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You are given a positive integer N and a length-N string s_0s_1\ldots s_{N-1} consisting only of 0 and 1. Consider a simple undirected graph G with (N+1) vertices numbered 0, 1, 2, \ldots, N, and the following edges: - For each i = 0, 1, \ldots, N-1, there is an undirected edge between vertices i and (i+1)\bmod N. - F...
[{"role": "system", "content": "You are a helpful coding assistant.\n\nYou have access to a Python interpreter.\nTo execute code, wrap it inside <interact></interact>. I will run it and return stdout/stderr in a subsequent turn.\n\nIMPORTANT CONTEXT:\n- This is a multi-turn conversation.\n- The Python interpreter is a ...
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[{"code": "# Test with sample input to verify my understanding\nN = 3\ns = \"010\"\n\n# Build graph\nedges = []\n\n# Cycle edges\nfor i in range(N):\n edges.append((i, (i+1) % N))\n\n# Star edges (from vertex N to vertex i if s[i] == '1')\nfor i in range(N):\n if s[i] == '1':\n edges.append((i, N))\n\nprin...
{"inputs": ["3\n010", "20\n00001100111010100101", "8\n01000101", "18\n101000001001101101", "8\n00111011", "43\n0110110101011001010110101100100111101110000", "12\n001101110111", "14\n01100000000001", "3\n000", "18\n110000001110010111", "7\n0101010", "199\n01001010001000111001011111101001111010000110111010000001110100100...
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================================================================================ Question: You are given a positive integer N and a length-N ... Reward: 0.07 | Turns: 2 | Terminated: True | Truncated: False ================================================================================ [SYSTEM] You are a helpful codi...
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You are given a positive integer N and a length-N string s_0s_1\ldots s_{N-1} consisting only of 0 and 1. Consider a simple undirected graph G with (N+1) vertices numbered 0, 1, 2, \ldots, N, and the following edges: - For each i = 0, 1, \ldots, N-1, there is an undirected edge between vertices i and (i+1)\bmod N. - F...
[{"role": "system", "content": "You are a helpful coding assistant.\n\nYou have access to a Python interpreter.\nTo execute code, wrap it inside <interact></interact>. I will run it and return stdout/stderr in a subsequent turn.\n\nIMPORTANT CONTEXT:\n- This is a multi-turn conversation.\n- The Python interpreter is a ...
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[{"code": "def solve(N, s):\n MOD = 998244353\n \n # Count the number of 1s in s\n num_ones = s.count('1')\n \n # Total number of edges in G\n total_edges = N + num_ones\n \n # The sum of all in-degrees must equal total_edges\n # We need to count distinct in-degree sequences\n \n # F...
{"inputs": ["3\n010", "20\n00001100111010100101", "8\n01000101", "18\n101000001001101101", "8\n00111011", "43\n0110110101011001010110101100100111101110000", "12\n001101110111", "14\n01100000000001", "3\n000", "18\n110000001110010111", "7\n0101010", "199\n01001010001000111001011111101001111010000110111010000001110100100...
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================================================================================ Question: You are given a positive integer N and a length-N ... Reward: 0.07 | Turns: 2 | Terminated: True | Truncated: False ================================================================================ [SYSTEM] You are a helpful codi...
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You are given a positive integer N and a length-N string s_0s_1\ldots s_{N-1} consisting only of 0 and 1. Consider a simple undirected graph G with (N+1) vertices numbered 0, 1, 2, \ldots, N, and the following edges: - For each i = 0, 1, \ldots, N-1, there is an undirected edge between vertices i and (i+1)\bmod N. - F...
[{"role": "system", "content": "You are a helpful coding assistant.\n\nYou have access to a Python interpreter.\nTo execute code, wrap it inside <interact></interact>. I will run it and return stdout/stderr in a subsequent turn.\n\nIMPORTANT CONTEXT:\n- This is a multi-turn conversation.\n- The Python interpreter is a ...
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[{"code": "N = 3\ns = \"010\"\n\n# Build the graph structure\ncycle_edges = [(i, (i+1) % N) for i in range(N)]\nradial_edges = [(i, N) for i in range(N) if s[i] == '1']\n\nprint(f\"Cycle edges: {cycle_edges}\")\nprint(f\"Radial edges: {radial_edges}\")\nprint(f\"Total edges: {len(cycle_edges) + len(radial_edges)}\")\np...
{"inputs": ["3\n010", "20\n00001100111010100101", "8\n01000101", "18\n101000001001101101", "8\n00111011", "43\n0110110101011001010110101100100111101110000", "12\n001101110111", "14\n01100000000001", "3\n000", "18\n110000001110010111", "7\n0101010", "199\n01001010001000111001011111101001111010000110111010000001110100100...
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================================================================================ Question: You are given a positive integer N and a length-N ... Reward: 0.07 | Turns: 2 | Terminated: True | Truncated: False ================================================================================ [SYSTEM] You are a helpful codi...
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"You are given a positive integer N and a length-N string s_0s_1\\ldots s_{N-1} consisting only of 0(...TRUNCATED)
"[{\"role\": \"system\", \"content\": \"You are a helpful coding assistant.\\n\\nYou have access to (...TRUNCATED)
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"[{\"code\": \"# Let's analyze the small example with N=3, s=\\\"010\\\"\\n# This means s_0=0, s_1=1(...TRUNCATED)
"{\"inputs\": [\"3\\n010\", \"20\\n00001100111010100101\", \"8\\n01000101\", \"18\\n1010000010011011(...TRUNCATED)
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"================================================================================\nQuestion: You are(...TRUNCATED)
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"You are given a positive integer N and a length-N string s_0s_1\\ldots s_{N-1} consisting only of 0(...TRUNCATED)
"[{\"role\": \"system\", \"content\": \"You are a helpful coding assistant.\\n\\nYou have access to (...TRUNCATED)
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"[{\"code\": \"N = 3\\ns = \\\"010\\\"\\nMOD = 998244353\\n\\n# Build the list of edges\\nedges = [](...TRUNCATED)
"{\"inputs\": [\"3\\n010\", \"20\\n00001100111010100101\", \"8\\n01000101\", \"18\\n1010000010011011(...TRUNCATED)
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"================================================================================\nQuestion: You are(...TRUNCATED)
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"You are given a positive integer N and a length-N string s_0s_1\\ldots s_{N-1} consisting only of 0(...TRUNCATED)
"[{\"role\": \"system\", \"content\": \"You are a helpful coding assistant.\\n\\nYou have access to (...TRUNCATED)
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"[{\"code\": \"from itertools import product\\n\\ndef solve(N, s):\\n # Build adjacency list for (...TRUNCATED)
"{\"inputs\": [\"3\\n010\", \"20\\n00001100111010100101\", \"8\\n01000101\", \"18\\n1010000010011011(...TRUNCATED)
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"================================================================================\nQuestion: You are(...TRUNCATED)
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"You are given a positive integer N and a length-N string s_0s_1\\ldots s_{N-1} consisting only of 0(...TRUNCATED)
"[{\"role\": \"system\", \"content\": \"You are a helpful coding assistant.\\n\\nYou have access to (...TRUNCATED)
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"[{\"code\": \"```python\\ndef solve(N, s):\\n MOD = 998244353\\n \\n # Count number of 1s (...TRUNCATED)
"{\"inputs\": [\"3\\n010\", \"20\\n00001100111010100101\", \"8\\n01000101\", \"18\\n1010000010011011(...TRUNCATED)
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"================================================================================\nQuestion: You are(...TRUNCATED)
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"You are given a positive integer N and a length-N string s_0s_1\\ldots s_{N-1} consisting only of 0(...TRUNCATED)
"[{\"role\": \"system\", \"content\": \"You are a helpful coding assistant.\\n\\nYou have access to (...TRUNCATED)
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"[{\"code\": \"N = 3\\ns = \\\"010\\\"\\n\\n# Build the graph G\\nedges = []\\n\\n# Cycle edges: (i,(...TRUNCATED)
"{\"inputs\": [\"3\\n010\", \"20\\n00001100111010100101\", \"8\\n01000101\", \"18\\n1010000010011011(...TRUNCATED)
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"================================================================================\nQuestion: You are(...TRUNCATED)
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"You are given a positive integer N and a length-N string s_0s_1\\ldots s_{N-1} consisting only of 0(...TRUNCATED)
"[{\"role\": \"system\", \"content\": \"You are a helpful coding assistant.\\n\\nYou have access to (...TRUNCATED)
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"[{\"code\": \"N = 3\\ns = \\\"010\\\"\\n\\n# Build the graph G\\n# Vertices: 0, 1, 2, 3\\n# Cycle e(...TRUNCATED)
"{\"inputs\": [\"3\\n010\", \"20\\n00001100111010100101\", \"8\\n01000101\", \"18\\n1010000010011011(...TRUNCATED)
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"================================================================================\nQuestion: You are(...TRUNCATED)
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"You are given a positive integer N and a length-N string s_0s_1\\ldots s_{N-1} consisting only of 0(...TRUNCATED)
"[{\"role\": \"system\", \"content\": \"You are a helpful coding assistant.\\n\\nYou have access to (...TRUNCATED)
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"[{\"code\": \"# Test the sample input to verify my understanding\\nN = 3\\ns = \\\"010\\\"\\n\\n# C(...TRUNCATED)
"{\"inputs\": [\"3\\n010\", \"20\\n00001100111010100101\", \"8\\n01000101\", \"18\\n1010000010011011(...TRUNCATED)
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"================================================================================\nQuestion: You are(...TRUNCATED)
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