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157 lines
4.6 KiB
Python
Executable file
157 lines
4.6 KiB
Python
Executable file
"""#
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### 谜题描述
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The Berland University is preparing to celebrate the 256-th anniversary of its founding! A specially appointed Vice Rector for the celebration prepares to decorate the campus. In the center of the campus n ice sculptures were erected. The sculptures are arranged in a circle at equal distances from each other, so they form a regular n-gon. They are numbered in clockwise order with numbers from 1 to n.
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The site of the University has already conducted a voting that estimated each sculpture's characteristic of ti — the degree of the sculpture's attractiveness. The values of ti can be positive, negative or zero.
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When the university rector came to evaluate the work, he said that this might be not the perfect arrangement. He suggested to melt some of the sculptures so that:
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* the remaining sculptures form a regular polygon (the number of vertices should be between 3 and n),
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* the sum of the ti values of the remaining sculptures is maximized.
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Help the Vice Rector to analyze the criticism — find the maximum value of ti sum which can be obtained in this way. It is allowed not to melt any sculptures at all. The sculptures can not be moved.
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Input
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The first input line contains an integer n (3 ≤ n ≤ 20000) — the initial number of sculptures. The second line contains a sequence of integers t1, t2, ..., tn, ti — the degree of the i-th sculpture's attractiveness ( - 1000 ≤ ti ≤ 1000). The numbers on the line are separated by spaces.
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Output
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Print the required maximum sum of the sculptures' attractiveness.
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Examples
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Input
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8
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1 2 -3 4 -5 5 2 3
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Output
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14
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Input
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6
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1 -2 3 -4 5 -6
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Output
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9
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Input
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6
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1 2 3 4 5 6
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Output
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21
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Note
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In the first sample it is best to leave every second sculpture, that is, leave sculptures with attractivenesses: 2, 4, 5 и 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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def main():
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n = int( raw_input() )
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L = [ int(i) for i in raw_input().split(\" \") ]
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maxi = -10**15
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for i in range(1,n+1):
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if n % i == 0:
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for k in range(0,i):
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ptotal = 0
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count = 0
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for j in range(k,n,i):
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ptotal += L[j]
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count += 1
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if count >= 3:
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maxi = max(ptotal,maxi)
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print maxi
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main()
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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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def calculate_max_sum(n, t_list):
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maxi = -10**15
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# 需要包含所有可能的因数（包括n自身）
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divisors = set()
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for step in range(1, int(n**0.5)+1):
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if n % step == 0:
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divisors.add(step)
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divisors.add(n//step)
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for step in sorted(divisors):
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m = n // step
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if m < 3:
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continue
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for k in range(step):
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total = sum(t_list[j] for j in range(k, n, step))
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if total > maxi:
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maxi = total
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return maxi
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class Dicesculpturesbootcamp(Basebootcamp):
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def __init__(self, n_min=3, n_max=20000, t_min=-1000, t_max=1000):
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super().__init__()
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self.n_min = n_min
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self.n_max = n_max
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self.t_min = t_min
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self.t_max = t_max
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def case_generator(self):
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while True:
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n = random.randint(self.n_min, self.n_max)
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t = [random.randint(self.t_min, self.t_max) for _ in range(n)]
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max_sum = calculate_max_sum(n, t)
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# 确保至少存在合法解
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if max_sum != -10**15:
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return {
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"n": n,
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"t": t,
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"max_sum": max_sum
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}
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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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t_list = question_case["t"]
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t_str = " ".join(map(str, t_list))
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return f"""Berland大学校庆需要装饰{n}个冰雕（编号1~{n}排列成正多边形），各冰雕吸引力值为：{t_str}
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规则：
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1. 融化部分冰雕，剩余冰雕必须构成正多边形
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2. 剩余数量k必须是{n}的因数且3 ≤ k ≤ {n}
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3. 冰雕间距必须相等（步长m = {n}/k）
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请计算最大可能的吸引力总和，答案置于[answer]标签内，如：[answer]21[/answer]。
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"""
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@staticmethod
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def extract_output(output):
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matches = re.findall(r'\[answer\]\s*(-?\d+)\s*\[/answer\]', output)
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return int(matches[-1]) if matches else None
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@classmethod
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def _verify_correction(cls, solution, identity):
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return solution == identity["max_sum"]
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