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183 lines
4.6 KiB
Python
Executable file
183 lines
4.6 KiB
Python
Executable file
"""#
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### 谜题描述
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Two best friends Serozha and Gena play a game.
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Initially there is one pile consisting of n stones on the table. During one move one pile should be taken and divided into an arbitrary number of piles consisting of a1 > a2 > ... > ak > 0 stones. The piles should meet the condition a1 - a2 = a2 - a3 = ... = ak - 1 - ak = 1. Naturally, the number of piles k should be no less than two.
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The friends play in turns. The player who cannot make a move loses. Serozha makes the first move. Who will win if both players play in the optimal way?
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Input
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The single line contains a single integer n (1 ≤ n ≤ 105).
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Output
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If Serozha wins, print k, which represents the minimal number of piles into which he can split the initial one during the first move in order to win the game.
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If Gena wins, print \"-1\" (without the quotes).
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Examples
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Input
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3
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Output
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2
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Input
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6
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Output
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-1
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Input
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100
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Output
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8
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Here is a reference code to solve this task. You can use this to help you genereate cases or validate the solution.
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```python
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n = input()
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spg = [0] * (n + 1)
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xor = [0] * (n + 1)
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for i in range(3, n + 1):
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k = 2
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movs = set()
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while k * (k + 1) <= 2 * i:
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s = 2 * i - k * (k - 1)
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if s % (2 * k) == 0:
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a = s / 2 / k
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movs.add(xor[a + k - 1] ^ xor[a - 1])
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k += 1
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mex = 0
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while mex in movs:
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mex += 1
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spg[i] = mex
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xor[i] = xor[i - 1] ^ mex
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if spg[n]:
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k = 2
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while k * (k + 1) <= 2 * i:
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s = 2 * i - k * (k - 1)
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if s % (2 * k) == 0:
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a = s / 2 / k
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if (xor[a + k - 1] ^ xor[a - 1]) == 0:
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break
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k += 1
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print(k)
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else:
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print(-1)
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```
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请完成上述谜题的训练场环境类实现，包括所有必要的方法。
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"""
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from bootcamp import Basebootcamp
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import random
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import re
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from bootcamp import Basebootcamp
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class Cinterestinggamebootcamp(Basebootcamp):
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def __init__(self, min_n=1, max_n=100000):
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self.min_n = min_n
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self.max_n = max_n
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def case_generator(self):
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n = random.randint(self.min_n, self.max_n)
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correct_answer = self._solve(n)
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return {"n": n, "correct_answer": correct_answer}
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@staticmethod
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def prompt_func(question_case):
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n = question_case['n']
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prompt = f"""你是石子游戏专家，请解决以下问题：
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游戏规则：
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1. 初始有一堆石子，共{n}个。
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2. 玩家轮流操作，每次操作必须选择一堆石子，并将其分成k堆（k≥2），且满足各堆石子数目严格递减且相邻两堆数目差为1。
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3. 无法操作的玩家输。Serozha先手，两人都采取最优策略。
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你的任务：确定Serozha是否能赢。若赢，输出他第一次分割的最小k值；否则输出-1。
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输入格式：整数n={n}
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输出格式：答案放在[answer]和[/answer]之间，例如[answer]2[/answer]。
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请仔细思考，给出正确的答案。"""
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return prompt
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@staticmethod
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def extract_output(output):
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matches = re.findall(r'\[answer\](.*?)\[/answer\]', output, re.DOTALL)
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return matches[-1].strip() if matches else None
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@classmethod
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def _verify_correction(cls, solution, identity):
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try:
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user_answer = int(solution)
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return user_answer == identity['correct_answer']
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except (ValueError, TypeError):
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return False
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@staticmethod
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def _solve(n):
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if n == 1:
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return -1
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spg = [0] * (n + 1)
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xor = [0] * (n + 1)
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for i in range(3, n + 1):
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movs = set()
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k = 2
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while k * (k + 1) <= 2 * i:
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s = 2 * i + k * (k - 1)
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if s % (2 * k) == 0:
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a = s // (2 * k)
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if a >= k: # 确保分割后的堆数满足严格递减条件
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xor_total = xor[a] ^ xor[a - k]
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movs.add(xor_total)
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k += 1
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mex = 0
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while mex in movs:
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mex += 1
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spg[i] = mex
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xor[i] = xor[i - 1] ^ spg[i]
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if spg[n] == 0:
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return -1
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else:
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min_k = None
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k = 2
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while k * (k + 1) <= 2 * n:
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s = 2 * n + k * (k - 1)
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if s % (2 * k) == 0:
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a = s // (2 * k)
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if a >= k:
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xor_total = xor[a] ^ xor[a - k]
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if xor_total == 0:
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min_k = k
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break
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k += 1
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return min_k if min_k is not None else -1
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