lcb-0072

[
  {
    "total": 3,
    "answer": "```python\nimport sys\nfrom collections import defaultdict\n\ndef find_odd_cycle(u, parent, graph, visited):\n    visited[u] = True\n    for v in graph[u]:\n        if not visited[v]:\n            if find_odd_cycle(v, u, graph, visited):\n                return True\n        elif v != parent:\n            return True\n    return False\n\ndef solve(N, M, edges):\n    graph = defaultdict(list)\n    for u, v in edges:\n        graph[u].append(v)\n        graph[v].append(u)\n\n    odd_cycle_exists = False\n    for u in range(1, N + 1):\n        if not visited[u]:\n            if find_odd_cycle(u, -1, graph, [False] * (N + 1)):\n                odd_cycle_exists = True\n                break\n\n    if odd_cycle_exists:\n        return \"Takahashi\"\n    else:\n        return \"Aoki\"\n\ndef main():\n    input_data = sys.stdin.read().splitlines()\n    N, M = map(int, input_data[0].split())\n    edges = [tuple(map(int, line.split())) for line in input_data[1:M+1]]\n    result = solve(N, M, edges)\n    print(result)\n\nif __name__ == \"__main__\":\n    main()\n```",
    "passed": 0,
    "test_error": "Error: runtime error: Traceback (most recent call last):\nE           File \"/tmp/llmlab-lcb-0072-nal69m17/solution.py\", line 40, in <module>\nE             main()\nE           File \"/tmp/llmlab-lcb-0072-nal69m17/solution.py\", line 36, in main\nE             result = solve(N, M, edges)\nE                      ^^^^^^^^^^^^^^^^^^\nE           File \"/tmp/llmlab-lcb-0072-nal69m17/solution.py\", line 22, in solve\nE             if not visited[u]:\nE                    ^^^^^^^\nE         NameError: name 'visited' is not defined\nE         \nE       assert 1 == 0\nE        +  where 1 = CompletedProcess(args=['/home/psc/miniconda3/bin/python', '/tmp/llmlab-lcb-0072-nal69m17/solution.py'], returncode=1, ...tion.py\", line 22, in solve\\n    if not visited[u]:\\n           ^^^^^^^\\nNameError: name \\'visited\\' is not defined\\n').returncode\n\ntest_lcb_0072.py:19: AssertionError\n_______________________________ test_lcb_0072[2] _______________________________\n\ni = 2\n\n    @pytest.mark.parametrize(\"i\", range(len(_CASES)))\n    def test_lcb_0072(i):\n        c = _CASES[i]\n        p = subprocess.run([sys.executable, str(_D / \"solution.py\")],\n                           input=c[\"input\"], capture_output=True, text=True, timeout=15)\n>       assert p.returncode == 0, f\"runtime error: {p.stderr[-800:]}\"\nE       AssertionError: runtime error: Traceback (most recent call last):\nE           File \"/tmp/llmlab-lcb-0072-nal69m17/solution.py\", line 40, in <module>\nE             main()\nE           File \"/tmp/llmlab-lcb-0072-nal69m17/solution.py\", line 36, in main\nE             result = solve(N, M, edges)\nE                      ^^^^^^^^^^^^^^^^^^\nE           File \"/tmp/llmlab-lcb-0072-nal69m17/solution.py\", line 22, in solve\nE             if not visited[u]:\nE                    ^^^^^^^\nE         NameError: name 'visited' is not defined\nE         \nE       assert 1 == 0\nE        +  where 1 = CompletedProcess(args=['/home/psc/miniconda3/bin/python', '/tmp/llmlab-lcb-0072-nal69m17/solution.py'], returncode=1, ...tion.py\", line 22, in solve\\n    if not visited[u]:\\n           ^^^^^^^\\nNameError: name \\'visited\\' is not defined\\n').returncode\n\ntest_lcb_0072.py:19: AssertionError\n=========================== short test summary info ============================\nFAILED test_lcb_0072.py::test_lcb_0072[0] - AssertionError: runtime error: Tr...\nFAILED test_lcb_0072.py::test_lcb_0072[1] - AssertionError: runtime error: Tr...\nFAILED test_lcb_0072.py::test_lcb_0072[2] - AssertionError: runtime error: Tr...\n3 failed in 0.05s"
  },
  {
    "total": 3,
    "answer": "```python\nimport sys\nfrom collections import defaultdict\n\ndef find_odd_cycle(u, parent, graph, visited):\n    visited[u] = True\n    for v in graph[u]:\n        if not visited[v]:\n            if find_odd_cycle(v, u, graph, visited):\n                return True\n        elif v != parent:\n            return True\n    return False\n\ndef solve(N, M, edges):\n    graph = defaultdict(list)\n    for u, v in edges:\n        graph[u].append(v)\n        graph[v].append(u)\n\n    odd_cycle_exists = False\n    visited = [False] * (N + 1)\n    for u in range(1, N + 1):\n        if not visited[u]:\n            if find_odd_cycle(u, -1, graph, visited):\n                odd_cycle_exists = True\n                break\n\n    if odd_cycle_exists:\n        return \"Takahashi\"\n    else:\n        return \"Aoki\"\n\ndef main():\n    input_data = sys.stdin.read().splitlines()\n    N, M = map(int, input_data[0].split())\n    edges = [tuple(map(int, line.split())) for line in input_data[1:M+1]]\n    result = solve(N, M, edges)\n    print(result)\n\nif __name__ == \"__main__\":\n    main()\n```",
    "passed": 2,
    "test_error": ".F.                                                                      [100%]\n=================================== FAILURES ===================================\n_______________________________ test_lcb_0072[1] _______________________________\n\ni = 1\n\n    @pytest.mark.parametrize(\"i\", range(len(_CASES)))\n    def test_lcb_0072(i):\n        c = _CASES[i]\n        p = subprocess.run([sys.executable, str(_D / \"solution.py\")],\n                           input=c[\"input\"], capture_output=True, text=True, timeout=15)\n        assert p.returncode == 0, f\"runtime error: {p.stderr[-800:]}\"\n>       assert _norm(p.stdout) == _norm(c[\"output\"]), (\n            f\"input={c['input']!r} expected={c['output']!r} got={p.stdout!r}\")\nE       AssertionError: input='4 2\\n1 2\\n3 4' expected='Takahashi' got='Aoki\\n'\nE       assert 'Aoki' == 'Takahashi'\nE         \nE         - Takahashi\nE         + Aoki\n\ntest_lcb_0072.py:20: AssertionError\n=========================== short test summary info ============================\nFAILED test_lcb_0072.py::test_lcb_0072[1] - AssertionError: input='4 2\\n1 2\\n...\n1 failed, 2 passed in 0.05s"
  },
  {
    "total": 3,
    "answer": "```python\nimport sys\nfrom collections import defaultdict\n\ndef find_odd_cycle(u, parent, graph, visited):\n    visited[u] = True\n    for v in graph[u]:\n        if not visited[v]:\n            if find_odd_cycle(v, u, graph, visited):\n                return True\n        elif v != parent:\n            return True\n    return False\n\ndef solve(N, M, edges):\n    graph = defaultdict(list)\n    for u, v in edges:\n        graph[u].append(v)\n        graph[v].append(u)\n\n    odd_cycle_exists = False\n    visited = [False] * (N + 1)\n    for u in range(1, N + 1):\n        if not visited[u]:\n            if find_odd_cycle(u, -1, graph, visited):\n                odd_cycle_exists = True\n                break\n\n    if odd_cycle_exists:\n        return \"Takahashi\"\n    else:\n        return \"Aoki\"\n\ndef main():\n    input_data = sys.stdin.read().splitlines()\n    N, M = map(int, input_data[0].split())\n    edges = [tuple(map(int, line.split())) for line in input_data[1:M+1]]\n    result = solve(N, M, edges)\n    print(result)\n\nif __name__ == \"__main__\":\n    main()\n```",
    "passed": 2,
    "test_error": ""
  }
]

You are an expert programmer. Solve the task exactly as specified. Output your solution as fenced code blocks using the required file name(s) and the exact function/type signatures requested. Prefer correctness; do not include prose outside code unless asked.