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:

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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.

Example:

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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.

思路

我们需要构建一个最小面积的矩形。周长一定，矩形越接近正方形，面积越大。构建一个符合题意的矩形就可以了。

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import math
class Solution(object):
    def constructRectangle(self, area):
        """
        :type area: int
        :rtype: List[int]
        """
        width = int(math.sqrt(area))
        length = 0
        ans = []
        for i in range(width, 0, -1):
            if (area % i == 0):
                length = area / i
                width = i
                break
            
        ans.append(length)
        ans.append(width)
        return ans