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internbootcamp/bootcamp/btaxes/btaxes.py

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+"""# 
+
+### 谜题描述
+Mr. Funt now lives in a country with a very specific tax laws. The total income of mr. Funt during this year is equal to n (n ≥ 2) burles and the amount of tax he has to pay is calculated as the maximum divisor of n (not equal to n, of course). For example, if n = 6 then Funt has to pay 3 burles, while for n = 25 he needs to pay 5 and if n = 2 he pays only 1 burle.
+
+As mr. Funt is a very opportunistic person he wants to cheat a bit. In particular, he wants to split the initial n in several parts n1 + n2 + ... + nk = n (here k is arbitrary, even k = 1 is allowed) and pay the taxes for each part separately. He can't make some part equal to 1 because it will reveal him. So, the condition ni ≥ 2 should hold for all i from 1 to k.
+
+Ostap Bender wonders, how many money Funt has to pay (i.e. minimal) if he chooses and optimal way to split n in parts.
+
+Input
+
+The first line of the input contains a single integer n (2 ≤ n ≤ 2·109) — the total year income of mr. Funt.
+
+Output
+
+Print one integer — minimum possible number of burles that mr. Funt has to pay as a tax.
+
+Examples
+
+Input
+
+4
+
+
+Output
+
+2
+
+
+Input
+
+27
+
+
+Output
+
+3
+
+Here is a reference code to solve this task. You can use this to help you genereate cases or validate the solution.
+```python
+n = int(raw_input())
+
+def prime(n):
+	if n<=3:
+		return True
+	for i in range(2,int(n**(0.5))+1):
+		if n%i==0:
+			return False
+	return True
+
+if prime(n):
+	print 1
+elif n % 2 == 0:
+	print 2
+elif prime(n-2):
+	print 2
+else:
+	print 3
+```
+
+
+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 Btaxesbootcamp(Basebootcamp):
+    def __init__(self, n_min=2, n_max=10**9):
+        """
+        参数校验优化，支持更大范围的n值生成
+        """
+        if n_min < 2:
+            raise ValueError("n_min must be ≥2")
+        if n_max < n_min:
+            raise ValueError("n_max must be ≥n_min")
+        
+        self.n_min = n_min
+        self.n_max = n_max
+    
+    def case_generator(self):
+        """主动构造四类典型案例，保证覆盖率"""
+        def is_prime(m):
+            if m <= 1:
+                return False
+            if m <=3:
+                return True
+            if m % 2 ==0 or m %3 ==0:
+                return False
+            i = 5
+            w = 2
+            while i*i <= m:
+                if m%i ==0:
+                    return False
+                i += w
+                w = 6 - w
+            return True
+        
+        # 主动生成四类案例的平衡策略
+        case_type = random.choice([
+            'prime',         # 质数案例
+            'even_composite',# 偶合数
+            'odd_case2',     # 奇合数(n-2是质数)
+            'odd_case3'      # 奇合数(n-2是合数)
+        ])
+        
+        max_attempts = 1000
+        for _ in range(max_attempts):
+            # 动态调整生成策略
+            if case_type == 'prime':
+                # 生成随机质数
+                n = random.randint(max(2, self.n_min), self.n_max)
+                if is_prime(n):
+                    return {'n': n, 'correct_answer': 1}
+                
+            elif case_type == 'even_composite':
+                # 生成至少有两个质因子的偶数
+                n = 2 * random.randint(2, self.n_max//2)
+                if n >= 2 and not is_prime(n):
+                    return {'n': n, 'correct_answer': 2}
+            
+            elif case_type == 'odd_case2':
+                # 生成奇合数并满足n-2是质数
+                base_prime = random.choice([3,5,7,11,13,17,19,23,29,31])
+                n = base_prime + 2
+                if n % 2 == 1 and not is_prime(n) and is_prime(base_prime):
+                    return {'n': n, 'correct_answer': 2}
+                # 动态生成
+                candidate = random.randint(max(3, self.n_min), self.n_max)
+                if candidate%2 ==1 and not is_prime(candidate) and is_prime(candidate-2):
+                    return {'n': candidate, 'correct_answer': 2}
+            
+            elif case_type == 'odd_case3':
+                # 确保生成正确结果为3的案例
+                candidates = [27, 35, 45, 49, 55, 81, 875, 12345]
+                for n in candidates:
+                    if self.n_min <= n <= self.n_max:
+                        if not is_prime(n) and n%2 ==1 and not is_prime(n-2):
+                            return {'n': n, 'correct_answer': 3}
+                # 动态生成
+                candidate = random.randint(max(9, self.n_min), self.n_max)
+                if candidate%2 ==1 and not is_prime(candidate) and not is_prime(candidate-2):
+                    return {'n': candidate, 'correct_answer': 3}
+        
+        # Fallback机制：确保至少返回有效案例
+        return {'n': 4, 'correct_answer': 2}
+    
+    @staticmethod
+    def prompt_func(question_case) -> str:
+        n = question_case['n']
+        return f"""根据俄罗斯税法规定，Funt先生的年收入为{n} burles，需要通过分割收入来最小化税款。规则如下：
+
+1. 将总金额分割为k个整数（k≥1），每个部分≥2
+2. 每个部分的税款为其最大真因子（即除自身外的最大约数）
+3. 最终税款为各部分税款之和
+
+请计算最小可能的税款金额，并将最终答案置于[answer]标签内，如：[answer]5[/answer]。"""
+
+    @staticmethod
+    def extract_output(output):
+        matches = re.findall(r'\[answer\](.*?)\[/answer\]', output, re.IGNORECASE)
+        if matches:
+            try:
+                return int(matches[-1].strip())
+            except (ValueError, TypeError):
+                return None
+        return None
+
+    @classmethod
+    def _verify_correction(cls, solution, identity):
+        return solution == identity.get('correct_answer')