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internbootcamp/bootcamp/dicesculptures/dicesculptures.py

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+"""# 
+
+### 谜题描述
+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.
+
+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.
+
+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: 
+
+  * the remaining sculptures form a regular polygon (the number of vertices should be between 3 and n), 
+  * the sum of the ti values of the remaining sculptures is maximized. 
+
+
+
+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.
+
+Input
+
+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.
+
+Output
+
+Print the required maximum sum of the sculptures' attractiveness.
+
+Examples
+
+Input
+
+8
+1 2 -3 4 -5 5 2 3
+
+
+Output
+
+14
+
+
+Input
+
+6
+1 -2 3 -4 5 -6
+
+
+Output
+
+9
+
+
+Input
+
+6
+1 2 3 4 5 6
+
+
+Output
+
+21
+
+Note
+
+In the first sample it is best to leave every second sculpture, that is, leave sculptures with attractivenesses: 2, 4, 5 и 3.
+
+Here is a reference code to solve this task. You can use this to help you genereate cases or validate the solution.
+```python
+def main():
+    n = int( raw_input() )
+    L = [ int(i) for i in raw_input().split(\" \") ]
+    
+    maxi = -10**15
+    for i in range(1,n+1):
+        if n % i == 0:
+            for k in range(0,i):
+                ptotal = 0
+                count = 0
+                for j in range(k,n,i):
+                    ptotal += L[j]
+                    count += 1
+                if count >= 3:
+                    maxi = max(ptotal,maxi)
+    
+    print maxi
+    
+main()
+```
+
+
+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
+
+def calculate_max_sum(n, t_list):
+    maxi = -10**15
+    # 需要包含所有可能的因数（包括n自身）
+    divisors = set()
+    for step in range(1, int(n**0.5)+1):
+        if n % step == 0:
+            divisors.add(step)
+            divisors.add(n//step)
+    
+    for step in sorted(divisors):
+        m = n // step
+        if m < 3:
+            continue
+        for k in range(step):
+            total = sum(t_list[j] for j in range(k, n, step))
+            if total > maxi:
+                maxi = total
+    return maxi
+
+class Dicesculpturesbootcamp(Basebootcamp):
+    def __init__(self, n_min=3, n_max=20000, t_min=-1000, t_max=1000):
+        super().__init__()
+        self.n_min = n_min
+        self.n_max = n_max
+        self.t_min = t_min
+        self.t_max = t_max
+    
+    def case_generator(self):
+        while True:
+            n = random.randint(self.n_min, self.n_max)
+            t = [random.randint(self.t_min, self.t_max) for _ in range(n)]
+            max_sum = calculate_max_sum(n, t)
+            # 确保至少存在合法解
+            if max_sum != -10**15:
+                return {
+                    "n": n,
+                    "t": t,
+                    "max_sum": max_sum
+                }
+    
+    @staticmethod
+    def prompt_func(question_case) -> str:
+        n = question_case["n"]
+        t_list = question_case["t"]
+        t_str = " ".join(map(str, t_list))
+        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}
+            
+规则：
+1. 融化部分冰雕，剩余冰雕必须构成正多边形
+2. 剩余数量k必须是{n}的因数且3 ≤ k ≤ {n}
+3. 冰雕间距必须相等（步长m = {n}/k）
+
+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]。
+"""
+    
+    @staticmethod
+    def extract_output(output):
+        matches = re.findall(r'\[answer\]\s*(-?\d+)\s*\[/answer\]', output)
+        return int(matches[-1]) if matches else None
+    
+    @classmethod
+    def _verify_correction(cls, solution, identity):
+        return solution == identity["max_sum"]