Leetcode-492的解题过程。

• 题目

  For a web developer, it is very important 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.
     
     You need to output the length L and the width W of the web page you designed in sequence.
     

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  Example: Input: 4 Output: [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.

Note:
1.The given area won’t exceed 10,000,000 and is a positive integer
2.The web page’s width and length you designed must be positive integers.

• 解析

    根据指定的面积，构造一个矩形的长和宽，要求二者为正整数且二者之差尽可能小。很简单的一道题目，给定面积的条件下，长宽之差最小的矩形当然是正方形，边长就是面积的平方根。题目中限定长和宽必须为正整数，那么就以等面积正方形的变长为起点进行遍历，如果面积能够整除长，就找到了所求的矩形。

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  import math class Solution(object): def constructRectangle(self, area): """ :type area: int :rtype: List[int] """ sq = int(math.sqrt(area)) while sq>0: #题目限定长度大于宽度，所以向下遍历 if area%sq==0: l = sq w = area/sq return [w,l] sq-=1