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0 | 0 | A positive integer X is called a good integer if and only if it satisfies the following condition:
- There exists a pair of positive integers (a,b) such that X = 2^a \times b^2.
For example, 400 is a good integer because 400 = 2^2 \times 10^2.
Given a positive integer N, find the number of good integers between 1 and... | [{"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 ... | 2 | 0.933333 | true | false | [{"code": "def count_good_integers(N):\n count = 0\n # Generate odd perfect squares: 1, 9, 25, 49, ...\n k = 1\n while True:\n m = k * k\n if m > N:\n break\n if m % 2 == 1: # m is odd\n # For this odd perfect square m, count powers of 2 with a >= 1\n p... | {"inputs": ["20", "400", "1234567890", "42451", "229054", "934974", "933489", "295529", "558434", "928134890243137027", "885441", "671373952662", "631141", "794773", "2", "146535", "146040", "953939", "739427", "1000000000000000000", "516815261791", "536111", "755273034069", "16189981213306186", "1", "792519", "9881601... | true | 0 | 1 | [
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Question: A positive integer X is called a good integer if a...
Reward: 0.93 | Turns: 2 | Terminated: True | Truncated: False
================================================================================
[SYSTEM]
You are a helpful codi... |
0 | 1 | A positive integer X is called a good integer if and only if it satisfies the following condition:
- There exists a pair of positive integers (a,b) such that X = 2^a \times b^2.
For example, 400 is a good integer because 400 = 2^2 \times 10^2.
Given a positive integer N, find the number of good integers between 1 and... | [{"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 ... | 2 | 0 | true | false | [{"code": "to test the logic.\n\n```python\nimport math\n\ndef count_good_integers(N):\n total = 0\n k = 1\n # k goes from 1 to floor(log2(N))\n while (1 << k) <= N: # 2^k <= N\n # L_k = N / 2^(k+1), R_k = N / 2^k\n # Use integer division? But we need the actual value for sqrt\n # Bett... | {"inputs": ["20", "400", "1234567890", "42451", "229054", "934974", "933489", "295529", "558434", "928134890243137027", "885441", "671373952662", "631141", "794773", "2", "146535", "146040", "953939", "739427", "1000000000000000000", "516815261791", "536111", "755273034069", "16189981213306186", "1", "792519", "9881601... | false | 0 | 0 | [
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Question: A positive integer X is called a good integer if a...
Reward: 0.00 | Turns: 2 | Terminated: True | Truncated: False
================================================================================
[SYSTEM]
You are a helpful codi... |
0 | 2 | A positive integer X is called a good integer if and only if it satisfies the following condition:
- There exists a pair of positive integers (a,b) such that X = 2^a \times b^2.
For example, 400 is a good integer because 400 = 2^2 \times 10^2.
Given a positive integer N, find the number of good integers between 1 and... | [{"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 ... | 3 | 0.933333 | true | false | [{"code": "import math\n\ndef count_good_integers(N):\n count = 0\n # For each odd perfect square m\n m = 1\n while m <= N:\n # For each power of 2 starting from 2^1 (since a must be positive)\n power_of_2 = 2 # start with 2^1\n while power_of_2 * m <= N:\n count += 1\n ... | {"inputs": ["20", "400", "1234567890", "42451", "229054", "934974", "933489", "295529", "558434", "928134890243137027", "885441", "671373952662", "631141", "794773", "2", "146535", "146040", "953939", "739427", "1000000000000000000", "516815261791", "536111", "755273034069", "16189981213306186", "1", "792519", "9881601... | true | 1 | 1 | [
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Question: A positive integer X is called a good integer if a...
Reward: 0.93 | Turns: 3 | Terminated: True | Truncated: False
================================================================================
[SYSTEM]
You are a helpful codi... |
0 | 3 | A positive integer X is called a good integer if and only if it satisfies the following condition:
- There exists a pair of positive integers (a,b) such that X = 2^a \times b^2.
For example, 400 is a good integer because 400 = 2^2 \times 10^2.
Given a positive integer N, find the number of good integers between 1 and... | [{"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 ... | 4 | 1 | true | false | [{"code": "import math\n\ndef solve(N):\n count = 0\n k = 1\n while (1 << k) <= N: # 2^k <= N\n # Find number of odd perfect squares <= N / (2^k)\n ratio = N / (1 << k)\n sqrt_ratio = math.isqrt(ratio)\n # Number of odd perfect squares <= sqrt_ratio is floor((sqrt_ratio + 1) / 2)\n... | {"inputs": ["20", "400", "1234567890", "42451", "229054", "934974", "933489", "295529", "558434", "928134890243137027", "885441", "671373952662", "631141", "794773", "2", "146535", "146040", "953939", "739427", "1000000000000000000", "516815261791", "536111", "755273034069", "16189981213306186", "1", "792519", "9881601... | true | 0 | 0 | [
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Question: A positive integer X is called a good integer if a...
Reward: 1.00 | Turns: 4 | Terminated: True | Truncated: False
================================================================================
[SYSTEM]
You are a helpful codi... |
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