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internbootcamp/bootcamp/cilyaandmatrix/cilyaandmatrix.py

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+"""# 
+
+### 谜题描述
+Ilya is a very good-natured lion. He likes maths. Of all mathematical objects, his favourite one is matrices. Now he's faced a complicated matrix problem he needs to solve.
+
+He's got a square 2n × 2n-sized matrix and 4n integers. You need to arrange all these numbers in the matrix (put each number in a single individual cell) so that the beauty of the resulting matrix with numbers is maximum.
+
+The beauty of a 2n × 2n-sized matrix is an integer, obtained by the following algorithm:
+
+  1. Find the maximum element in the matrix. Let's denote it as m. 
+  2. If n = 0, then the beauty of the matrix equals m. Otherwise, a matrix can be split into 4 non-intersecting 2n - 1 × 2n - 1-sized submatrices, then the beauty of the matrix equals the sum of number m and other four beauties of the described submatrices. 
+
+
+
+As you can see, the algorithm is recursive.
+
+Help Ilya, solve the problem and print the resulting maximum beauty of the matrix.
+
+Input
+
+The first line contains integer 4n (1 ≤ 4n ≤ 2·106). The next line contains 4n integers ai (1 ≤ ai ≤ 109) — the numbers you need to arrange in the 2n × 2n-sized matrix.
+
+Output
+
+On a single line print the maximum value of the beauty of the described matrix.
+
+Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.
+
+Examples
+
+Input
+
+1
+13
+
+
+Output
+
+13
+
+
+Input
+
+4
+1 2 3 4
+
+
+Output
+
+14
+
+Note
+
+Consider the second sample. You need to arrange the numbers in the matrix as follows:
+    
+    
+      
+    1 2  
+    3 4  
+    
+
+Then the beauty of the matrix will equal: 4 + 1 + 2 + 3 + 4 = 14.
+
+Here is a reference code to solve this task. You can use this to help you genereate cases or validate the solution.
+```python
+from sys import stdin
+
+def solver():
+    stdin.readline()
+    num = map(float, stdin.readline().split())
+
+    num.sort(reverse=True)
+    ans = 0
+
+    while num:
+        ans += sum(num)
+        num = num[:len(num)/4]
+        
+    print int(ans)
+    
+
+if __name__ == \"__main__\":
+   
+    solver()
+```
+
+
+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
+
+class Cilyaandmatrixbootcamp(Basebootcamp):
+    def __init__(self, m=1):
+        super().__init__()  # 显式调用父类初始化
+        if not isinstance(m, int) or m < 0:
+            raise ValueError("m must be non-negative integer")
+        self.m = m
+        self.size = 4 ** m  # 保证生成的数字数量为4的整数次幂
+    
+    def case_generator(self):
+        # 严格保证数字数量为4的m次幂（兼容m=0的情况）
+        size = max(1, 4 ** self.m)  # 处理m=0时4^0=1
+        numbers = [random.randint(1, 10**9) for _ in range(size)]
+        sorted_nums = sorted(numbers, reverse=True)
+        
+        ans = 0
+        current = sorted_nums.copy()
+        while current:
+            ans += sum(current)
+            current = current[:len(current)//4]
+            
+        return {
+            'input_numbers': numbers,
+            'correct_answer': ans,
+            'size': size,
+            'm': self.m  # 保存参数确保验证时可追溯
+        }
+    
+    @staticmethod
+    def prompt_func(question_case):
+        numbers = question_case['input_numbers']
+        numbers_str = ' '.join(map(str, numbers))
+        example = "\nExample workflow:" + (
+            "\nFor input [1,2,3,4]: sorted=[4,3,2,1]"
+            "\n1st sum: 4+3+2+1=10 → keep first 1 element (4)"
+            "\n2nd sum: 4 → total beauty=10+4=14"
+        ) if question_case['m'] == 1 else ""
+        
+        return f"""Given {question_case['size']} numbers: {numbers_str}
+Arrange them in a 2n×2n matrix to maximize recursive beauty. The optimal solution requires:
+1. Sort numbers in descending order
+2. Sum all numbers (1st layer sum)
+3. Keep first quarter of numbers
+4. Repeat steps 2-3 until empty
+
+{example}
+
+Format your answer as [answer]{{value}}[/answer]. What is the maximum beauty?"""
+    
+    @staticmethod
+    def extract_output(output):
+        matches = re.findall(r'\[answer\](.*?)\[/answer\]', output, re.DOTALL)
+        if not matches:
+            return None
+        last_match = matches[-1].strip()
+        if re.fullmatch(r'\d+', last_match):  # 严格匹配整数格式
+            return int(last_match)
+        return None
+    
+    @classmethod
+    def _verify_correction(cls, solution, identity):
+        try:
+            return int(solution) == identity['correct_answer']
+        except (ValueError, TypeError):
+            return False