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internbootcamp/bootcamp/cmaximumsplitting/cmaximumsplitting.py

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+"""# 
+
+### 谜题描述
+You are given several queries. In the i-th query you are given a single positive integer ni. You are to represent ni as a sum of maximum possible number of composite summands and print this maximum number, or print -1, if there are no such splittings.
+
+An integer greater than 1 is composite, if it is not prime, i.e. if it has positive divisors not equal to 1 and the integer itself.
+
+Input
+
+The first line contains single integer q (1 ≤ q ≤ 105) — the number of queries.
+
+q lines follow. The (i + 1)-th line contains single integer ni (1 ≤ ni ≤ 109) — the i-th query.
+
+Output
+
+For each query print the maximum possible number of summands in a valid splitting to composite summands, or -1, if there are no such splittings.
+
+Examples
+
+Input
+
+1
+12
+
+
+Output
+
+3
+
+
+Input
+
+2
+6
+8
+
+
+Output
+
+1
+2
+
+
+Input
+
+3
+1
+2
+3
+
+
+Output
+
+-1
+-1
+-1
+
+Note
+
+12 = 4 + 4 + 4 = 4 + 8 = 6 + 6 = 12, but the first splitting has the maximum possible number of summands.
+
+8 = 4 + 4, 6 can't be split into several composite summands.
+
+1, 2, 3 are less than any composite number, so they do not have valid splittings.
+
+Here is a reference code to solve this task. You can use this to help you genereate cases or validate the solution.
+```python
+q = input()
+for i in xrange(q):
+	n = input()
+	div = 4
+	dic = {}
+	dic[0] = (0,0)
+	dic[1] = (9,-1)
+	dic[2] = (6,0)
+	dic[3] = (15,-1)
+	if n <=3 :
+		print -1
+	else:
+		ans = n/div
+		rem = n%div
+		ans += dic[rem][1]
+		if ans <=0 or n < (dic[rem][0]):
+			ans = -1
+		print ans
+```
+
+
+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
+from bootcamp import Basebootcamp
+import re
+import random
+
+class Cmaximumsplittingbootcamp(Basebootcamp):
+    def __init__(self, max_n=10**9, **params):
+        super().__init__(**params)
+        self.max_n = max_n  # 修正：遵守题目1e9的上限要求
+
+    def calculate_answer(self, n):
+        """严格遵循参考代码逻辑的实现"""
+        if n <= 3:
+            return -1
+        rem = n % 4
+        correction_map = {
+            0: (0, 0),
+            1: (9, -1),  # 保证n >= 9
+            2: (6, 0),   # 保证n >= 6
+            3: (15, -1)  # 保证n >= 15
+        }
+        base, offset = correction_map.get(rem, (0, 0))
+        
+        if n < base:
+            return -1
+        
+        count = (n - base) // 4 + offset
+        return count if count > 0 else -1
+
+    def case_generator(self):
+        # 生成策略优化：按余数分布生成代表性案例
+        case_type = random.choice(['edge', 'normal'] * 3 + ['remainder_case'])
+        
+        if case_type == 'edge':
+            n = random.choice([
+                1, 2, 3, 4, 5, 6, 7, 8, 9,
+                12, 15, 16, 20, 21, 10**9
+            ])
+        elif case_type == 'remainder_case':
+            rem = random.choice([0, 1, 2, 3])
+            min_val = {0:4, 1:9, 2:6, 3:15}[rem]
+            n = random.randint(min_val, min(self.max_n, min_val + 100))
+            n = (n - rem) // 4 * 4 + rem  # 强制对齐余数
+        else:
+            n = random.randint(4, self.max_n)
+
+        # 确保n不超过限制
+        n = min(n, self.max_n)
+        expected = self.calculate_answer(n)
+        return {'n': n, 'expected': expected}
+
+    @staticmethod
+    def prompt_func(question_case):
+        n = question_case['n']
+        return f"""You are given a positive integer n. Your task is to represent n as a sum of the maximum possible number of composite numbers. If impossible, return -1.
+
+Input:
+n = {n}
+
+Rules:
+1. Composite number: integer >1 that is not prime
+2. Summands must be composite numbers
+3. Maximize the number of summands
+4. Return -1 if impossible
+
+Examples:
+n=12 → 3 (4+4+4)
+n=6 → 1 (6)
+n=8 → 2 (4+4)
+n=9 → -1 (9=9但必须拆分成多个数)
+
+Answer format: 
+[answer]<integer>[/answer]
+
+Your answer must be within [answer] tags."""
+
+    @staticmethod
+    def extract_output(output):
+        # 严格匹配最后一个有效答案
+        matches = re.findall(r'\[answer\s*]([-]?\d+)\s*\[/answer\s*]', output, re.IGNORECASE)
+        valid_matches = [m for m in matches if m.lstrip('-').isdigit()]
+        return int(valid_matches[-1]) if valid_matches else None
+
+    @classmethod
+    def _verify_correction(cls, solution, identity):
+        # 重新实现验证逻辑，不依赖预存答案
+        n = identity['n']
+        expected = identity['expected']
+        
+        # 双重验证逻辑
+        try:
+            calc_ans = cls.calculate_answer(cls, n)
+            return solution == calc_ans == expected
+        except:
+            return solution == expected