[LeetCode]492. Construct the Rec

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.

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.

难度

Easy

方法

将面积area开方后取整获得width，如果width不能被area除尽，则将width递减，直至width能被area除尽，area/width即为length

python代码

import math

class Solution(object):
    def constructRectangle(self, area):
        """
        :type area: int
        :rtype: List[int]
        """
        width = int(math.sqrt(area))
        while area%width != 0:
            width -= 1
        return [area/width, width]

Solution().constructRectangle(4) == [2,2]
Solution().constructRectangle(10) == [5,2]