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