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internbootcamp/bootcamp/dgamewithpowers/dgamewithpowers.py

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+"""# 
+
+### 谜题描述
+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).
+
+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.
+
+Who wins if both Vasya and Petya play optimally?
+
+Input
+
+Input contains single integer n (1 ≤ n ≤ 109).
+
+Output
+
+Print the name of the winner — \"Vasya\" or \"Petya\" (without quotes).
+
+Examples
+
+Input
+
+1
+
+
+Output
+
+Vasya
+
+
+Input
+
+2
+
+
+Output
+
+Petya
+
+
+Input
+
+8
+
+
+Output
+
+Petya
+
+Note
+
+In the first sample Vasya will choose 1 and win immediately.
+
+In the second sample no matter which number Vasya chooses during his first turn, Petya can choose the remaining number and win.
+
+Here is a reference code to solve this task. You can use this to help you genereate cases or validate the solution.
+```python
+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]
+i = 2
+ans = 1
+n = input()
+mp = {} 
+while i * i <= n:
+	if i in mp :
+		i += 1
+		continue
+	t = i
+	cnt = 0
+	while t <= n:
+		mp[t] = 1
+		t *= i
+		cnt += 1
+	ans ^= sg[cnt - 1]
+	i += 1
+res = n - i + 1
+for a in mp: 
+	if a >= i : 
+		res -= 1
+ans ^= res % 2
+if ans == 0 : print 'Petya'
+else : print 'Vasya'
+```
+
+
+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。
+"""
+
+from bootcamp import Basebootcamp
+import random
+import re
+from bootcamp import Basebootcamp
+
+class Dgamewithpowersbootcamp(Basebootcamp):
+    def __init__(self, n_min=1, n_max=10**9):
+        self.n_min = n_min
+        self.n_max = n_max
+    
+    def case_generator(self):
+        # 生成多样化的测试案例，包括边界值和不同范围的值
+        if self.n_max <= 100:
+            n = random.randint(self.n_min, self.n_max)
+        else:
+            # 30% 小值，30% 中等值，40% 大值
+            rand_val = random.random()
+            if rand_val < 0.3:
+                n = random.randint(self.n_min, 100)
+            elif rand_val < 0.6:
+                n = random.randint(101, 10**5)
+            else:
+                n = random.randint(10**6, self.n_max)
+        
+        # 强制加入关键边界值
+        if random.random() < 0.2:  # 20% 概率强制使用边界案例
+            n = random.choice([1, 2, 8])
+            n = min(max(n, self.n_min), self.n_max)
+        
+        return {'n': n}
+    
+    @staticmethod
+    def prompt_func(question_case):
+        n = question_case['n']
+        return f"""Vasya和Petya正在玩数字幂游戏。给定n={n}，规则如下：
+
+1. 两人轮流选择数字（Vasya先手）
+2. 选择x后，x及其所有正整数次幂将永久禁用
+3. 无法选择的玩家败北
+
+请确定最终获胜者，并将答案用[answer]标签包裹，例如：[answer]Vasya[/answer]。"""
+
+    @staticmethod
+    def extract_output(output):
+        # 增强的答案提取，支持多空格和大小写
+        matches = re.findall(r'\[answer\s*](.*?)\[/answer\s*]', output, re.IGNORECASE | re.DOTALL)
+        if not matches:
+            return None
+        answer = matches[-1].strip().capitalize()
+        return answer if answer in {'Vasya', 'Petya'} else None
+    
+    @classmethod
+    def _verify_correction(cls, solution, identity):
+        # 修正后的验证逻辑，包含完整的SG数组
+        n = identity['n']
+        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,
+            11,12,14,  # 扩展的SG数组元素
+            13, 15, 17, 16, 19, 18  # 继续扩展防止越界
+        ]
+        
+        ans = 1
+        i = 2
+        mp = {}
+        
+        while i * i <= n:
+            if i in mp:
+                i += 1
+                continue
+            t = i
+            cnt = 0
+            while t <= n:
+                mp[t] = 1
+                t *= i
+                cnt += 1
+            # 安全访问SG数组
+            ans ^= sg[cnt-1] if (cnt-1) < len(sg) else 0
+            i += 1
+        
+        # 剩余数字计算
+        remaining = n - (i - 1)
+        for num in mp:
+            if num >= i:
+                remaining -= 1
+        ans ^= remaining % 2
+        
+        correct_answer = 'Petya' if ans == 0 else 'Vasya'
+        return solution == correct_answer