動機

對ㄟ，除2是一半，sqrt也是一半

insight: sqrt也是一半

Problem

A web developer needs to know how to design a web page's size. So, given a specific rectangular web page’s area, your job by now is to design a rectangular web page, whose length L and width W satisfy the following requirements:

  1. The area of the rectangular web page you designed must equal to the given target area.
  2. The width W should not be larger than the length L, which means L >= W.
  3. The difference between length L and width W should be as small as possible.

Return an array [L, W] where L and W are the length and width of the web page you designed in sequence.

 

Example 1:

Input: area = 4Output: [2,2]Explanation: The target area is 4, and all the possible ways to construct it are [1,4], [2,2], [4,1]. But according to requirement 2, [1,4] is illegal; according to requirement 3,  [4,1] is not optimal compared to [2,2]. So the length L is 2, and the width W is 2.

Example 2:

Input: area = 37Output: [37,1]

Example 3:

Input: area = 122122Output: [427,286]

 

Constraints:

  • 1 <= area <= 107

Sol

class Solution:
    def constructRectangle(self, area: int) -> List[int]:
        w = ceil(sqrt(area))
        
        while area%w > 0:
            w -= 1
        return sorted([area//w, w], reverse=True)