【LeetCode】492. Construct the Rectangle【E】【73】

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.

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很简单的 从 根号area 开始遍历，直到找到能被area整除的输就行了

有点类似于判断是不是质数

class Solution(object):
    def constructRectangle(self, area):
        
        l = int(math.ceil(math.sqrt(area)))
        
        while l > 0:
            if area % l == 0:
                return [max(area/l,l),min(area/l,l)]
            l -= 1