\nnode 7 should be visited before node 15\nnode 7 should be visited before node 11\nnode 7 should be visited before node 6\nnode 8 should be visited before node 3\nnode 8 should be visited before node 15\nnode 8 should be visited before node 10\nnode 8 should be visited before node 16\nnode 8 should be visited before node 6\nnode 10 should be visited before node 16\nnode 10 should be visited before node 1\nnode 11 should be visited before node 16\nnode 12 should be visited before node 14\nnode 12 should be visited before node 6\nnode 13 should be visited before node 0\nnode 13 should be visited before node 7\nnode 13 should be visited before node 3\nnode 13 should be visited before node 9\nnode 13 should be visited before node 6\nnode 14 should be visited before node 9\nnode 15 should be visited before node 11\nnode 15 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 2,5,13,4,17,0,8,7,3,15,12,10,11,14,6,16,9,1.", "difficulty": "medium", "doc_id": "99"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 9 nodes numbered from 0 to 8:\nnode 2 should be visited before node 1\nnode 3 should be visited before node 6\nnode 3 should be visited before node 2\nnode 3 should be visited before node 5\nnode 4 should be visited before node 6\nnode 4 should be visited before node 2\nnode 4 should be visited before node 7\nnode 4 should be visited before node 5\nnode 4 should be visited before node 8\nnode 6 should be visited before node 2\nnode 6 should be visited before node 1\nnode 7 should be visited before node 8\nnode 8 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 0,3,4,6,7,5,2,8,1.", "difficulty": "easy", "doc_id": "100"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 0\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 3 should be visited before node 2\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 1,3,4,6,2,0,5.", "difficulty": "easy", "doc_id": "101"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 12 nodes numbered from 0 to 11:\nnode 0 should be visited before node 3\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 0 should be visited before node 6\nnode 1 should be visited before node 6\nnode 1 should be visited before node 7\nnode 1 should be visited before node 9\nnode 2 should be visited before node 9\nnode 3 should be visited before node 4\nnode 3 should be visited before node 1\nnode 3 should be visited before node 6\nnode 3 should be visited before node 7\nnode 3 should be visited before node 10\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 4\nnode 5 should be visited before node 6\nnode 5 should be visited before node 10\nnode 5 should be visited before node 2\nnode 6 should be visited before node 9\nnode 7 should be visited before node 10\nnode 7 should be visited before node 2\nnode 8 should be visited before node 5\nnode 8 should be visited before node 7\nnode 8 should be visited before node 9\nnode 10 should be visited before node 9\nnode 11 should be visited before node 4\nnode 11 should be visited before node 10\nnode 11 should be visited before node 2\nnode 11 should be visited before node 9\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 0,8,11,3,5,4,1,6,7,10,2,9.", "difficulty": "medium", "doc_id": "102"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 27 nodes numbered from 0 to 26:\nnode 0 should be visited before node 18\nnode 0 should be visited before node 21\nnode 0 should be visited before node 25\nnode 0 should be visited before node 11\nnode 0 should be visited before node 13\nnode 1 should be visited before node 5\nnode 1 should be visited before node 11\nnode 1 should be visited before node 10\nnode 2 should be visited before node 8\nnode 2 should be visited before node 3\nnode 2 should be visited before node 25\nnode 2 should be visited before node 11\nnode 3 should be visited before node 17\nnode 3 should be visited before node 11\nnode 4 should be visited before node 8\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 17\nnode 4 should be visited before node 5\nnode 4 should be visited before node 13\nnode 5 should be visited before node 11\nnode 5 should be visited before node 10\nnode 6 should be visited before node 9\nnode 6 should be visited before node 3\nnode 6 should be visited before node 25\nnode 7 should be visited before node 16\nnode 7 should be visited before node 6\nnode 7 should be visited before node 17\nnode 7 should be visited before node 25\nnode 8 should be visited before node 3\nnode 8 should be visited before node 17\nnode 8 should be visited before node 21\nnode 8 should be visited before node 25\nnode 9 should be visited before node 1\nnode 9 should be visited before node 5\nnode 9 should be visited before node 13\nnode 12 should be visited before node 21\nnode 14 should be visited before node 6\nnode 14 should be visited before node 9\nnode 14 should be visited before node 3\nnode 14 should be visited before node 0\nnode 14 should be visited before node 23\nnode 14 should be visited before node 17\nnode 14 should be visited before node 25\nnode 14 should be visited before node 11\nnode 15 should be visited before node 2\nnode 15 should be visited before node 21\nnode 15 should be visited before node 13\nnode 16 should be visited before node 20\nnode 16 should be visited before node 15\nnode 16 should be visited before node 8\nnode 16 should be visited before node 0\nnode 16 should be visited before node 1\nnode 17 should be visited before node 21\nnode 17 should be visited before node 25\nnode 17 should be visited before node 13\nnode 18 should be visited before node 17\nnode 18 should be visited before node 21\nnode 18 should be visited before node 5\nnode 19 should be visited before node 22\nnode 19 should be visited before node 15\nnode 19 should be visited before node 6\nnode 19 should be visited before node 13\nnode 20 should be visited before node 22\nnode 20 should be visited before node 4\nnode 20 should be visited before node 6\nnode 20 should be visited before node 1\nnode 20 should be visited before node 17\nnode 20 should be visited before node 25\nnode 20 should be visited before node 5\nnode 20 should be visited before node 10\nnode 20 should be visited before node 13\nnode 21 should be visited before node 13\nnode 22 should be visited before node 4\nnode 22 should be visited before node 6\nnode 22 should be visited before node 1\nnode 22 should be visited before node 5\nnode 23 should be visited before node 5\nnode 24 should be visited before node 26\nnode 24 should be visited before node 12\nnode 24 should be visited before node 2\nnode 24 should be visited before node 14\nnode 24 should be visited before node 3\nnode 24 should be visited before node 1\nnode 24 should be visited before node 5\nnode 24 should be visited before node 10\nnode 24 should be visited before node 13\nnode 25 should be visited before node 11\nnode 25 should be visited before node 13\nnode 26 should be visited before node 2\nnode 26 should be visited before node 0\nnode 26 should be visited before node 18\nnode 26 should be visited before node 11\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 7,19,24,16,26,12,14,20,15,23,22,2,4,6,8,0,9,3,18,1,17,5,21,25,10,11,13.", "difficulty": "hard", "doc_id": "103"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 8 nodes numbered from 0 to 7:\nnode 3 should be visited before node 0\nnode 3 should be visited before node 2\nnode 4 should be visited before node 7\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 6 should be visited before node 3\nnode 7 should be visited before node 0\nnode 7 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 4,5,6,7,1,3,0,2.", "difficulty": "easy", "doc_id": "104"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 30 nodes numbered from 0 to 29:\nnode 0 should be visited before node 18\nnode 0 should be visited before node 8\nnode 0 should be visited before node 14\nnode 0 should be visited before node 7\nnode 0 should be visited before node 6\nnode 0 should be visited before node 11\nnode 0 should be visited before node 2\nnode 0 should be visited before node 12\nnode 0 should be visited before node 23\nnode 0 should be visited before node 25\nnode 0 should be visited before node 26\nnode 0 should be visited before node 10\nnode 1 should be visited before node 20\nnode 1 should be visited before node 24\nnode 1 should be visited before node 13\nnode 1 should be visited before node 3\nnode 1 should be visited before node 27\nnode 1 should be visited before node 29\nnode 1 should be visited before node 8\nnode 1 should be visited before node 14\nnode 1 should be visited before node 28\nnode 1 should be visited before node 7\nnode 1 should be visited before node 6\nnode 1 should be visited before node 11\nnode 1 should be visited before node 21\nnode 1 should be visited before node 23\nnode 1 should be visited before node 16\nnode 2 should be visited before node 12\nnode 2 should be visited before node 23\nnode 2 should be visited before node 15\nnode 2 should be visited before node 22\nnode 2 should be visited before node 10\nnode 3 should be visited before node 0\nnode 3 should be visited before node 14\nnode 3 should be visited before node 7\nnode 3 should be visited before node 23\nnode 3 should be visited before node 25\nnode 3 should be visited before node 26\nnode 3 should be visited before node 16\nnode 4 should be visited before node 24\nnode 4 should be visited before node 13\nnode 4 should be visited before node 3\nnode 4 should be visited before node 27\nnode 4 should be visited before node 29\nnode 4 should be visited before node 8\nnode 4 should be visited before node 19\nnode 4 should be visited before node 9\nnode 4 should be visited before node 7\nnode 4 should be visited before node 6\nnode 4 should be visited before node 11\nnode 4 should be visited before node 12\nnode 4 should be visited before node 26\nnode 4 should be visited before node 22\nnode 4 should be visited before node 16\nnode 5 should be visited before node 1\nnode 5 should be visited before node 24\nnode 5 should be visited before node 13\nnode 5 should be visited before node 3\nnode 5 should be visited before node 27\nnode 5 should be visited before node 29\nnode 5 should be visited before node 18\nnode 5 should be visited before node 9\nnode 5 should be visited before node 7\nnode 5 should be visited before node 11\nnode 5 should be visited before node 2\nnode 5 should be visited before node 26\nnode 5 should be visited before node 22\nnode 6 should be visited before node 21\nnode 6 should be visited before node 22\nnode 7 should be visited before node 21\nnode 7 should be visited before node 15\nnode 7 should be visited before node 25\nnode 7 should be visited before node 26\nnode 7 should be visited before node 10\nnode 7 should be visited before node 16\nnode 8 should be visited before node 14\nnode 8 should be visited before node 21\nnode 8 should be visited before node 2\nnode 8 should be visited before node 25\nnode 8 should be visited before node 16\nnode 9 should be visited before node 28\nnode 9 should be visited before node 7\nnode 9 should be visited before node 6\nnode 9 should be visited before node 11\nnode 9 should be visited before node 2\nnode 9 should be visited before node 23\nnode 10 should be visited before node 16\nnode 11 should be visited before node 25\nnode 11 should be visited before node 26\nnode 11 should be visited before node 22\nnode 11 should be visited before node 10\nnode 11 should be visited before node 16\nnode 12 should be visited before node 25\nnode 12 should be visited before node 26\nnode 12 should be visited before node 16\nnode 13 should be visited before node 27\nnode 13 should be visited before node 18\nnode 13 should be visited before node 8\nnode 13 should be visited before node 19\nnode 13 should be visited before node 25\nnode 13 should be visited before node 26\nnode 13 should be visited before node 22\nnode 13 should be visited before node 10\nnode 14 should be visited before node 19\nnode 14 should be visited before node 28\nnode 14 should be visited before node 6\nnode 14 should be visited before node 2\nnode 14 should be visited before node 15\nnode 14 should be visited before node 25\nnode 14 should be visited before node 26\nnode 14 should be visited before node 22\nnode 15 should be visited before node 26\nnode 15 should be visited before node 22\nnode 17 should be visited before node 20\nnode 17 should be visited before node 3\nnode 17 should be visited before node 0\nnode 17 should be visited before node 18\nnode 17 should be visited before node 8\nnode 17 should be visited before node 14\nnode 17 should be visited before node 9\nnode 17 should be visited before node 28\nnode 17 should be visited before node 6\nnode 17 should be visited before node 23\nnode 17 should be visited before node 25\nnode 17 should be visited before node 10\nnode 17 should be visited before node 16\nnode 18 should be visited before node 8\nnode 18 should be visited before node 14\nnode 18 should be visited before node 19\nnode 18 should be visited before node 9\nnode 18 should be visited before node 11\nnode 18 should be visited before node 21\nnode 18 should be visited before node 2\nnode 18 should be visited before node 12\nnode 18 should be visited before node 23\nnode 18 should be visited before node 15\nnode 18 should be visited before node 25\nnode 18 should be visited before node 26\nnode 18 should be visited before node 22\nnode 18 should be visited before node 10\nnode 19 should be visited before node 9\nnode 19 should be visited before node 28\nnode 19 should be visited before node 21\nnode 19 should be visited before node 2\nnode 19 should be visited before node 12\nnode 19 should be visited before node 23\nnode 19 should be visited before node 15\nnode 19 should be visited before node 25\nnode 19 should be visited before node 26\nnode 19 should be visited before node 22\nnode 20 should be visited before node 24\nnode 20 should be visited before node 13\nnode 20 should be visited before node 3\nnode 20 should be visited before node 29\nnode 20 should be visited before node 9\nnode 20 should be visited before node 28\nnode 20 should be visited before node 7\nnode 20 should be visited before node 6\nnode 20 should be visited before node 11\nnode 20 should be visited before node 2\nnode 20 should be visited before node 12\nnode 20 should be visited before node 23\nnode 20 should be visited before node 25\nnode 20 should be visited before node 26\nnode 20 should be visited before node 22\nnode 20 should be visited before node 16\nnode 21 should be visited before node 2\nnode 21 should be visited before node 12\nnode 21 should be visited before node 23\nnode 21 should be visited before node 25\nnode 21 should be visited before node 10\nnode 22 should be visited before node 16\nnode 23 should be visited before node 25\nnode 23 should be visited before node 22\nnode 24 should be visited before node 13\nnode 24 should be visited before node 3\nnode 24 should be visited before node 27\nnode 24 should be visited before node 0\nnode 24 should be visited before node 14\nnode 24 should be visited before node 19\nnode 24 should be visited before node 7\nnode 24 should be visited before node 2\nnode 24 should be visited before node 12\nnode 24 should be visited before node 15\nnode 24 should be visited before node 25\nnode 24 should be visited before node 26\nnode 24 should be visited before node 10\nnode 24 should be visited before node 16\nnode 25 should be visited before node 10\nnode 26 should be visited before node 10\nnode 27 should be visited before node 18\nnode 27 should be visited before node 19\nnode 27 should be visited before node 9\nnode 27 should be visited before node 28\nnode 27 should be visited before node 7\nnode 27 should be visited before node 6\nnode 27 should be visited before node 11\nnode 27 should be visited before node 21\nnode 27 should be visited before node 15\nnode 27 should be visited before node 25\nnode 27 should be visited before node 22\nnode 27 should be visited before node 10\nnode 27 should be visited before node 16\nnode 28 should be visited before node 2\nnode 28 should be visited before node 12\nnode 28 should be visited before node 25\nnode 28 should be visited before node 22\nnode 28 should be visited before node 10\nnode 29 should be visited before node 19\nnode 29 should be visited before node 7\nnode 29 should be visited before node 11\nnode 29 should be visited before node 12\nnode 29 should be visited before node 23\nnode 29 should be visited before node 15\nnode 29 should be visited before node 26\nnode 29 should be visited before node 22\nnode 29 should be visited before node 10\nnode 29 should be visited before node 16\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 4,5,17,1,20,24,29,13,3,27,0,18,8,14,19,9,28,7,6,11,21,2,12,23,15,25,26,22,10,16.", "difficulty": "hard", "doc_id": "105"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 29 nodes numbered from 0 to 28:\nnode 0 should be visited before node 2\nnode 0 should be visited before node 18\nnode 0 should be visited before node 23\nnode 0 should be visited before node 17\nnode 1 should be visited before node 17\nnode 2 should be visited before node 18\nnode 3 should be visited before node 6\nnode 3 should be visited before node 7\nnode 3 should be visited before node 21\nnode 3 should be visited before node 14\nnode 3 should be visited before node 23\nnode 3 should be visited before node 17\nnode 4 should be visited before node 8\nnode 4 should be visited before node 9\nnode 4 should be visited before node 18\nnode 5 should be visited before node 26\nnode 5 should be visited before node 3\nnode 5 should be visited before node 7\nnode 5 should be visited before node 23\nnode 5 should be visited before node 17\nnode 6 should be visited before node 1\nnode 6 should be visited before node 14\nnode 7 should be visited before node 21\nnode 7 should be visited before node 17\nnode 8 should be visited before node 9\nnode 9 should be visited before node 2\nnode 9 should be visited before node 23\nnode 10 should be visited before node 5\nnode 10 should be visited before node 20\nnode 10 should be visited before node 12\nnode 10 should be visited before node 3\nnode 10 should be visited before node 4\nnode 10 should be visited before node 8\nnode 10 should be visited before node 0\nnode 10 should be visited before node 9\nnode 10 should be visited before node 14\nnode 10 should be visited before node 18\nnode 11 should be visited before node 20\nnode 11 should be visited before node 8\nnode 11 should be visited before node 2\nnode 12 should be visited before node 4\nnode 12 should be visited before node 6\nnode 12 should be visited before node 0\nnode 12 should be visited before node 21\nnode 12 should be visited before node 1\nnode 12 should be visited before node 17\nnode 13 should be visited before node 10\nnode 13 should be visited before node 4\nnode 13 should be visited before node 9\nnode 13 should be visited before node 2\nnode 15 should be visited before node 10\nnode 15 should be visited before node 12\nnode 15 should be visited before node 21\nnode 15 should be visited before node 1\nnode 15 should be visited before node 18\nnode 16 should be visited before node 22\nnode 16 should be visited before node 12\nnode 16 should be visited before node 3\nnode 16 should be visited before node 4\nnode 16 should be visited before node 21\nnode 16 should be visited before node 9\nnode 16 should be visited before node 23\nnode 19 should be visited before node 20\nnode 19 should be visited before node 24\nnode 19 should be visited before node 8\nnode 19 should be visited before node 7\nnode 19 should be visited before node 0\nnode 19 should be visited before node 1\nnode 19 should be visited before node 14\nnode 20 should be visited before node 3\nnode 20 should be visited before node 9\nnode 20 should be visited before node 17\nnode 21 should be visited before node 9\nnode 22 should be visited before node 26\nnode 22 should be visited before node 24\nnode 22 should be visited before node 23\nnode 24 should be visited before node 6\nnode 24 should be visited before node 8\nnode 24 should be visited before node 0\nnode 24 should be visited before node 21\nnode 24 should be visited before node 9\nnode 24 should be visited before node 23\nnode 25 should be visited before node 19\nnode 25 should be visited before node 27\nnode 25 should be visited before node 15\nnode 25 should be visited before node 16\nnode 25 should be visited before node 10\nnode 25 should be visited before node 12\nnode 25 should be visited before node 1\nnode 26 should be visited before node 12\nnode 26 should be visited before node 3\nnode 26 should be visited before node 4\nnode 27 should be visited before node 10\nnode 27 should be visited before node 26\nnode 27 should be visited before node 7\nnode 27 should be visited before node 0\nnode 27 should be visited before node 9\nnode 27 should be visited before node 1\nnode 27 should be visited before node 23\nnode 27 should be visited before node 17\nnode 28 should be visited before node 11\nnode 28 should be visited before node 20\nnode 28 should be visited before node 3\nnode 28 should be visited before node 21\nnode 28 should be visited before node 1\nnode 28 should be visited before node 2\nnode 28 should be visited before node 17\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 13,25,28,19,27,15,16,11,10,22,5,20,24,26,12,3,4,0,6,7,8,1,14,21,17,9,2,23,18.", "difficulty": "hard", "doc_id": "106"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 12 nodes numbered from 0 to 11:\nnode 1 should be visited before node 10\nnode 1 should be visited before node 7\nnode 1 should be visited before node 6\nnode 1 should be visited before node 3\nnode 1 should be visited before node 5\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 3 should be visited before node 2\nnode 3 should be visited before node 0\nnode 3 should be visited before node 8\nnode 4 should be visited before node 0\nnode 4 should be visited before node 5\nnode 4 should be visited before node 8\nnode 6 should be visited before node 3\nnode 6 should be visited before node 0\nnode 6 should be visited before node 8\nnode 7 should be visited before node 6\nnode 7 should be visited before node 9\nnode 7 should be visited before node 2\nnode 9 should be visited before node 2\nnode 9 should be visited before node 4\nnode 9 should be visited before node 5\nnode 10 should be visited before node 7\nnode 10 should be visited before node 6\nnode 10 should be visited before node 9\nnode 10 should be visited before node 3\nnode 10 should be visited before node 2\nnode 10 should be visited before node 0\nnode 10 should be visited before node 5\nnode 11 should be visited before node 6\nnode 11 should be visited before node 2\nnode 11 should be visited before node 0\nnode 11 should be visited before node 5\nnode 11 should be visited before node 8\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 1,11,10,7,6,9,3,4,2,8,0,5.", "difficulty": "medium", "doc_id": "107"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 34 nodes numbered from 0 to 33:\nnode 0 should be visited before node 11\nnode 0 should be visited before node 4\nnode 0 should be visited before node 30\nnode 0 should be visited before node 14\nnode 0 should be visited before node 18\nnode 0 should be visited before node 33\nnode 0 should be visited before node 6\nnode 0 should be visited before node 27\nnode 0 should be visited before node 7\nnode 0 should be visited before node 8\nnode 0 should be visited before node 23\nnode 1 should be visited before node 5\nnode 1 should be visited before node 4\nnode 1 should be visited before node 15\nnode 1 should be visited before node 8\nnode 1 should be visited before node 23\nnode 2 should be visited before node 5\nnode 2 should be visited before node 22\nnode 2 should be visited before node 14\nnode 2 should be visited before node 18\nnode 2 should be visited before node 33\nnode 2 should be visited before node 27\nnode 2 should be visited before node 20\nnode 2 should be visited before node 26\nnode 2 should be visited before node 23\nnode 3 should be visited before node 25\nnode 3 should be visited before node 28\nnode 3 should be visited before node 9\nnode 3 should be visited before node 17\nnode 3 should be visited before node 0\nnode 3 should be visited before node 11\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 3 should be visited before node 22\nnode 3 should be visited before node 6\nnode 3 should be visited before node 27\nnode 3 should be visited before node 26\nnode 3 should be visited before node 8\nnode 3 should be visited before node 23\nnode 4 should be visited before node 15\nnode 4 should be visited before node 14\nnode 4 should be visited before node 18\nnode 4 should be visited before node 27\nnode 4 should be visited before node 20\nnode 4 should be visited before node 26\nnode 4 should be visited before node 7\nnode 4 should be visited before node 8\nnode 5 should be visited before node 22\nnode 5 should be visited before node 4\nnode 5 should be visited before node 30\nnode 5 should be visited before node 33\nnode 5 should be visited before node 23\nnode 6 should be visited before node 27\nnode 6 should be visited before node 20\nnode 6 should be visited before node 7\nnode 7 should be visited before node 8\nnode 9 should be visited before node 31\nnode 9 should be visited before node 24\nnode 9 should be visited before node 16\nnode 9 should be visited before node 12\nnode 9 should be visited before node 5\nnode 9 should be visited before node 4\nnode 9 should be visited before node 14\nnode 9 should be visited before node 18\nnode 9 should be visited before node 7\nnode 9 should be visited before node 23\nnode 10 should be visited before node 3\nnode 10 should be visited before node 24\nnode 10 should be visited before node 16\nnode 10 should be visited before node 0\nnode 10 should be visited before node 11\nnode 10 should be visited before node 1\nnode 10 should be visited before node 22\nnode 10 should be visited before node 4\nnode 10 should be visited before node 15\nnode 10 should be visited before node 14\nnode 10 should be visited before node 33\nnode 10 should be visited before node 20\nnode 10 should be visited before node 7\nnode 11 should be visited before node 5\nnode 11 should be visited before node 4\nnode 11 should be visited before node 15\nnode 11 should be visited before node 18\nnode 11 should be visited before node 20\nnode 11 should be visited before node 26\nnode 11 should be visited before node 7\nnode 11 should be visited before node 8\nnode 12 should be visited before node 15\nnode 12 should be visited before node 30\nnode 12 should be visited before node 27\nnode 12 should be visited before node 26\nnode 12 should be visited before node 7\nnode 12 should be visited before node 23\nnode 13 should be visited before node 29\nnode 13 should be visited before node 3\nnode 13 should be visited before node 9\nnode 13 should be visited before node 24\nnode 13 should be visited before node 0\nnode 13 should be visited before node 11\nnode 13 should be visited before node 1\nnode 13 should be visited before node 2\nnode 13 should be visited before node 22\nnode 13 should be visited before node 4\nnode 13 should be visited before node 18\nnode 13 should be visited before node 33\nnode 13 should be visited before node 27\nnode 13 should be visited before node 20\nnode 13 should be visited before node 7\nnode 13 should be visited before node 23\nnode 14 should be visited before node 33\nnode 14 should be visited before node 20\nnode 14 should be visited before node 26\nnode 14 should be visited before node 7\nnode 14 should be visited before node 8\nnode 15 should be visited before node 33\nnode 15 should be visited before node 7\nnode 15 should be visited before node 8\nnode 15 should be visited before node 23\nnode 16 should be visited before node 21\nnode 16 should be visited before node 1\nnode 16 should be visited before node 12\nnode 16 should be visited before node 2\nnode 16 should be visited before node 5\nnode 16 should be visited before node 22\nnode 16 should be visited before node 4\nnode 16 should be visited before node 26\nnode 17 should be visited before node 19\nnode 17 should be visited before node 16\nnode 17 should be visited before node 0\nnode 17 should be visited before node 1\nnode 17 should be visited before node 2\nnode 17 should be visited before node 22\nnode 17 should be visited before node 30\nnode 17 should be visited before node 14\nnode 17 should be visited before node 18\nnode 17 should be visited before node 27\nnode 17 should be visited before node 20\nnode 17 should be visited before node 26\nnode 17 should be visited before node 7\nnode 18 should be visited before node 33\nnode 18 should be visited before node 26\nnode 18 should be visited before node 8\nnode 18 should be visited before node 23\nnode 19 should be visited before node 16\nnode 19 should be visited before node 0\nnode 19 should be visited before node 1\nnode 19 should be visited before node 12\nnode 19 should be visited before node 5\nnode 19 should be visited before node 22\nnode 19 should be visited before node 4\nnode 19 should be visited before node 15\nnode 19 should be visited before node 30\nnode 19 should be visited before node 14\nnode 19 should be visited before node 27\nnode 19 should be visited before node 20\nnode 19 should be visited before node 26\nnode 21 should be visited before node 11\nnode 21 should be visited before node 12\nnode 21 should be visited before node 2\nnode 21 should be visited before node 5\nnode 21 should be visited before node 4\nnode 21 should be visited before node 30\nnode 21 should be visited before node 14\nnode 21 should be visited before node 33\nnode 21 should be visited before node 6\nnode 21 should be visited before node 20\nnode 21 should be visited before node 26\nnode 21 should be visited before node 7\nnode 21 should be visited before node 8\nnode 22 should be visited before node 14\nnode 22 should be visited before node 18\nnode 22 should be visited before node 27\nnode 22 should be visited before node 8\nnode 24 should be visited before node 16\nnode 24 should be visited before node 22\nnode 24 should be visited before node 4\nnode 24 should be visited before node 15\nnode 24 should be visited before node 14\nnode 24 should be visited before node 33\nnode 24 should be visited before node 27\nnode 24 should be visited before node 7\nnode 24 should be visited before node 8\nnode 25 should be visited before node 28\nnode 25 should be visited before node 9\nnode 25 should be visited before node 17\nnode 25 should be visited before node 16\nnode 25 should be visited before node 21\nnode 25 should be visited before node 11\nnode 25 should be visited before node 5\nnode 25 should be visited before node 22\nnode 25 should be visited before node 4\nnode 25 should be visited before node 30\nnode 25 should be visited before node 14\nnode 25 should be visited before node 33\nnode 25 should be visited before node 6\nnode 25 should be visited before node 8\nnode 26 should be visited before node 7\nnode 26 should be visited before node 8\nnode 27 should be visited before node 26\nnode 27 should be visited before node 7\nnode 27 should be visited before node 8\nnode 28 should be visited before node 9\nnode 28 should be visited before node 31\nnode 28 should be visited before node 17\nnode 28 should be visited before node 19\nnode 28 should be visited before node 11\nnode 28 should be visited before node 12\nnode 28 should be visited before node 5\nnode 28 should be visited before node 22\nnode 28 should be visited before node 30\nnode 28 should be visited before node 20\nnode 28 should be visited before node 26\nnode 28 should be visited before node 7\nnode 28 should be visited before node 8\nnode 29 should be visited before node 10\nnode 29 should be visited before node 3\nnode 29 should be visited before node 28\nnode 29 should be visited before node 9\nnode 29 should be visited before node 19\nnode 29 should be visited before node 0\nnode 29 should be visited before node 11\nnode 29 should be visited before node 2\nnode 29 should be visited before node 5\nnode 29 should be visited before node 22\nnode 29 should be visited before node 14\nnode 29 should be visited before node 18\nnode 29 should be visited before node 20\nnode 29 should be visited before node 7\nnode 29 should be visited before node 8\nnode 30 should be visited before node 14\nnode 30 should be visited before node 33\nnode 30 should be visited before node 27\nnode 30 should be visited before node 20\nnode 30 should be visited before node 7\nnode 30 should be visited before node 23\nnode 31 should be visited before node 24\nnode 31 should be visited before node 19\nnode 31 should be visited before node 0\nnode 31 should be visited before node 21\nnode 31 should be visited before node 11\nnode 31 should be visited before node 5\nnode 31 should be visited before node 22\nnode 31 should be visited before node 15\nnode 31 should be visited before node 18\nnode 31 should be visited before node 27\nnode 31 should be visited before node 20\nnode 31 should be visited before node 26\nnode 32 should be visited before node 28\nnode 32 should be visited before node 9\nnode 32 should be visited before node 31\nnode 32 should be visited before node 19\nnode 32 should be visited before node 21\nnode 32 should be visited before node 11\nnode 32 should be visited before node 1\nnode 32 should be visited before node 2\nnode 32 should be visited before node 5\nnode 32 should be visited before node 22\nnode 32 should be visited before node 4\nnode 32 should be visited before node 15\nnode 32 should be visited before node 14\nnode 32 should be visited before node 18\nnode 32 should be visited before node 33\nnode 32 should be visited before node 6\nnode 32 should be visited before node 26\nnode 32 should be visited before node 23\nnode 33 should be visited before node 27\nnode 33 should be visited before node 20\nnode 33 should be visited before node 7\nnode 33 should be visited before node 8\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 13,32,29,10,3,25,28,9,17,31,24,19,16,0,21,1,11,12,2,6,5,22,4,30,15,18,14,23,33,27,20,26,7,8.", "difficulty": "hard", "doc_id": "108"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 29 nodes numbered from 0 to 28:\nnode 0 should be visited before node 21\nnode 0 should be visited before node 13\nnode 0 should be visited before node 19\nnode 0 should be visited before node 25\nnode 0 should be visited before node 22\nnode 0 should be visited before node 2\nnode 0 should be visited before node 12\nnode 0 should be visited before node 24\nnode 1 should be visited before node 22\nnode 1 should be visited before node 17\nnode 2 should be visited before node 28\nnode 2 should be visited before node 17\nnode 2 should be visited before node 12\nnode 2 should be visited before node 20\nnode 3 should be visited before node 8\nnode 3 should be visited before node 18\nnode 3 should be visited before node 2\nnode 3 should be visited before node 28\nnode 3 should be visited before node 7\nnode 3 should be visited before node 24\nnode 3 should be visited before node 20\nnode 4 should be visited before node 0\nnode 4 should be visited before node 9\nnode 4 should be visited before node 2\nnode 4 should be visited before node 28\nnode 4 should be visited before node 16\nnode 4 should be visited before node 10\nnode 4 should be visited before node 12\nnode 5 should be visited before node 27\nnode 6 should be visited before node 28\nnode 6 should be visited before node 16\nnode 7 should be visited before node 20\nnode 8 should be visited before node 19\nnode 8 should be visited before node 23\nnode 8 should be visited before node 10\nnode 9 should be visited before node 2\nnode 9 should be visited before node 15\nnode 9 should be visited before node 16\nnode 9 should be visited before node 27\nnode 9 should be visited before node 7\nnode 9 should be visited before node 12\nnode 10 should be visited before node 5\nnode 10 should be visited before node 24\nnode 11 should be visited before node 4\nnode 11 should be visited before node 1\nnode 11 should be visited before node 15\nnode 11 should be visited before node 24\nnode 11 should be visited before node 20\nnode 13 should be visited before node 1\nnode 13 should be visited before node 19\nnode 13 should be visited before node 25\nnode 13 should be visited before node 6\nnode 13 should be visited before node 10\nnode 14 should be visited before node 1\nnode 14 should be visited before node 9\nnode 14 should be visited before node 28\nnode 14 should be visited before node 16\nnode 14 should be visited before node 10\nnode 14 should be visited before node 7\nnode 15 should be visited before node 16\nnode 15 should be visited before node 17\nnode 15 should be visited before node 27\nnode 16 should be visited before node 17\nnode 16 should be visited before node 27\nnode 16 should be visited before node 7\nnode 17 should be visited before node 27\nnode 17 should be visited before node 24\nnode 18 should be visited before node 2\nnode 18 should be visited before node 10\nnode 18 should be visited before node 17\nnode 19 should be visited before node 9\nnode 19 should be visited before node 25\nnode 19 should be visited before node 22\nnode 19 should be visited before node 26\nnode 19 should be visited before node 2\nnode 19 should be visited before node 28\nnode 19 should be visited before node 16\nnode 19 should be visited before node 12\nnode 19 should be visited before node 20\nnode 21 should be visited before node 13\nnode 21 should be visited before node 22\nnode 21 should be visited before node 16\nnode 21 should be visited before node 10\nnode 21 should be visited before node 20\nnode 22 should be visited before node 2\nnode 22 should be visited before node 15\nnode 22 should be visited before node 10\nnode 22 should be visited before node 5\nnode 23 should be visited before node 6\nnode 23 should be visited before node 5\nnode 23 should be visited before node 27\nnode 23 should be visited before node 20\nnode 25 should be visited before node 26\nnode 25 should be visited before node 10\nnode 25 should be visited before node 17\nnode 25 should be visited before node 27\nnode 26 should be visited before node 2\nnode 26 should be visited before node 5\nnode 26 should be visited before node 27\nnode 26 should be visited before node 7\nnode 27 should be visited before node 7\nnode 27 should be visited before node 12\nnode 28 should be visited before node 7\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 3,11,14,8,18,4,23,0,21,13,1,19,6,9,25,22,26,15,10,2,16,5,28,17,27,24,7,12,20.", "difficulty": "hard", "doc_id": "109"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 12 nodes numbered from 0 to 11:\nnode 0 should be visited before node 6\nnode 0 should be visited before node 2\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 11\nnode 3 should be visited before node 0\nnode 3 should be visited before node 6\nnode 3 should be visited before node 2\nnode 4 should be visited before node 7\nnode 4 should be visited before node 1\nnode 5 should be visited before node 11\nnode 5 should be visited before node 0\nnode 7 should be visited before node 2\nnode 7 should be visited before node 1\nnode 8 should be visited before node 5\nnode 8 should be visited before node 3\nnode 8 should be visited before node 9\nnode 8 should be visited before node 0\nnode 9 should be visited before node 1\nnode 10 should be visited before node 8\nnode 10 should be visited before node 11\nnode 11 should be visited before node 0\nnode 11 should be visited before node 6\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 4,10,7,8,5,3,9,11,0,6,2,1.", "difficulty": "medium", "doc_id": "110"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 11 nodes numbered from 0 to 10:\nnode 0 should be visited before node 4\nnode 2 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 4\nnode 2 should be visited before node 9\nnode 3 should be visited before node 9\nnode 4 should be visited before node 3\nnode 4 should be visited before node 9\nnode 6 should be visited before node 7\nnode 7 should be visited before node 10\nnode 7 should be visited before node 9\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 1,2,5,8,6,0,7,4,10,3,9.", "difficulty": "medium", "doc_id": "111"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 17 nodes numbered from 0 to 16:\nnode 0 should be visited before node 10\nnode 0 should be visited before node 13\nnode 0 should be visited before node 15\nnode 0 should be visited before node 7\nnode 0 should be visited before node 16\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 1 should be visited before node 4\nnode 1 should be visited before node 8\nnode 1 should be visited before node 3\nnode 1 should be visited before node 10\nnode 1 should be visited before node 13\nnode 1 should be visited before node 15\nnode 1 should be visited before node 6\nnode 1 should be visited before node 7\nnode 1 should be visited before node 16\nnode 2 should be visited before node 5\nnode 2 should be visited before node 8\nnode 2 should be visited before node 3\nnode 2 should be visited before node 15\nnode 2 should be visited before node 14\nnode 2 should be visited before node 7\nnode 2 should be visited before node 16\nnode 3 should be visited before node 10\nnode 3 should be visited before node 13\nnode 3 should be visited before node 15\nnode 4 should be visited before node 8\nnode 4 should be visited before node 10\nnode 4 should be visited before node 15\nnode 4 should be visited before node 7\nnode 4 should be visited before node 16\nnode 5 should be visited before node 8\nnode 5 should be visited before node 15\nnode 5 should be visited before node 6\nnode 5 should be visited before node 16\nnode 7 should be visited before node 16\nnode 8 should be visited before node 3\nnode 8 should be visited before node 15\nnode 8 should be visited before node 14\nnode 8 should be visited before node 7\nnode 8 should be visited before node 16\nnode 9 should be visited before node 11\nnode 9 should be visited before node 8\nnode 9 should be visited before node 3\nnode 9 should be visited before node 15\nnode 9 should be visited before node 16\nnode 10 should be visited before node 13\nnode 10 should be visited before node 15\nnode 10 should be visited before node 6\nnode 10 should be visited before node 7\nnode 10 should be visited before node 16\nnode 11 should be visited before node 12\nnode 11 should be visited before node 2\nnode 11 should be visited before node 3\nnode 11 should be visited before node 10\nnode 11 should be visited before node 13\nnode 11 should be visited before node 16\nnode 12 should be visited before node 0\nnode 12 should be visited before node 4\nnode 12 should be visited before node 8\nnode 12 should be visited before node 3\nnode 12 should be visited before node 10\nnode 12 should be visited before node 6\nnode 13 should be visited before node 14\nnode 13 should be visited before node 6\nnode 13 should be visited before node 7\nnode 13 should be visited before node 16\nnode 14 should be visited before node 6\nnode 15 should be visited before node 14\nnode 15 should be visited before node 6\nnode 15 should be visited before node 16\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 1,9,11,12,2,0,4,5,8,3,10,13,15,7,14,16,6.", "difficulty": "medium", "doc_id": "112"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 17 nodes numbered from 0 to 16:\nnode 0 should be visited before node 6\nnode 0 should be visited before node 16\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 2 should be visited before node 12\nnode 3 should be visited before node 11\nnode 3 should be visited before node 16\nnode 3 should be visited before node 9\nnode 5 should be visited before node 15\nnode 5 should be visited before node 11\nnode 5 should be visited before node 13\nnode 5 should be visited before node 16\nnode 6 should be visited before node 8\nnode 7 should be visited before node 4\nnode 7 should be visited before node 1\nnode 7 should be visited before node 9\nnode 8 should be visited before node 12\nnode 9 should be visited before node 12\nnode 10 should be visited before node 7\nnode 10 should be visited before node 15\nnode 10 should be visited before node 11\nnode 10 should be visited before node 8\nnode 10 should be visited before node 1\nnode 11 should be visited before node 16\nnode 11 should be visited before node 1\nnode 11 should be visited before node 12\nnode 13 should be visited before node 4\nnode 13 should be visited before node 8\nnode 13 should be visited before node 16\nnode 13 should be visited before node 9\nnode 14 should be visited before node 2\nnode 14 should be visited before node 16\nnode 14 should be visited before node 9\nnode 15 should be visited before node 9\nnode 16 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 0,3,5,10,14,6,13,7,15,11,2,8,4,9,16,12,1.", "difficulty": "medium", "doc_id": "113"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 26 nodes numbered from 0 to 25:\nnode 0 should be visited before node 15\nnode 0 should be visited before node 14\nnode 0 should be visited before node 5\nnode 0 should be visited before node 10\nnode 0 should be visited before node 25\nnode 0 should be visited before node 21\nnode 0 should be visited before node 1\nnode 2 should be visited before node 15\nnode 2 should be visited before node 18\nnode 2 should be visited before node 7\nnode 2 should be visited before node 24\nnode 2 should be visited before node 5\nnode 2 should be visited before node 19\nnode 2 should be visited before node 12\nnode 2 should be visited before node 23\nnode 2 should be visited before node 10\nnode 2 should be visited before node 25\nnode 2 should be visited before node 21\nnode 2 should be visited before node 3\nnode 4 should be visited before node 5\nnode 4 should be visited before node 19\nnode 4 should be visited before node 20\nnode 4 should be visited before node 25\nnode 4 should be visited before node 16\nnode 4 should be visited before node 17\nnode 4 should be visited before node 21\nnode 5 should be visited before node 12\nnode 5 should be visited before node 20\nnode 5 should be visited before node 10\nnode 5 should be visited before node 16\nnode 5 should be visited before node 17\nnode 6 should be visited before node 0\nnode 6 should be visited before node 2\nnode 6 should be visited before node 7\nnode 6 should be visited before node 24\nnode 6 should be visited before node 5\nnode 6 should be visited before node 12\nnode 6 should be visited before node 20\nnode 6 should be visited before node 10\nnode 6 should be visited before node 16\nnode 6 should be visited before node 17\nnode 6 should be visited before node 21\nnode 7 should be visited before node 24\nnode 7 should be visited before node 19\nnode 7 should be visited before node 20\nnode 7 should be visited before node 25\nnode 7 should be visited before node 21\nnode 7 should be visited before node 3\nnode 7 should be visited before node 1\nnode 8 should be visited before node 13\nnode 8 should be visited before node 2\nnode 8 should be visited before node 4\nnode 8 should be visited before node 5\nnode 8 should be visited before node 23\nnode 8 should be visited before node 25\nnode 8 should be visited before node 21\nnode 8 should be visited before node 3\nnode 9 should be visited before node 22\nnode 9 should be visited before node 11\nnode 9 should be visited before node 13\nnode 9 should be visited before node 6\nnode 9 should be visited before node 15\nnode 9 should be visited before node 24\nnode 9 should be visited before node 4\nnode 9 should be visited before node 5\nnode 9 should be visited before node 20\nnode 9 should be visited before node 23\nnode 9 should be visited before node 10\nnode 9 should be visited before node 25\nnode 9 should be visited before node 21\nnode 9 should be visited before node 3\nnode 9 should be visited before node 1\nnode 10 should be visited before node 17\nnode 10 should be visited before node 21\nnode 10 should be visited before node 3\nnode 10 should be visited before node 1\nnode 11 should be visited before node 6\nnode 11 should be visited before node 15\nnode 11 should be visited before node 18\nnode 11 should be visited before node 7\nnode 11 should be visited before node 14\nnode 11 should be visited before node 24\nnode 11 should be visited before node 4\nnode 11 should be visited before node 19\nnode 11 should be visited before node 12\nnode 11 should be visited before node 10\nnode 11 should be visited before node 25\nnode 11 should be visited before node 16\nnode 11 should be visited before node 17\nnode 11 should be visited before node 21\nnode 11 should be visited before node 3\nnode 11 should be visited before node 1\nnode 12 should be visited before node 20\nnode 12 should be visited before node 10\nnode 12 should be visited before node 21\nnode 12 should be visited before node 3\nnode 13 should be visited before node 0\nnode 13 should be visited before node 12\nnode 13 should be visited before node 25\nnode 13 should be visited before node 16\nnode 13 should be visited before node 17\nnode 13 should be visited before node 21\nnode 13 should be visited before node 1\nnode 14 should be visited before node 24\nnode 14 should be visited before node 12\nnode 14 should be visited before node 20\nnode 14 should be visited before node 25\nnode 14 should be visited before node 16\nnode 14 should be visited before node 21\nnode 14 should be visited before node 1\nnode 15 should be visited before node 18\nnode 15 should be visited before node 7\nnode 15 should be visited before node 24\nnode 15 should be visited before node 4\nnode 15 should be visited before node 5\nnode 15 should be visited before node 12\nnode 15 should be visited before node 16\nnode 15 should be visited before node 17\nnode 15 should be visited before node 3\nnode 15 should be visited before node 1\nnode 16 should be visited before node 17\nnode 16 should be visited before node 21\nnode 18 should be visited before node 12\nnode 18 should be visited before node 20\nnode 18 should be visited before node 16\nnode 19 should be visited before node 20\nnode 19 should be visited before node 23\nnode 19 should be visited before node 10\nnode 19 should be visited before node 3\nnode 20 should be visited before node 17\nnode 20 should be visited before node 21\nnode 21 should be visited before node 1\nnode 22 should be visited before node 13\nnode 22 should be visited before node 2\nnode 22 should be visited before node 18\nnode 22 should be visited before node 14\nnode 22 should be visited before node 5\nnode 22 should be visited before node 19\nnode 22 should be visited before node 20\nnode 22 should be visited before node 10\nnode 22 should be visited before node 21\nnode 22 should be visited before node 3\nnode 23 should be visited before node 25\nnode 23 should be visited before node 16\nnode 23 should be visited before node 17\nnode 23 should be visited before node 21\nnode 24 should be visited before node 4\nnode 24 should be visited before node 19\nnode 24 should be visited before node 12\nnode 24 should be visited before node 23\nnode 24 should be visited before node 10\nnode 24 should be visited before node 25\nnode 24 should be visited before node 16\nnode 24 should be visited before node 17\nnode 24 should be visited before node 3\nnode 25 should be visited before node 16\nnode 25 should be visited before node 17\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 8,9,22,11,13,6,0,2,14,15,18,7,24,4,5,19,12,23,20,10,25,3,16,17,21,1.", "difficulty": "hard", "doc_id": "114"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 15 nodes numbered from 0 to 14:\nnode 0 should be visited before node 3\nnode 0 should be visited before node 8\nnode 0 should be visited before node 9\nnode 0 should be visited before node 6\nnode 1 should be visited before node 3\nnode 1 should be visited before node 8\nnode 1 should be visited before node 9\nnode 1 should be visited before node 6\nnode 2 should be visited before node 13\nnode 2 should be visited before node 12\nnode 2 should be visited before node 5\nnode 2 should be visited before node 11\nnode 2 should be visited before node 7\nnode 2 should be visited before node 3\nnode 2 should be visited before node 8\nnode 2 should be visited before node 6\nnode 3 should be visited before node 8\nnode 3 should be visited before node 9\nnode 3 should be visited before node 6\nnode 4 should be visited before node 2\nnode 4 should be visited before node 13\nnode 4 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 11\nnode 4 should be visited before node 7\nnode 4 should be visited before node 0\nnode 5 should be visited before node 1\nnode 5 should be visited before node 0\nnode 5 should be visited before node 3\nnode 5 should be visited before node 8\nnode 5 should be visited before node 6\nnode 7 should be visited before node 0\nnode 7 should be visited before node 3\nnode 7 should be visited before node 8\nnode 7 should be visited before node 9\nnode 8 should be visited before node 9\nnode 9 should be visited before node 6\nnode 10 should be visited before node 14\nnode 10 should be visited before node 4\nnode 10 should be visited before node 13\nnode 10 should be visited before node 12\nnode 10 should be visited before node 11\nnode 10 should be visited before node 7\nnode 10 should be visited before node 0\nnode 10 should be visited before node 3\nnode 11 should be visited before node 3\nnode 11 should be visited before node 8\nnode 11 should be visited before node 9\nnode 11 should be visited before node 6\nnode 12 should be visited before node 5\nnode 12 should be visited before node 0\nnode 12 should be visited before node 3\nnode 12 should be visited before node 8\nnode 12 should be visited before node 9\nnode 12 should be visited before node 6\nnode 13 should be visited before node 12\nnode 13 should be visited before node 5\nnode 13 should be visited before node 1\nnode 13 should be visited before node 11\nnode 13 should be visited before node 7\nnode 13 should be visited before node 0\nnode 13 should be visited before node 6\nnode 14 should be visited before node 2\nnode 14 should be visited before node 13\nnode 14 should be visited before node 12\nnode 14 should be visited before node 1\nnode 14 should be visited before node 11\nnode 14 should be visited before node 7\nnode 14 should be visited before node 0\nnode 14 should be visited before node 9\nnode 14 should be visited before node 6\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 10,14,4,2,13,12,11,7,5,1,0,3,8,9,6.", "difficulty": "medium", "doc_id": "115"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 0 should be visited before node 2\nnode 0 should be visited before node 3\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 5\nnode 2 should be visited before node 5\nnode 3 should be visited before node 5\nnode 4 should be visited before node 6\nnode 4 should be visited before node 1\nnode 6 should be visited before node 1\nnode 6 should be visited before node 2\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 0,4,6,1,3,2,5.", "difficulty": "easy", "doc_id": "116"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 11 nodes numbered from 0 to 10:\nnode 0 should be visited before node 1\nnode 0 should be visited before node 3\nnode 1 should be visited before node 9\nnode 2 should be visited before node 4\nnode 2 should be visited before node 0\nnode 2 should be visited before node 8\nnode 2 should be visited before node 5\nnode 2 should be visited before node 9\nnode 2 should be visited before node 6\nnode 4 should be visited before node 0\nnode 4 should be visited before node 10\nnode 4 should be visited before node 1\nnode 5 should be visited before node 1\nnode 5 should be visited before node 9\nnode 5 should be visited before node 6\nnode 7 should be visited before node 0\nnode 7 should be visited before node 10\nnode 7 should be visited before node 8\nnode 7 should be visited before node 5\nnode 7 should be visited before node 3\nnode 8 should be visited before node 5\nnode 8 should be visited before node 9\nnode 8 should be visited before node 6\nnode 8 should be visited before node 3\nnode 9 should be visited before node 6\nnode 10 should be visited before node 9\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 2,7,4,8,0,10,5,3,1,9,6.", "difficulty": "medium", "doc_id": "117"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 24 nodes numbered from 0 to 23:\nnode 1 should be visited before node 15\nnode 1 should be visited before node 4\nnode 1 should be visited before node 23\nnode 2 should be visited before node 19\nnode 2 should be visited before node 0\nnode 3 should be visited before node 9\nnode 3 should be visited before node 20\nnode 3 should be visited before node 22\nnode 3 should be visited before node 16\nnode 3 should be visited before node 7\nnode 3 should be visited before node 18\nnode 3 should be visited before node 4\nnode 4 should be visited before node 23\nnode 4 should be visited before node 6\nnode 5 should be visited before node 13\nnode 5 should be visited before node 9\nnode 5 should be visited before node 20\nnode 5 should be visited before node 16\nnode 5 should be visited before node 17\nnode 5 should be visited before node 7\nnode 5 should be visited before node 18\nnode 6 should be visited before node 0\nnode 7 should be visited before node 11\nnode 7 should be visited before node 0\nnode 8 should be visited before node 21\nnode 8 should be visited before node 22\nnode 8 should be visited before node 11\nnode 8 should be visited before node 4\nnode 8 should be visited before node 6\nnode 9 should be visited before node 20\nnode 9 should be visited before node 16\nnode 9 should be visited before node 1\nnode 9 should be visited before node 17\nnode 9 should be visited before node 11\nnode 9 should be visited before node 10\nnode 9 should be visited before node 15\nnode 9 should be visited before node 23\nnode 10 should be visited before node 18\nnode 10 should be visited before node 19\nnode 10 should be visited before node 23\nnode 11 should be visited before node 15\nnode 11 should be visited before node 23\nnode 12 should be visited before node 2\nnode 12 should be visited before node 15\nnode 12 should be visited before node 4\nnode 13 should be visited before node 8\nnode 13 should be visited before node 14\nnode 13 should be visited before node 9\nnode 13 should be visited before node 1\nnode 13 should be visited before node 12\nnode 13 should be visited before node 11\nnode 13 should be visited before node 4\nnode 13 should be visited before node 19\nnode 13 should be visited before node 6\nnode 14 should be visited before node 9\nnode 14 should be visited before node 16\nnode 14 should be visited before node 11\nnode 14 should be visited before node 10\nnode 14 should be visited before node 2\nnode 14 should be visited before node 18\nnode 14 should be visited before node 15\nnode 14 should be visited before node 6\nnode 14 should be visited before node 0\nnode 15 should be visited before node 6\nnode 16 should be visited before node 11\nnode 16 should be visited before node 2\nnode 16 should be visited before node 18\nnode 16 should be visited before node 4\nnode 17 should be visited before node 11\nnode 17 should be visited before node 23\nnode 18 should be visited before node 23\nnode 18 should be visited before node 6\nnode 19 should be visited before node 6\nnode 19 should be visited before node 0\nnode 20 should be visited before node 22\nnode 20 should be visited before node 2\nnode 20 should be visited before node 18\nnode 20 should be visited before node 23\nnode 21 should be visited before node 9\nnode 21 should be visited before node 20\nnode 21 should be visited before node 7\nnode 21 should be visited before node 12\nnode 21 should be visited before node 0\nnode 22 should be visited before node 1\nnode 22 should be visited before node 7\nnode 22 should be visited before node 18\nnode 22 should be visited before node 15\nnode 22 should be visited before node 4\nnode 22 should be visited before node 0\nnode 23 should be visited before node 6\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 3,5,13,8,14,21,9,12,20,16,17,10,22,2,1,7,18,19,4,11,15,23,6,0.", "difficulty": "medium", "doc_id": "118"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 1 should be visited before node 4\nnode 2 should be visited before node 4\nnode 2 should be visited before node 0\nnode 3 should be visited before node 2\nnode 3 should be visited before node 0\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 1,3,2,4,0.", "difficulty": "easy", "doc_id": "119"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 26 nodes numbered from 0 to 25:\nnode 0 should be visited before node 9\nnode 0 should be visited before node 8\nnode 1 should be visited before node 8\nnode 1 should be visited before node 15\nnode 2 should be visited before node 11\nnode 2 should be visited before node 0\nnode 2 should be visited before node 9\nnode 2 should be visited before node 24\nnode 2 should be visited before node 12\nnode 2 should be visited before node 15\nnode 2 should be visited before node 21\nnode 3 should be visited before node 22\nnode 3 should be visited before node 5\nnode 3 should be visited before node 7\nnode 3 should be visited before node 11\nnode 3 should be visited before node 20\nnode 3 should be visited before node 0\nnode 5 should be visited before node 0\nnode 5 should be visited before node 24\nnode 5 should be visited before node 19\nnode 6 should be visited before node 13\nnode 6 should be visited before node 7\nnode 6 should be visited before node 0\nnode 6 should be visited before node 4\nnode 6 should be visited before node 21\nnode 7 should be visited before node 25\nnode 7 should be visited before node 9\nnode 8 should be visited before node 15\nnode 8 should be visited before node 19\nnode 9 should be visited before node 17\nnode 9 should be visited before node 8\nnode 10 should be visited before node 24\nnode 10 should be visited before node 19\nnode 11 should be visited before node 24\nnode 11 should be visited before node 15\nnode 11 should be visited before node 19\nnode 12 should be visited before node 4\nnode 12 should be visited before node 19\nnode 13 should be visited before node 10\nnode 13 should be visited before node 17\nnode 13 should be visited before node 8\nnode 13 should be visited before node 4\nnode 13 should be visited before node 15\nnode 13 should be visited before node 19\nnode 14 should be visited before node 25\nnode 14 should be visited before node 0\nnode 14 should be visited before node 17\nnode 14 should be visited before node 12\nnode 15 should be visited before node 19\nnode 16 should be visited before node 1\nnode 16 should be visited before node 6\nnode 16 should be visited before node 2\nnode 16 should be visited before node 7\nnode 16 should be visited before node 14\nnode 16 should be visited before node 25\nnode 16 should be visited before node 9\nnode 16 should be visited before node 10\nnode 16 should be visited before node 24\nnode 16 should be visited before node 8\nnode 16 should be visited before node 4\nnode 16 should be visited before node 19\nnode 17 should be visited before node 15\nnode 17 should be visited before node 19\nnode 18 should be visited before node 11\nnode 18 should be visited before node 14\nnode 18 should be visited before node 17\nnode 18 should be visited before node 8\nnode 18 should be visited before node 19\nnode 20 should be visited before node 15\nnode 22 should be visited before node 6\nnode 22 should be visited before node 7\nnode 22 should be visited before node 11\nnode 22 should be visited before node 14\nnode 22 should be visited before node 25\nnode 22 should be visited before node 0\nnode 22 should be visited before node 17\nnode 22 should be visited before node 12\nnode 22 should be visited before node 19\nnode 23 should be visited before node 22\nnode 23 should be visited before node 13\nnode 23 should be visited before node 2\nnode 23 should be visited before node 7\nnode 23 should be visited before node 11\nnode 23 should be visited before node 25\nnode 23 should be visited before node 8\nnode 23 should be visited before node 19\nnode 24 should be visited before node 8\nnode 24 should be visited before node 4\nnode 24 should be visited before node 15\nnode 25 should be visited before node 4\nnode 25 should be visited before node 19\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 3,16,18,23,5,20,1,22,2,6,14,11,13,7,21,0,12,10,25,9,24,17,8,4,15,19.", "difficulty": "hard", "doc_id": "120"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 24 nodes numbered from 0 to 23:\nnode 0 should be visited before node 13\nnode 0 should be visited before node 5\nnode 0 should be visited before node 17\nnode 0 should be visited before node 22\nnode 0 should be visited before node 21\nnode 0 should be visited before node 15\nnode 0 should be visited before node 8\nnode 0 should be visited before node 9\nnode 0 should be visited before node 18\nnode 0 should be visited before node 1\nnode 0 should be visited before node 2\nnode 0 should be visited before node 10\nnode 0 should be visited before node 19\nnode 1 should be visited before node 4\nnode 1 should be visited before node 2\nnode 1 should be visited before node 12\nnode 1 should be visited before node 7\nnode 1 should be visited before node 10\nnode 1 should be visited before node 19\nnode 1 should be visited before node 20\nnode 1 should be visited before node 6\nnode 1 should be visited before node 23\nnode 2 should be visited before node 7\nnode 2 should be visited before node 10\nnode 2 should be visited before node 20\nnode 2 should be visited before node 6\nnode 2 should be visited before node 23\nnode 3 should be visited before node 15\nnode 3 should be visited before node 9\nnode 3 should be visited before node 18\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 3 should be visited before node 7\nnode 3 should be visited before node 10\nnode 3 should be visited before node 19\nnode 3 should be visited before node 20\nnode 3 should be visited before node 6\nnode 3 should be visited before node 23\nnode 4 should be visited before node 2\nnode 4 should be visited before node 12\nnode 4 should be visited before node 7\nnode 4 should be visited before node 10\nnode 4 should be visited before node 19\nnode 4 should be visited before node 20\nnode 4 should be visited before node 23\nnode 5 should be visited before node 17\nnode 5 should be visited before node 22\nnode 5 should be visited before node 21\nnode 5 should be visited before node 15\nnode 5 should be visited before node 8\nnode 5 should be visited before node 9\nnode 5 should be visited before node 4\nnode 5 should be visited before node 2\nnode 5 should be visited before node 12\nnode 5 should be visited before node 10\nnode 5 should be visited before node 19\nnode 5 should be visited before node 20\nnode 5 should be visited before node 6\nnode 5 should be visited before node 23\nnode 6 should be visited before node 23\nnode 7 should be visited before node 10\nnode 7 should be visited before node 19\nnode 7 should be visited before node 6\nnode 7 should be visited before node 23\nnode 8 should be visited before node 18\nnode 8 should be visited before node 1\nnode 8 should be visited before node 4\nnode 8 should be visited before node 2\nnode 8 should be visited before node 12\nnode 8 should be visited before node 7\nnode 8 should be visited before node 10\nnode 8 should be visited before node 19\nnode 8 should be visited before node 20\nnode 8 should be visited before node 6\nnode 8 should be visited before node 23\nnode 9 should be visited before node 18\nnode 9 should be visited before node 1\nnode 9 should be visited before node 4\nnode 9 should be visited before node 2\nnode 9 should be visited before node 12\nnode 9 should be visited before node 10\nnode 9 should be visited before node 19\nnode 9 should be visited before node 20\nnode 9 should be visited before node 6\nnode 10 should be visited before node 6\nnode 10 should be visited before node 23\nnode 11 should be visited before node 13\nnode 11 should be visited before node 17\nnode 11 should be visited before node 22\nnode 11 should be visited before node 21\nnode 11 should be visited before node 8\nnode 11 should be visited before node 9\nnode 11 should be visited before node 18\nnode 11 should be visited before node 2\nnode 11 should be visited before node 12\nnode 11 should be visited before node 7\nnode 11 should be visited before node 10\nnode 11 should be visited before node 19\nnode 11 should be visited before node 6\nnode 11 should be visited before node 23\nnode 12 should be visited before node 10\nnode 12 should be visited before node 19\nnode 12 should be visited before node 20\nnode 12 should be visited before node 6\nnode 12 should be visited before node 23\nnode 13 should be visited before node 5\nnode 13 should be visited before node 17\nnode 13 should be visited before node 21\nnode 13 should be visited before node 3\nnode 13 should be visited before node 15\nnode 13 should be visited before node 18\nnode 13 should be visited before node 2\nnode 13 should be visited before node 10\nnode 13 should be visited before node 19\nnode 13 should be visited before node 20\nnode 14 should be visited before node 5\nnode 14 should be visited before node 17\nnode 14 should be visited before node 22\nnode 14 should be visited before node 3\nnode 14 should be visited before node 15\nnode 14 should be visited before node 8\nnode 14 should be visited before node 9\nnode 14 should be visited before node 18\nnode 14 should be visited before node 4\nnode 14 should be visited before node 12\nnode 14 should be visited before node 7\nnode 14 should be visited before node 10\nnode 14 should be visited before node 19\nnode 14 should be visited before node 20\nnode 14 should be visited before node 6\nnode 14 should be visited before node 23\nnode 15 should be visited before node 9\nnode 15 should be visited before node 18\nnode 15 should be visited before node 1\nnode 15 should be visited before node 4\nnode 15 should be visited before node 2\nnode 15 should be visited before node 10\nnode 15 should be visited before node 19\nnode 15 should be visited before node 20\nnode 15 should be visited before node 6\nnode 15 should be visited before node 23\nnode 16 should be visited before node 11\nnode 16 should be visited before node 0\nnode 16 should be visited before node 14\nnode 16 should be visited before node 13\nnode 16 should be visited before node 5\nnode 16 should be visited before node 17\nnode 16 should be visited before node 22\nnode 16 should be visited before node 18\nnode 16 should be visited before node 1\nnode 16 should be visited before node 4\nnode 16 should be visited before node 2\nnode 16 should be visited before node 12\nnode 16 should be visited before node 7\nnode 16 should be visited before node 10\nnode 16 should be visited before node 19\nnode 16 should be visited before node 20\nnode 16 should be visited before node 6\nnode 16 should be visited before node 23\nnode 17 should be visited before node 22\nnode 17 should be visited before node 21\nnode 17 should be visited before node 3\nnode 17 should be visited before node 15\nnode 17 should be visited before node 9\nnode 17 should be visited before node 18\nnode 17 should be visited before node 1\nnode 17 should be visited before node 4\nnode 17 should be visited before node 2\nnode 17 should be visited before node 12\nnode 17 should be visited before node 10\nnode 17 should be visited before node 19\nnode 17 should be visited before node 20\nnode 17 should be visited before node 6\nnode 17 should be visited before node 23\nnode 18 should be visited before node 2\nnode 18 should be visited before node 12\nnode 18 should be visited before node 10\nnode 18 should be visited before node 19\nnode 18 should be visited before node 20\nnode 18 should be visited before node 6\nnode 18 should be visited before node 23\nnode 19 should be visited before node 20\nnode 19 should be visited before node 6\nnode 19 should be visited before node 23\nnode 20 should be visited before node 6\nnode 20 should be visited before node 23\nnode 21 should be visited before node 3\nnode 21 should be visited before node 8\nnode 21 should be visited before node 9\nnode 21 should be visited before node 18\nnode 21 should be visited before node 1\nnode 21 should be visited before node 4\nnode 21 should be visited before node 2\nnode 21 should be visited before node 10\nnode 21 should be visited before node 19\nnode 21 should be visited before node 20\nnode 21 should be visited before node 6\nnode 21 should be visited before node 23\nnode 22 should be visited before node 21\nnode 22 should be visited before node 3\nnode 22 should be visited before node 8\nnode 22 should be visited before node 9\nnode 22 should be visited before node 1\nnode 22 should be visited before node 4\nnode 22 should be visited before node 12\nnode 22 should be visited before node 10\nnode 22 should be visited before node 19\nnode 22 should be visited before node 20\nnode 22 should be visited before node 6\nnode 22 should be visited before node 23\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 16,11,0,14,13,5,17,22,21,3,8,15,9,18,1,4,2,12,7,10,19,20,6,23.", "difficulty": "medium", "doc_id": "121"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 1,4,3,2,0,5.", "difficulty": "easy", "doc_id": "122"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 13 nodes numbered from 0 to 12:\nnode 1 should be visited before node 4\nnode 1 should be visited before node 10\nnode 2 should be visited before node 12\nnode 3 should be visited before node 7\nnode 3 should be visited before node 4\nnode 3 should be visited before node 10\nnode 3 should be visited before node 12\nnode 5 should be visited before node 11\nnode 5 should be visited before node 4\nnode 6 should be visited before node 7\nnode 6 should be visited before node 10\nnode 7 should be visited before node 4\nnode 8 should be visited before node 11\nnode 8 should be visited before node 7\nnode 8 should be visited before node 4\nnode 8 should be visited before node 2\nnode 9 should be visited before node 8\nnode 9 should be visited before node 7\nnode 9 should be visited before node 10\nnode 9 should be visited before node 2\nnode 11 should be visited before node 10\nnode 11 should be visited before node 12\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 0,1,3,5,6,9,8,11,7,2,10,4,12.", "difficulty": "medium", "doc_id": "123"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 25 nodes numbered from 0 to 24:\nnode 0 should be visited before node 11\nnode 0 should be visited before node 19\nnode 0 should be visited before node 15\nnode 0 should be visited before node 3\nnode 0 should be visited before node 8\nnode 0 should be visited before node 14\nnode 0 should be visited before node 5\nnode 1 should be visited before node 6\nnode 1 should be visited before node 12\nnode 1 should be visited before node 0\nnode 1 should be visited before node 15\nnode 1 should be visited before node 23\nnode 1 should be visited before node 24\nnode 1 should be visited before node 4\nnode 1 should be visited before node 3\nnode 1 should be visited before node 10\nnode 1 should be visited before node 8\nnode 1 should be visited before node 21\nnode 2 should be visited before node 6\nnode 2 should be visited before node 11\nnode 2 should be visited before node 19\nnode 2 should be visited before node 15\nnode 2 should be visited before node 24\nnode 2 should be visited before node 9\nnode 2 should be visited before node 18\nnode 2 should be visited before node 3\nnode 2 should be visited before node 13\nnode 2 should be visited before node 14\nnode 2 should be visited before node 5\nnode 2 should be visited before node 21\nnode 2 should be visited before node 20\nnode 3 should be visited before node 17\nnode 3 should be visited before node 5\nnode 3 should be visited before node 16\nnode 3 should be visited before node 21\nnode 3 should be visited before node 20\nnode 4 should be visited before node 10\nnode 4 should be visited before node 8\nnode 4 should be visited before node 17\nnode 4 should be visited before node 5\nnode 4 should be visited before node 21\nnode 4 should be visited before node 20\nnode 5 should be visited before node 16\nnode 5 should be visited before node 21\nnode 5 should be visited before node 20\nnode 6 should be visited before node 11\nnode 6 should be visited before node 19\nnode 6 should be visited before node 23\nnode 6 should be visited before node 24\nnode 6 should be visited before node 3\nnode 6 should be visited before node 8\nnode 6 should be visited before node 14\nnode 6 should be visited before node 17\nnode 6 should be visited before node 16\nnode 7 should be visited before node 9\nnode 7 should be visited before node 4\nnode 7 should be visited before node 13\nnode 7 should be visited before node 14\nnode 7 should be visited before node 21\nnode 7 should be visited before node 20\nnode 8 should be visited before node 17\nnode 8 should be visited before node 16\nnode 9 should be visited before node 13\nnode 9 should be visited before node 17\nnode 9 should be visited before node 5\nnode 10 should be visited before node 8\nnode 10 should be visited before node 13\nnode 10 should be visited before node 14\nnode 10 should be visited before node 21\nnode 11 should be visited before node 19\nnode 11 should be visited before node 15\nnode 11 should be visited before node 24\nnode 11 should be visited before node 22\nnode 11 should be visited before node 9\nnode 11 should be visited before node 4\nnode 11 should be visited before node 10\nnode 11 should be visited before node 8\nnode 11 should be visited before node 13\nnode 11 should be visited before node 16\nnode 12 should be visited before node 24\nnode 12 should be visited before node 7\nnode 12 should be visited before node 9\nnode 12 should be visited before node 10\nnode 12 should be visited before node 8\nnode 12 should be visited before node 17\nnode 12 should be visited before node 5\nnode 12 should be visited before node 16\nnode 13 should be visited before node 17\nnode 13 should be visited before node 5\nnode 14 should be visited before node 17\nnode 14 should be visited before node 16\nnode 14 should be visited before node 21\nnode 14 should be visited before node 20\nnode 15 should be visited before node 23\nnode 15 should be visited before node 22\nnode 15 should be visited before node 9\nnode 15 should be visited before node 18\nnode 15 should be visited before node 10\nnode 15 should be visited before node 17\nnode 15 should be visited before node 5\nnode 15 should be visited before node 20\nnode 16 should be visited before node 20\nnode 17 should be visited before node 20\nnode 18 should be visited before node 4\nnode 18 should be visited before node 8\nnode 18 should be visited before node 13\nnode 18 should be visited before node 14\nnode 18 should be visited before node 5\nnode 18 should be visited before node 16\nnode 18 should be visited before node 20\nnode 19 should be visited before node 24\nnode 19 should be visited before node 22\nnode 19 should be visited before node 9\nnode 19 should be visited before node 18\nnode 19 should be visited before node 3\nnode 19 should be visited before node 5\nnode 19 should be visited before node 16\nnode 19 should be visited before node 20\nnode 21 should be visited before node 20\nnode 22 should be visited before node 7\nnode 22 should be visited before node 4\nnode 22 should be visited before node 3\nnode 22 should be visited before node 10\nnode 22 should be visited before node 8\nnode 22 should be visited before node 14\nnode 22 should be visited before node 5\nnode 22 should be visited before node 20\nnode 23 should be visited before node 7\nnode 23 should be visited before node 18\nnode 23 should be visited before node 4\nnode 23 should be visited before node 3\nnode 23 should be visited before node 10\nnode 23 should be visited before node 13\nnode 23 should be visited before node 17\nnode 23 should be visited before node 5\nnode 23 should be visited before node 21\nnode 23 should be visited before node 20\nnode 24 should be visited before node 7\nnode 24 should be visited before node 18\nnode 24 should be visited before node 4\nnode 24 should be visited before node 13\nnode 24 should be visited before node 14\nnode 24 should be visited before node 17\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 1,2,12,0,6,11,19,15,24,23,22,18,7,3,9,4,10,8,13,14,5,17,16,21,20.", "difficulty": "medium", "doc_id": "124"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 25 nodes numbered from 0 to 24:\nnode 1 should be visited before node 10\nnode 1 should be visited before node 3\nnode 1 should be visited before node 20\nnode 1 should be visited before node 16\nnode 1 should be visited before node 4\nnode 1 should be visited before node 22\nnode 1 should be visited before node 6\nnode 1 should be visited before node 0\nnode 1 should be visited before node 5\nnode 1 should be visited before node 18\nnode 2 should be visited before node 9\nnode 2 should be visited before node 14\nnode 3 should be visited before node 8\nnode 3 should be visited before node 4\nnode 3 should be visited before node 2\nnode 3 should be visited before node 9\nnode 3 should be visited before node 14\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 2\nnode 4 should be visited before node 9\nnode 4 should be visited before node 11\nnode 4 should be visited before node 6\nnode 6 should be visited before node 0\nnode 6 should be visited before node 5\nnode 6 should be visited before node 18\nnode 7 should be visited before node 3\nnode 7 should be visited before node 16\nnode 7 should be visited before node 4\nnode 7 should be visited before node 22\nnode 7 should be visited before node 6\nnode 7 should be visited before node 5\nnode 8 should be visited before node 16\nnode 8 should be visited before node 4\nnode 8 should be visited before node 13\nnode 8 should be visited before node 2\nnode 8 should be visited before node 22\nnode 8 should be visited before node 9\nnode 8 should be visited before node 6\nnode 8 should be visited before node 18\nnode 9 should be visited before node 18\nnode 10 should be visited before node 7\nnode 10 should be visited before node 20\nnode 10 should be visited before node 4\nnode 10 should be visited before node 13\nnode 10 should be visited before node 2\nnode 10 should be visited before node 22\nnode 10 should be visited before node 14\nnode 10 should be visited before node 6\nnode 10 should be visited before node 0\nnode 10 should be visited before node 5\nnode 11 should be visited before node 5\nnode 12 should be visited before node 23\nnode 12 should be visited before node 24\nnode 12 should be visited before node 10\nnode 12 should be visited before node 21\nnode 12 should be visited before node 19\nnode 12 should be visited before node 7\nnode 12 should be visited before node 20\nnode 12 should be visited before node 9\nnode 12 should be visited before node 11\nnode 12 should be visited before node 18\nnode 13 should be visited before node 2\nnode 13 should be visited before node 9\nnode 13 should be visited before node 6\nnode 13 should be visited before node 0\nnode 13 should be visited before node 5\nnode 13 should be visited before node 18\nnode 14 should be visited before node 18\nnode 15 should be visited before node 12\nnode 15 should be visited before node 23\nnode 15 should be visited before node 1\nnode 15 should be visited before node 10\nnode 15 should be visited before node 17\nnode 15 should be visited before node 21\nnode 15 should be visited before node 19\nnode 15 should be visited before node 8\nnode 15 should be visited before node 13\nnode 15 should be visited before node 2\nnode 15 should be visited before node 9\nnode 15 should be visited before node 14\nnode 15 should be visited before node 18\nnode 16 should be visited before node 4\nnode 16 should be visited before node 13\nnode 16 should be visited before node 2\nnode 16 should be visited before node 22\nnode 16 should be visited before node 9\nnode 16 should be visited before node 18\nnode 17 should be visited before node 21\nnode 17 should be visited before node 19\nnode 17 should be visited before node 8\nnode 17 should be visited before node 4\nnode 17 should be visited before node 14\nnode 17 should be visited before node 6\nnode 19 should be visited before node 3\nnode 19 should be visited before node 8\nnode 19 should be visited before node 13\nnode 19 should be visited before node 2\nnode 19 should be visited before node 22\nnode 19 should be visited before node 14\nnode 19 should be visited before node 11\nnode 19 should be visited before node 5\nnode 19 should be visited before node 18\nnode 20 should be visited before node 9\nnode 20 should be visited before node 5\nnode 20 should be visited before node 18\nnode 21 should be visited before node 7\nnode 21 should be visited before node 3\nnode 21 should be visited before node 8\nnode 21 should be visited before node 20\nnode 21 should be visited before node 4\nnode 21 should be visited before node 2\nnode 21 should be visited before node 9\nnode 21 should be visited before node 6\nnode 21 should be visited before node 0\nnode 21 should be visited before node 5\nnode 22 should be visited before node 14\nnode 22 should be visited before node 5\nnode 23 should be visited before node 1\nnode 23 should be visited before node 24\nnode 23 should be visited before node 10\nnode 23 should be visited before node 19\nnode 23 should be visited before node 7\nnode 23 should be visited before node 3\nnode 23 should be visited before node 8\nnode 23 should be visited before node 20\nnode 23 should be visited before node 13\nnode 23 should be visited before node 2\nnode 23 should be visited before node 14\nnode 23 should be visited before node 11\nnode 23 should be visited before node 5\nnode 24 should be visited before node 10\nnode 24 should be visited before node 17\nnode 24 should be visited before node 3\nnode 24 should be visited before node 8\nnode 24 should be visited before node 20\nnode 24 should be visited before node 16\nnode 24 should be visited before node 13\nnode 24 should be visited before node 14\nnode 24 should be visited before node 11\nnode 24 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 15,12,23,1,24,10,17,21,19,7,20,3,8,16,4,13,22,11,2,6,9,14,0,5,18.", "difficulty": "medium", "doc_id": "125"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 16 nodes numbered from 0 to 15:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 2\nnode 0 should be visited before node 14\nnode 0 should be visited before node 15\nnode 0 should be visited before node 10\nnode 0 should be visited before node 9\nnode 0 should be visited before node 13\nnode 0 should be visited before node 8\nnode 0 should be visited before node 1\nnode 0 should be visited before node 12\nnode 1 should be visited before node 12\nnode 2 should be visited before node 5\nnode 2 should be visited before node 10\nnode 2 should be visited before node 9\nnode 2 should be visited before node 8\nnode 2 should be visited before node 1\nnode 2 should be visited before node 12\nnode 3 should be visited before node 2\nnode 3 should be visited before node 14\nnode 3 should be visited before node 9\nnode 3 should be visited before node 6\nnode 3 should be visited before node 13\nnode 3 should be visited before node 8\nnode 3 should be visited before node 1\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 14\nnode 4 should be visited before node 5\nnode 4 should be visited before node 15\nnode 4 should be visited before node 10\nnode 4 should be visited before node 9\nnode 4 should be visited before node 13\nnode 4 should be visited before node 8\nnode 4 should be visited before node 1\nnode 4 should be visited before node 12\nnode 5 should be visited before node 10\nnode 5 should be visited before node 9\nnode 5 should be visited before node 6\nnode 5 should be visited before node 13\nnode 5 should be visited before node 12\nnode 6 should be visited before node 13\nnode 6 should be visited before node 8\nnode 6 should be visited before node 12\nnode 7 should be visited before node 11\nnode 7 should be visited before node 0\nnode 7 should be visited before node 4\nnode 7 should be visited before node 3\nnode 7 should be visited before node 14\nnode 7 should be visited before node 5\nnode 7 should be visited before node 10\nnode 7 should be visited before node 9\nnode 7 should be visited before node 6\nnode 7 should be visited before node 8\nnode 7 should be visited before node 12\nnode 8 should be visited before node 1\nnode 8 should be visited before node 12\nnode 9 should be visited before node 6\nnode 9 should be visited before node 13\nnode 9 should be visited before node 8\nnode 9 should be visited before node 1\nnode 9 should be visited before node 12\nnode 10 should be visited before node 9\nnode 10 should be visited before node 6\nnode 10 should be visited before node 8\nnode 10 should be visited before node 1\nnode 11 should be visited before node 0\nnode 11 should be visited before node 2\nnode 11 should be visited before node 14\nnode 11 should be visited before node 5\nnode 11 should be visited before node 15\nnode 11 should be visited before node 10\nnode 11 should be visited before node 9\nnode 11 should be visited before node 13\nnode 11 should be visited before node 8\nnode 11 should be visited before node 1\nnode 11 should be visited before node 12\nnode 13 should be visited before node 8\nnode 13 should be visited before node 12\nnode 14 should be visited before node 5\nnode 14 should be visited before node 10\nnode 14 should be visited before node 6\nnode 14 should be visited before node 8\nnode 14 should be visited before node 1\nnode 14 should be visited before node 12\nnode 15 should be visited before node 9\nnode 15 should be visited before node 6\nnode 15 should be visited before node 13\nnode 15 should be visited before node 8\nnode 15 should be visited before node 1\nnode 15 should be visited before node 12\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 7,11,0,4,3,15,2,14,5,10,9,6,13,8,1,12.", "difficulty": "medium", "doc_id": "126"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 12 nodes numbered from 0 to 11:\nnode 0 should be visited before node 3\nnode 0 should be visited before node 9\nnode 2 should be visited before node 3\nnode 2 should be visited before node 9\nnode 4 should be visited before node 10\nnode 4 should be visited before node 11\nnode 4 should be visited before node 1\nnode 4 should be visited before node 8\nnode 5 should be visited before node 11\nnode 5 should be visited before node 1\nnode 5 should be visited before node 0\nnode 5 should be visited before node 2\nnode 5 should be visited before node 9\nnode 6 should be visited before node 7\nnode 6 should be visited before node 1\nnode 6 should be visited before node 0\nnode 6 should be visited before node 8\nnode 6 should be visited before node 2\nnode 6 should be visited before node 9\nnode 7 should be visited before node 10\nnode 7 should be visited before node 11\nnode 7 should be visited before node 1\nnode 7 should be visited before node 2\nnode 7 should be visited before node 3\nnode 10 should be visited before node 11\nnode 10 should be visited before node 1\nnode 10 should be visited before node 0\nnode 10 should be visited before node 3\nnode 10 should be visited before node 9\nnode 11 should be visited before node 1\nnode 11 should be visited before node 0\nnode 11 should be visited before node 9\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 4,5,6,7,8,10,2,11,1,0,3,9.", "difficulty": "medium", "doc_id": "127"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 12 nodes numbered from 0 to 11:\nnode 0 should be visited before node 9\nnode 0 should be visited before node 5\nnode 0 should be visited before node 4\nnode 0 should be visited before node 6\nnode 0 should be visited before node 10\nnode 1 should be visited before node 0\nnode 1 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 4\nnode 1 should be visited before node 6\nnode 1 should be visited before node 10\nnode 2 should be visited before node 4\nnode 2 should be visited before node 6\nnode 2 should be visited before node 11\nnode 2 should be visited before node 10\nnode 2 should be visited before node 8\nnode 3 should be visited before node 1\nnode 3 should be visited before node 7\nnode 3 should be visited before node 0\nnode 3 should be visited before node 9\nnode 3 should be visited before node 5\nnode 3 should be visited before node 2\nnode 3 should be visited before node 6\nnode 3 should be visited before node 11\nnode 3 should be visited before node 10\nnode 3 should be visited before node 8\nnode 4 should be visited before node 6\nnode 4 should be visited before node 11\nnode 4 should be visited before node 8\nnode 5 should be visited before node 2\nnode 5 should be visited before node 4\nnode 5 should be visited before node 6\nnode 5 should be visited before node 11\nnode 5 should be visited before node 10\nnode 5 should be visited before node 8\nnode 6 should be visited before node 11\nnode 6 should be visited before node 10\nnode 6 should be visited before node 8\nnode 7 should be visited before node 0\nnode 7 should be visited before node 9\nnode 7 should be visited before node 5\nnode 7 should be visited before node 2\nnode 7 should be visited before node 4\nnode 7 should be visited before node 6\nnode 7 should be visited before node 11\nnode 7 should be visited before node 10\nnode 7 should be visited before node 8\nnode 9 should be visited before node 2\nnode 9 should be visited before node 4\nnode 9 should be visited before node 6\nnode 9 should be visited before node 11\nnode 9 should be visited before node 8\nnode 10 should be visited before node 8\nnode 11 should be visited before node 8\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 3,1,7,0,9,5,2,4,6,11,10,8.", "difficulty": "medium", "doc_id": "128"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 9 nodes numbered from 0 to 8:\nnode 0 should be visited before node 2\nnode 0 should be visited before node 6\nnode 0 should be visited before node 3\nnode 1 should be visited before node 3\nnode 4 should be visited before node 8\nnode 4 should be visited before node 5\nnode 6 should be visited before node 8\nnode 6 should be visited before node 5\nnode 7 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 0,1,4,7,2,6,3,8,5.", "difficulty": "easy", "doc_id": "129"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 8 nodes numbered from 0 to 7:\nnode 0 should be visited before node 4\nnode 1 should be visited before node 4\nnode 2 should be visited before node 1\nnode 2 should be visited before node 6\nnode 2 should be visited before node 7\nnode 3 should be visited before node 1\nnode 3 should be visited before node 4\nnode 3 should be visited before node 5\nnode 4 should be visited before node 5\nnode 4 should be visited before node 7\nnode 5 should be visited before node 7\nnode 6 should be visited before node 0\nnode 6 should be visited before node 7\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 2,3,6,1,0,4,5,7.", "difficulty": "easy", "doc_id": "130"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 1 should be visited before node 6\nnode 1 should be visited before node 4\nnode 3 should be visited before node 1\nnode 5 should be visited before node 4\nnode 5 should be visited before node 2\nnode 6 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 0,3,5,1,6,4,2.", "difficulty": "easy", "doc_id": "131"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 11 nodes numbered from 0 to 10:\nnode 0 should be visited before node 2\nnode 0 should be visited before node 6\nnode 0 should be visited before node 10\nnode 0 should be visited before node 5\nnode 0 should be visited before node 8\nnode 1 should be visited before node 9\nnode 1 should be visited before node 0\nnode 1 should be visited before node 7\nnode 1 should be visited before node 10\nnode 1 should be visited before node 8\nnode 2 should be visited before node 6\nnode 2 should be visited before node 5\nnode 3 should be visited before node 1\nnode 3 should be visited before node 4\nnode 3 should be visited before node 7\nnode 3 should be visited before node 2\nnode 3 should be visited before node 5\nnode 4 should be visited before node 0\nnode 4 should be visited before node 2\nnode 4 should be visited before node 6\nnode 4 should be visited before node 5\nnode 5 should be visited before node 8\nnode 6 should be visited before node 10\nnode 6 should be visited before node 5\nnode 6 should be visited before node 8\nnode 7 should be visited before node 2\nnode 7 should be visited before node 6\nnode 7 should be visited before node 5\nnode 9 should be visited before node 4\nnode 9 should be visited before node 7\nnode 9 should be visited before node 6\nnode 10 should be visited before node 8\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 3,1,9,4,7,0,2,6,10,5,8.", "difficulty": "medium", "doc_id": "132"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 13 nodes numbered from 0 to 12:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 5\nnode 3 should be visited before node 9\nnode 3 should be visited before node 0\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 7\nnode 4 should be visited before node 2\nnode 5 should be visited before node 11\nnode 5 should be visited before node 9\nnode 5 should be visited before node 8\nnode 5 should be visited before node 6\nnode 5 should be visited before node 7\nnode 5 should be visited before node 2\nnode 6 should be visited before node 1\nnode 8 should be visited before node 2\nnode 9 should be visited before node 6\nnode 9 should be visited before node 7\nnode 9 should be visited before node 2\nnode 10 should be visited before node 12\nnode 10 should be visited before node 3\nnode 10 should be visited before node 11\nnode 10 should be visited before node 0\nnode 10 should be visited before node 6\nnode 10 should be visited before node 1\nnode 10 should be visited before node 7\nnode 11 should be visited before node 9\nnode 11 should be visited before node 0\nnode 11 should be visited before node 6\nnode 11 should be visited before node 1\nnode 11 should be visited before node 7\nnode 11 should be visited before node 2\nnode 12 should be visited before node 4\nnode 12 should be visited before node 5\nnode 12 should be visited before node 9\nnode 12 should be visited before node 0\nnode 12 should be visited before node 6\nnode 12 should be visited before node 1\nnode 12 should be visited before node 7\nnode 12 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 10,12,3,4,5,11,8,9,0,6,7,1,2.", "difficulty": "medium", "doc_id": "133"}
{"question": "In a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 1\nnode 2 should be visited before node 1\nnode 3 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.\nSince visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.\nSince visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.\nSince visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.\n\nIn a directed graph with 5 nodes numbered from 0 to 4:\nnode 0 should be visited before node 1\nnode 1 should be visited before node 2\nnode 3 should be visited before node 1\nnode 3 should be visited before node 2\nnode 4 should be visited before node 3\nnode 4 should be visited before node 0\nnode 4 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 4, node 4 can be visited first.\nSince visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.\nSince visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 3\nnode 1 should be visited before node 2\nnode 3 should be visited before node 2\nnode 4 should be visited before node 1\nnode 4 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 2\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.\nSince visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.\nSince visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.\nSince visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.\n\nIn a directed graph with 6 nodes numbered from 0 to 5:\nnode 0 should be visited before node 5\nnode 1 should be visited before node 2\nnode 1 should be visited before node 0\nnode 3 should be visited before node 0\nnode 3 should be visited before node 5\nnode 4 should be visited before node 3\nnode 4 should be visited before node 2\nnode 4 should be visited before node 0\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.\nSince visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.\nSince visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.\nSince visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.\nSince visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.\n\nIn a directed graph with 7 nodes numbered from 0 to 6:\nnode 0 should be visited before node 6\nnode 2 should be visited before node 0\nnode 2 should be visited before node 5\nnode 4 should be visited before node 1\nnode 4 should be visited before node 3\nnode 6 should be visited before node 3\nnode 6 should be visited before node 5\nQ: Can all the nodes be visited? Give the solution.\nA: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.\nSince visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.\nSince visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.\nSince visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.\nSince visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.\nSince visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.\n\nIn a directed graph with 28 nodes numbered from 0 to 27:\nnode 0 should be visited before node 4\nnode 0 should be visited before node 21\nnode 0 should be visited before node 3\nnode 0 should be visited before node 6\nnode 0 should be visited before node 19\nnode 1 should be visited before node 26\nnode 2 should be visited before node 1\nnode 3 should be visited before node 5\nnode 3 should be visited before node 8\nnode 4 should be visited before node 3\nnode 4 should be visited before node 9\nnode 4 should be visited before node 22\nnode 4 should be visited before node 19\nnode 5 should be visited before node 22\nnode 5 should be visited before node 17\nnode 5 should be visited before node 2\nnode 5 should be visited before node 1\nnode 5 should be visited before node 8\nnode 5 should be visited before node 26\nnode 6 should be visited before node 24\nnode 6 should be visited before node 19\nnode 6 should be visited before node 8\nnode 7 should be visited before node 27\nnode 7 should be visited before node 0\nnode 7 should be visited before node 4\nnode 7 should be visited before node 18\nnode 7 should be visited before node 3\nnode 7 should be visited before node 9\nnode 7 should be visited before node 5\nnode 7 should be visited before node 22\nnode 7 should be visited before node 24\nnode 7 should be visited before node 8\nnode 9 should be visited before node 24\nnode 9 should be visited before node 8\nnode 10 should be visited before node 12\nnode 10 should be visited before node 9\nnode 10 should be visited before node 6\nnode 10 should be visited before node 2\nnode 10 should be visited before node 26\nnode 11 should be visited before node 6\nnode 11 should be visited before node 24\nnode 11 should be visited before node 17\nnode 11 should be visited before node 26\nnode 12 should be visited before node 14\nnode 12 should be visited before node 11\nnode 12 should be visited before node 5\nnode 12 should be visited before node 2\nnode 13 should be visited before node 18\nnode 13 should be visited before node 14\nnode 13 should be visited before node 5\nnode 13 should be visited before node 19\nnode 13 should be visited before node 1\nnode 14 should be visited before node 22\nnode 14 should be visited before node 24\nnode 14 should be visited before node 19\nnode 14 should be visited before node 17\nnode 14 should be visited before node 1\nnode 15 should be visited before node 13\nnode 15 should be visited before node 18\nnode 15 should be visited before node 12\nnode 15 should be visited before node 19\nnode 15 should be visited before node 1\nnode 17 should be visited before node 2\nnode 17 should be visited before node 1\nnode 18 should be visited before node 12\nnode 18 should be visited before node 3\nnode 18 should be visited before node 11\nnode 18 should be visited before node 19\nnode 18 should be visited before node 1\nnode 20 should be visited before node 15\nnode 20 should be visited before node 10\nnode 20 should be visited before node 12\nnode 20 should be visited before node 16\nnode 20 should be visited before node 22\nnode 20 should be visited before node 17\nnode 20 should be visited before node 2\nnode 21 should be visited before node 3\nnode 21 should be visited before node 16\nnode 21 should be visited before node 1\nnode 21 should be visited before node 8\nnode 22 should be visited before node 8\nnode 23 should be visited before node 18\nnode 23 should be visited before node 21\nnode 23 should be visited before node 17\nnode 23 should be visited before node 8\nnode 24 should be visited before node 17\nnode 24 should be visited before node 8\nnode 25 should be visited before node 13\nnode 25 should be visited before node 12\nnode 25 should be visited before node 14\nnode 25 should be visited before node 16\nnode 25 should be visited before node 5\nnode 25 should be visited before node 22\nnode 25 should be visited before node 6\nnode 25 should be visited before node 2\nnode 25 should be visited before node 1\nnode 27 should be visited before node 15\nnode 27 should be visited before node 0\nnode 27 should be visited before node 14\nnode 27 should be visited before node 22\nnode 27 should be visited before node 1\nQ: Can all the nodes be visited? Give the solution.\nA:", "answer": "The solution is: 7,20,23,25,27,10,15,0,13,4,21,18,9,16,12,3,14,11,5,6,22,24,19,17,8,2,1,26.", "difficulty": "hard", "doc_id": "134"}