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173 lines
5.8 KiB
Python
Executable file
173 lines
5.8 KiB
Python
Executable file
"""#
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### 谜题描述
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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.
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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.
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Ostap Bender wonders, how many money Funt has to pay (i.e. minimal) if he chooses and optimal way to split n in parts.
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Input
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The first line of the input contains a single integer n (2 ≤ n ≤ 2·109) — the total year income of mr. Funt.
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Output
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Print one integer — minimum possible number of burles that mr. Funt has to pay as a tax.
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Examples
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Input
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4
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Output
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2
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Input
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27
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Output
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3
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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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n = int(raw_input())
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def prime(n):
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if n<=3:
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return True
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for i in range(2,int(n**(0.5))+1):
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if n%i==0:
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return False
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return True
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if prime(n):
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print 1
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elif n % 2 == 0:
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print 2
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elif prime(n-2):
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print 2
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else:
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print 3
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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 Btaxesbootcamp(Basebootcamp):
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def __init__(self, n_min=2, n_max=10**9):
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"""
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参数校验优化，支持更大范围的n值生成
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"""
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if n_min < 2:
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raise ValueError("n_min must be ≥2")
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if n_max < n_min:
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raise ValueError("n_max must be ≥n_min")
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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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"""主动构造四类典型案例，保证覆盖率"""
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def is_prime(m):
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if m <= 1:
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return False
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if m <=3:
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return True
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if m % 2 ==0 or m %3 ==0:
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return False
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i = 5
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w = 2
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while i*i <= m:
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if m%i ==0:
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return False
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i += w
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w = 6 - w
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return True
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# 主动生成四类案例的平衡策略
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case_type = random.choice([
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'prime', # 质数案例
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'even_composite',# 偶合数
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'odd_case2', # 奇合数(n-2是质数)
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'odd_case3' # 奇合数(n-2是合数)
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])
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max_attempts = 1000
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for _ in range(max_attempts):
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# 动态调整生成策略
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if case_type == 'prime':
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# 生成随机质数
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n = random.randint(max(2, self.n_min), self.n_max)
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if is_prime(n):
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return {'n': n, 'correct_answer': 1}
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elif case_type == 'even_composite':
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# 生成至少有两个质因子的偶数
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n = 2 * random.randint(2, self.n_max//2)
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if n >= 2 and not is_prime(n):
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return {'n': n, 'correct_answer': 2}
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elif case_type == 'odd_case2':
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# 生成奇合数并满足n-2是质数
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base_prime = random.choice([3,5,7,11,13,17,19,23,29,31])
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n = base_prime + 2
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if n % 2 == 1 and not is_prime(n) and is_prime(base_prime):
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return {'n': n, 'correct_answer': 2}
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# 动态生成
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candidate = random.randint(max(3, self.n_min), self.n_max)
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if candidate%2 ==1 and not is_prime(candidate) and is_prime(candidate-2):
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return {'n': candidate, 'correct_answer': 2}
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elif case_type == 'odd_case3':
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# 确保生成正确结果为3的案例
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candidates = [27, 35, 45, 49, 55, 81, 875, 12345]
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for n in candidates:
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if self.n_min <= n <= self.n_max:
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if not is_prime(n) and n%2 ==1 and not is_prime(n-2):
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return {'n': n, 'correct_answer': 3}
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# 动态生成
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candidate = random.randint(max(9, self.n_min), self.n_max)
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if candidate%2 ==1 and not is_prime(candidate) and not is_prime(candidate-2):
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return {'n': candidate, 'correct_answer': 3}
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# Fallback机制：确保至少返回有效案例
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return {'n': 4, 'correct_answer': 2}
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@staticmethod
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def prompt_func(question_case) -> str:
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n = question_case['n']
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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：
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1. 将总金额分割为k个整数（k≥1），每个部分≥2
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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）
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3. 最终税款为各部分税款之和
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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]。"""
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@staticmethod
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def extract_output(output):
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matches = re.findall(r'\[answer\](.*?)\[/answer\]', output, re.IGNORECASE)
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if matches:
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try:
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return int(matches[-1].strip())
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except (ValueError, TypeError):
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return None
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return None
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@classmethod
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def _verify_correction(cls, solution, identity):
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return solution == identity.get('correct_answer')
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