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174 lines
4.4 KiB
Python
Executable file
174 lines
4.4 KiB
Python
Executable file
"""#
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### 谜题描述
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Vasya and Petya wrote down all integers from 1 to n to play the \"powers\" game (n can be quite large; however, Vasya and Petya are not confused by this fact).
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Players choose numbers in turn (Vasya chooses first). If some number x is chosen at the current turn, it is forbidden to choose x or all of its other positive integer powers (that is, x2, x3, ...) at the next turns. For instance, if the number 9 is chosen at the first turn, one cannot choose 9 or 81 later, while it is still allowed to choose 3 or 27. The one who cannot make a move loses.
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Who wins if both Vasya and Petya play optimally?
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Input
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Input contains single integer n (1 ≤ n ≤ 109).
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Output
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Print the name of the winner — \"Vasya\" or \"Petya\" (without quotes).
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Examples
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Input
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1
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Output
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Vasya
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Input
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2
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Output
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Petya
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Input
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8
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Output
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Petya
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Note
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In the first sample Vasya will choose 1 and win immediately.
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In the second sample no matter which number Vasya chooses during his first turn, Petya can choose the remaining number and win.
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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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sg = [1,2,1,4,3,2,1,5,6,2,1,8,7,5,9,8,7,3,4,7,4,2,1,10,9,3,6,11,12]
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i = 2
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ans = 1
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n = input()
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mp = {}
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while i * i <= n:
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if i in mp :
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i += 1
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continue
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t = i
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cnt = 0
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while t <= n:
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mp[t] = 1
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t *= i
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cnt += 1
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ans ^= sg[cnt - 1]
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i += 1
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res = n - i + 1
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for a in mp:
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if a >= i :
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res -= 1
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ans ^= res % 2
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if ans == 0 : print 'Petya'
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else : print 'Vasya'
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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 Dgamewithpowersbootcamp(Basebootcamp):
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def __init__(self, n_min=1, n_max=10**9):
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self.n_min = n_min
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self.n_max = n_max
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def case_generator(self):
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# 生成多样化的测试案例，包括边界值和不同范围的值
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if self.n_max <= 100:
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n = random.randint(self.n_min, self.n_max)
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else:
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# 30% 小值，30% 中等值，40% 大值
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rand_val = random.random()
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if rand_val < 0.3:
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n = random.randint(self.n_min, 100)
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elif rand_val < 0.6:
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n = random.randint(101, 10**5)
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else:
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n = random.randint(10**6, self.n_max)
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# 强制加入关键边界值
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if random.random() < 0.2: # 20% 概率强制使用边界案例
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n = random.choice([1, 2, 8])
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n = min(max(n, self.n_min), self.n_max)
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return {'n': n}
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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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return f"""Vasya和Petya正在玩数字幂游戏。给定n={n}，规则如下：
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1. 两人轮流选择数字（Vasya先手）
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2. 选择x后，x及其所有正整数次幂将永久禁用
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3. 无法选择的玩家败北
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请确定最终获胜者，并将答案用[answer]标签包裹，例如：[answer]Vasya[/answer]。"""
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@staticmethod
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def extract_output(output):
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# 增强的答案提取，支持多空格和大小写
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matches = re.findall(r'\[answer\s*](.*?)\[/answer\s*]', output, re.IGNORECASE | re.DOTALL)
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if not matches:
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return None
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answer = matches[-1].strip().capitalize()
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return answer if answer in {'Vasya', 'Petya'} else None
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@classmethod
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def _verify_correction(cls, solution, identity):
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# 修正后的验证逻辑，包含完整的SG数组
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n = identity['n']
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sg = [
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1,2,1,4,3,2,1,5,6,2,1,8,7,5,9,8,7,3,4,7,4,2,1,10,9,3,6,
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11,12,14, # 扩展的SG数组元素
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13, 15, 17, 16, 19, 18 # 继续扩展防止越界
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]
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ans = 1
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i = 2
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mp = {}
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while i * i <= n:
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if i in mp:
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i += 1
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continue
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t = i
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cnt = 0
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while t <= n:
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mp[t] = 1
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t *= i
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cnt += 1
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# 安全访问SG数组
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ans ^= sg[cnt-1] if (cnt-1) < len(sg) else 0
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i += 1
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# 剩余数字计算
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remaining = n - (i - 1)
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for num in mp:
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if num >= i:
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remaining -= 1
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ans ^= remaining % 2
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correct_answer = 'Petya' if ans == 0 else 'Vasya'
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return solution == correct_answer
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