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159 lines
4.5 KiB
Python
Executable file
159 lines
4.5 KiB
Python
Executable file
"""#
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### 谜题描述
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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.
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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.
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The beauty of a 2n × 2n-sized matrix is an integer, obtained by the following algorithm:
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1. Find the maximum element in the matrix. Let's denote it as m.
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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.
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As you can see, the algorithm is recursive.
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Help Ilya, solve the problem and print the resulting maximum beauty of the matrix.
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Input
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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.
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Output
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On a single line print the maximum value of the beauty of the described matrix.
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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.
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Examples
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Input
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1
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13
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Output
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13
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Input
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4
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1 2 3 4
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Output
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14
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Note
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Consider the second sample. You need to arrange the numbers in the matrix as follows:
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1 2
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3 4
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Then the beauty of the matrix will equal: 4 + 1 + 2 + 3 + 4 = 14.
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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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from sys import stdin
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def solver():
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stdin.readline()
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num = map(float, stdin.readline().split())
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num.sort(reverse=True)
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ans = 0
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while num:
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ans += sum(num)
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num = num[:len(num)/4]
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print int(ans)
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if __name__ == \"__main__\":
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solver()
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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 Cilyaandmatrixbootcamp(Basebootcamp):
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def __init__(self, m=1):
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super().__init__() # 显式调用父类初始化
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if not isinstance(m, int) or m < 0:
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raise ValueError("m must be non-negative integer")
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self.m = m
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self.size = 4 ** m # 保证生成的数字数量为4的整数次幂
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def case_generator(self):
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# 严格保证数字数量为4的m次幂（兼容m=0的情况）
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size = max(1, 4 ** self.m) # 处理m=0时4^0=1
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numbers = [random.randint(1, 10**9) for _ in range(size)]
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sorted_nums = sorted(numbers, reverse=True)
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ans = 0
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current = sorted_nums.copy()
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while current:
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ans += sum(current)
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current = current[:len(current)//4]
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return {
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'input_numbers': numbers,
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'correct_answer': ans,
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'size': size,
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'm': self.m # 保存参数确保验证时可追溯
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}
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@staticmethod
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def prompt_func(question_case):
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numbers = question_case['input_numbers']
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numbers_str = ' '.join(map(str, numbers))
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example = "\nExample workflow:" + (
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"\nFor input [1,2,3,4]: sorted=[4,3,2,1]"
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"\n1st sum: 4+3+2+1=10 → keep first 1 element (4)"
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"\n2nd sum: 4 → total beauty=10+4=14"
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) if question_case['m'] == 1 else ""
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return f"""Given {question_case['size']} numbers: {numbers_str}
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Arrange them in a 2n×2n matrix to maximize recursive beauty. The optimal solution requires:
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1. Sort numbers in descending order
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2. Sum all numbers (1st layer sum)
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3. Keep first quarter of numbers
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4. Repeat steps 2-3 until empty
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{example}
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Format your answer as [answer]{{value}}[/answer]. What is the maximum beauty?"""
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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.DOTALL)
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if not matches:
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return None
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last_match = matches[-1].strip()
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if re.fullmatch(r'\d+', last_match): # 严格匹配整数格式
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return int(last_match)
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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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try:
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return int(solution) == identity['correct_answer']
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except (ValueError, TypeError):
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return False
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